CN114039519A - Torque ripple suppression method for permanent magnet synchronous motor, servo system and storage medium - Google Patents

Torque ripple suppression method for permanent magnet synchronous motor, servo system and storage medium Download PDF

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CN114039519A
CN114039519A CN202110469036.4A CN202110469036A CN114039519A CN 114039519 A CN114039519 A CN 114039519A CN 202110469036 A CN202110469036 A CN 202110469036A CN 114039519 A CN114039519 A CN 114039519A
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robust
fractional order
controller
formula
order vector
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邓永停
李洪文
黄明飞
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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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
    • H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
    • 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
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • 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
    • H02P21/22—Current control, e.g. using a current control loop
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
    • 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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Abstract

The invention discloses a method for inhibiting torque ripple of a permanent magnet synchronous motor based on robust fractional order vector resonance, which comprises the following steps: collecting parameters of a permanent magnet synchronous motor in real time, and establishing a mathematical model of the permanent magnet synchronous motor; designing a robust internal model controller and a fractional order vector resonance controller for designing the robust fractional order vector resonance controller; and based on the robust fractional order vector resonance controller, driving the permanent magnet synchronous motor to operate by adopting an SVPWM control strategy. The invention also discloses a permanent magnet synchronous motor rotating speed servo system based on robust fractional order vector resonance and a computer readable storage medium. According to the invention, through the combination of robust internal model control and fractional order vector resonance control, the robustness of a current loop of the permanent magnet synchronous motor is improved, and the torque pulsation of the permanent magnet synchronous motor can be effectively inhibited.

Description

Torque ripple suppression method for permanent magnet synchronous motor, servo system and storage medium
Technical Field
The invention relates to the technical field of rotating speed control of permanent magnet synchronous motors, in particular to a torque ripple suppression method of a permanent magnet synchronous motor, a servo system and a storage medium.
Background
The permanent magnet synchronous motor has been widely applied to the technical fields of electric automobiles, numerical control machines, robot servo control and the like due to the advantages of simple structure, small size, reliable operation, less electric energy loss, high efficiency, good speed regulation performance and the like. However, parameter mismatch, non-linearity of the controlled model and uncertain disturbances inevitably exist in the motor servo system, thereby generating torque ripple, reducing tracking performance and stability. Therefore, for a permanent magnet synchronous motor, the influence of the difference in the design of the motor body and the selection of its control strategy on the motor torque ripple is large.
The existing methods for solving the torque ripple of the permanent magnet synchronous motor can be divided into two categories, one is to reduce the torque ripple by optimizing the key size of the motor; another is to suppress torque ripple by designing the relevant controller at the motor speed and current loop. The resonant controller is a common control strategy for suppressing torque ripple, and a plurality of resonant controllers are usually connected in parallel in a current loop or a speed loop to achieve the purpose of reducing torque ripple. In practical applications, a common resonance control method, such as a resonance controller, has a large gain and is robust to resonance frequency variation, so that a steady-state error exists during use, and incomplete suppression exists. The robust internal model control is a common control method in a servo control system, can realize preset dynamic response by designing two low-pass filters, and has good robustness on parameter change of a controlled object. In fact, any control strategy is established that increases the complexity of the system. Therefore, there is a need in the art for a control strategy that can effectively suppress the torque ripple of the permanent magnet synchronous motor, improve the robustness control of the parameters of the permanent magnet synchronous motor, and simultaneously, does not bring much pressure to the system.
Disclosure of Invention
The invention mainly aims to provide a torque ripple suppression method of a permanent magnet synchronous motor, a servo system and a storage medium, and aims to solve the technical problem of how to effectively suppress the torque ripple of the permanent magnet synchronous motor, improve the robust control of parameters of the permanent magnet synchronous motor and simultaneously avoid a control strategy which brings great pressure to the system.
In order to achieve the above object, the present invention provides a method for suppressing torque ripple of a permanent magnet synchronous motor based on robust fractional order vector resonance, the method for suppressing torque ripple of a permanent magnet synchronous motor includes the following steps:
collecting parameters of a permanent magnet synchronous motor in real time, and establishing a mathematical model of the permanent magnet synchronous motor;
designing a robust internal model controller and a fractional order vector resonance controller for designing the robust fractional order vector resonance controller;
and based on the robust fractional order vector resonance controller, driving the permanent magnet synchronous motor to operate by adopting an SVPWM control strategy.
Optionally, the establishing of the mathematical model of the permanent magnet synchronous motor specifically adopts the following form:
the formula I is as follows:
Figure RE-GDA0003221088590000021
in the formula of Ud、UqD-axis voltage and q-axis voltage under a rotating coordinate system respectively; i.e. id、iqD-axis and q-axis currents, respectively; rd、RqD-axis and q-axis inductances, respectively; l isd、LqD-axis and q-axis resistors respectively; omegahIs the electrical angular frequency of the motor; ΨfIs a motor magnetic linkage; t is time;
and carrying out discretization treatment on the model to complete the establishment of the model.
Optionally, the designing a robust internal model controller and a fractional order vector resonance controller to design a robust fractional order vector resonance controller includes:
designing a robust internal model controller, and controlling the stability of the robust internal model controller, wherein the robust internal model controller specifically adopts the following form:
defining the preset dynamic response transfer function of the robust internal model controller, wherein the preset dynamic response transfer function is expressed by a formula two:
Figure RE-GDA0003221088590000022
the disturbance rejection filter is represented by formula three:
Figure RE-GDA0003221088590000023
wherein τ represents a time constant; λ is a constant related to the bandwidth of the disturbance rejection filter, wherein the parameter is chosen to be 1/τ < 1/λ;
designing the robust internal model controller according to a formula II and a formula III, wherein the robust internal model controller is represented by a formula IV:
Figure RE-GDA0003221088590000031
the following time-domain control law is given by equation five by the inverse laplace transform:
Figure RE-GDA0003221088590000032
in the formula
Figure RE-GDA0003221088590000033
Figure RE-GDA0003221088590000034
To avoid integration iteration errors, the following state variables are defined:
x1＝e(t)
Figure RE-GDA0003221088590000035
Figure RE-GDA0003221088590000036
Figure RE-GDA0003221088590000037
wherein the parameter satisfies
Figure RE-GDA0003221088590000038
Based on the integral iterative error definition, the time domain control law is represented by a formula five conversion and a formula six:
uIMO＝(kpe+kpy)x1+(kie1+kiy1)x2+(kie2+kiy2)x8+kie8x4
the differentiated form of the current loop transfer function is represented by equation seven:
Figure RE-GDA0003221088590000041
according to the formula six and the formula seven, the state equation of the current loop is obtained
Figure RE-GDA0003221088590000042
When in use
Figure RE-GDA0003221088590000043
When the state variable is A and A is a Helverz matrix, the robust internal model controller is stable;
and designing a robust fractional order vector resonance controller according to the designed robust internal model controller and the fractional order vector resonance controller.
Optionally, the designing a robust internal model controller and a fractional order vector resonance controller to design a robust fractional order vector resonance controller includes:
designing a fractional order vector resonance controller, and controlling the stability of the fractional order vector resonance controller, wherein the fractional order vector resonance controller specifically adopts the following form:
and introducing the fractional calculus into the resonance controller to obtain the following control law of the fractional vector resonance controller, wherein the control law is expressed by a formula eight:
Figure RE-GDA0003221088590000044
in the formula kr，ωeAnd alpha represents the controller gain coefficient, damping frequency, and fractional order, respectively;
rewrite equation eight to equation nine:
Figure RE-GDA0003221088590000045
in the formula, Y(s)k，R(s)kRespectively representing the fractional order vector resonance controller kthInputting and outputting time;
and designing a robust fractional order vector resonance controller according to the designed robust internal model controller and the fractional order vector resonance controller.
Optionally, the designing a robust internal model controller and a fractional order vector resonance controller to design a robust fractional order vector resonance controller includes:
designing a robust fractional order vector resonance controller according to the designed robust internal model controller and the fractional order vector resonance controller, wherein the robust fractional order vector resonance controller specifically adopts the following form:
F(s)，CA(s) and CB(s) is a component of the internal model controller, and the closed-loop transfer function of the robust fractional order vector resonance controller obtained as follows is expressed by a formula ten:
Figure RE-GDA0003221088590000051
in which i(s) and iref(s) represents i (t) and iref(t) a transfer function in the s-domain;
at GFOVRThe transfer function of the integral order pole-zero obtained by the fractional order pole-zero in(s) through an outlaid method is formula eleven:
Figure RE-GDA0003221088590000052
and carrying out importing processing on the formula to finish the design of the robust fractional order vector resonance controller.
Optionally, after the designing the robust fractional order vector resonance controller, the method for suppressing torque ripple of the permanent magnet synchronous motor further includes:
performing stability analysis on the robust fractional order vector resonance controller, wherein the following form is specifically adopted:
the robust fractional order vector resonance controller has the stability that meets the following conditions, and uses a formula of twelve:
Figure RE-GDA0003221088590000053
in the formula | · | non-conducting phosphor∞Table infinite norm;
obtaining a closed loop transfer function formula thirteen of the current loop according to the formula ten and the formula eleven:
Figure RE-GDA0003221088590000054
when A is a Helverz matrix, 1+ Gp(s)(CA(s)+CB(s)) all feature roots fall in the left half plane of the s domain, then stability is determined by the following transfer function equation fourteen:
Figure RE-GDA0003221088590000055
from the small gain theorem, the closed loop satisfies the following condition, which is expressed by equation fifteen:
Figure RE-GDA0003221088590000056
if the formula fifteen can prove that the formula twelve, the robust fractional order vector resonance controller is stable.
Optionally, after the designing the robust fractional order vector resonance controller, the method for suppressing torque ripple of the permanent magnet synchronous motor further includes:
performing robust stability analysis on the robust fractional order vector resonance controller, wherein the robust stability analysis specifically adopts the following form:
when the mathematical model of the permanent magnet synchronous motor is mismatched, the controlled object can be represented by the formula sixteen:
Figure RE-GDA0003221088590000061
in the formula,. DELTA.Gp(s) represents a model error;
the robust stability of the robust fractional order vector resonance controller meets the following conditions, and is expressed by a formula seventeen:
Figure RE-GDA0003221088590000062
when the mathematical model of the permanent magnet synchronous motor is mismatched, the current loop characteristic polynomial can be expressed by a formula eighteen:
Figure RE-GDA0003221088590000063
in the formula
Figure RE-GDA0003221088590000064
The robust stability of the current loop meets the following conditions, which can be obtained by the small gain theorem, and is expressed by a formula of nineteen:
||Q(s)ΔGp(s)||∞≤||Q(s)||∞||ΔGp(s)||∞＜1
from this, the formula twenty can be derived:
Figure RE-GDA0003221088590000065
and if the formula twenty can prove the formula seventeen, the robust fractional order vector resonance controller is robust and stable.
In addition, to achieve the above object, the present invention further provides a rotating speed servo system of a permanent magnet synchronous motor based on robust fractional order vector resonance, comprising: the system comprises a processor, a permanent magnet synchronous motor, a three-phase inverter, a speed PI controller, a space voltage vector pulse width modulation (SVPWM) and a robust fractional order vector resonance controller;
the robust fractional order vector resonance controller is used for generating a control voltage;
the speed PI controller is used for generating control current;
the processor is used for controlling the on-off of the three-phase inverter power device by adopting an SVPWM control strategy so as to drive the permanent magnet synchronous motor to operate;
the processor is further configured to execute the steps of the robust fractional order vector resonance-based permanent magnet synchronous motor torque ripple suppression method according to any one of the above.
Further, to achieve the above object, the present invention also provides a computer readable storage medium having stored thereon a torque ripple suppression program, which when executed by a processor, implements the steps of the robust fractional order vector resonance-based permanent magnet synchronous motor torque ripple suppression method according to any one of the above.
The method comprises the steps of firstly collecting parameters of the permanent magnet synchronous motor in real time, establishing a mathematical model of the permanent magnet synchronous motor, designing a robust internal model controller and a fractional order vector resonance controller for designing the robust fractional order vector resonance controller, and finally driving the permanent magnet synchronous motor to operate by adopting an SVPWM control strategy based on the robust fractional order vector resonance controller. According to the invention, through the combination of robust internal model control and fractional order vector resonance control, the robustness of a current loop of the permanent magnet synchronous motor is improved, and the torque pulsation of the permanent magnet synchronous motor can be effectively inhibited.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention or in the description of the prior art will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without paying creative efforts.
FIG. 1 is a schematic structural diagram of an operating environment of a rotating speed servo system of a permanent magnet synchronous motor based on robust fractional order vector resonance according to an embodiment of the present invention;
FIG. 2 is a schematic flowchart of an embodiment of a torque ripple suppression method for a permanent magnet synchronous motor based on robust fractional order vector resonance;
FIG. 3 is a block diagram of a fractional order vector resonance controller;
FIG. 4 is a graph of the frequency response of a fractional order vector resonance controller;
FIG. 5 is a block diagram of a robust fractional order vector resonance controller;
FIG. 6 is a block diagram of a system structure of an embodiment of a robust fractional order vector resonance-based PMSM speed servo system of the present invention.
The implementation, functional features and advantages of the objects of the present invention will be further described with reference to the accompanying drawings.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, fig. 1 is a schematic structural diagram of an operating environment of a rotating speed servo system of a permanent magnet synchronous motor based on robust fractional order vector resonance according to an embodiment of the present invention.
As shown in fig. 1, the system for controlling the rotational speed of a permanent magnet synchronous motor based on robust fractional order vector resonance may include: a processor 1001, such as a CPU, a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. Wherein a communication bus 1002 is used to enable connective communication between these components. The user interface 1003 may include a Display (Display), an input unit such as a Keyboard (Keyboard), and the network interface 1004 may optionally include a standard wired interface, a wireless interface (e.g., WI-FI interface). The memory 1005 may be a high-speed RAM memory or a non-volatile memory (e.g., a magnetic disk memory). The memory 1005 may alternatively be a storage device separate from the processor 1001 described above.
Those skilled in the art will appreciate that the hardware configuration of the PMSM speed servo system based on robust fractional order vector resonance shown in FIG. 1 does not constitute a limitation of the PMSM speed servo system, and may include more or fewer components than shown, or some components in combination, or a different arrangement of components.
As shown in fig. 1, a memory 1005, which is a kind of computer-readable storage medium, may include therein an operating system, a network communication module, a user interface module, and a computer program. The operating system is a program for managing and controlling a permanent magnet synchronous motor rotating speed servo system and software resources, and supports the running of a torque ripple suppression program and other software and/or programs.
In the hardware structure of the rotational speed servo system of the permanent magnet synchronous motor shown in fig. 1, the network interface 1004 is mainly used for accessing a network; the user interface 1003 is mainly used for detecting a confirmation instruction, an editing instruction, and the like. And the processor 1001 may be configured to invoke the torque ripple suppression program stored in the memory 1005 and execute the torque ripple suppression program.
Based on the hardware structure of the permanent magnet synchronous motor rotating speed servo system based on the robust fractional order vector resonance, the invention provides various embodiments of the permanent magnet synchronous motor torque ripple suppression method based on the robust fractional order vector resonance in the running state of the permanent magnet synchronous motor rotating speed servo system.
Referring to fig. 2, fig. 2 is a schematic flowchart of an embodiment of a method for suppressing torque ripple of a permanent magnet synchronous motor based on robust fractional order vector resonance according to the present invention.
In this embodiment, a method for suppressing torque ripple of a permanent magnet synchronous motor based on robust fractional order vector resonance includes the following steps:
step S10, collecting parameters of the permanent magnet synchronous motor in real time, and establishing a mathematical model of the permanent magnet synchronous motor;
step S20, designing a robust internal model controller and a fractional order vector resonance controller for designing the robust fractional order vector resonance controller;
in this embodiment, the resonant controller is a common control strategy for suppressing torque ripple, and a plurality of resonant controllers are usually connected in parallel in a current loop or a speed loop to achieve the purpose of reducing torque ripple. In practical applications, the resonance controller is a common type of resonance control method, because it has a large gain and is robust to resonance frequency variations. However, this type of controller has a steady state error when in use. Therefore, fractional calculus is introduced into the design of the resonant controller to achieve the aim of further suppressing current loop harmonics.
In this embodiment, the robust internal model control is a control method commonly used in a servo control system. The method can realize preset dynamic response by designing two low-pass filters, and has good robustness to parameter change of a controlled object. The control strategy is therefore applied herein to the design of a current loop controller to achieve good dynamic response of the current loop and to suppress unmodeled interference of the current loop.
And step S30, driving the permanent magnet synchronous motor to operate by adopting an SVPWM control strategy based on the robust fractional order vector resonance controller.
In the embodiment, the fractional order vector resonance control technology can effectively inhibit periodic harmonic waves existing in a current loop and inhibit torque pulsation generated by the periodic harmonic waves; the robust internal model control is used for solving the non-periodic disturbance caused by the mismatch of the current loop resistance and inductance parameters and improving the dynamic response of the current loop. Aiming at the defects of gain and phase margin of the traditional resonance control, fractional calculus is introduced into the design of the resonance controller, and the harmonic suppression capability is improved. The invention combines the advantages of robust internal model control and fractional order resonance control, not only improves the robustness of the current loop of the permanent magnet synchronous motor, but also can effectively inhibit the torque pulsation of the permanent magnet synchronous motor. The invention can effectively inhibit the current loop harmonic wave and ensure the good robustness and dynamic response performance of the control system.
Based on the above embodiment, in this embodiment, the mathematical model of the permanent magnet synchronous motor is established in step S10, and the following form is specifically adopted:
the formula I is as follows:
Figure RE-GDA0003221088590000101
in the formula of Ud、UqD-axis voltage and q-axis voltage under a rotating coordinate system respectively; i.e. id、iqD-axis and q-axis currents, respectively; rd、RqD-axis and q-axis inductances, respectively; l isd、LqD-axis and q-axis resistors respectively; omegahIs the electrical angular frequency of the motor; ΨfIs a motor magnetic linkage; t is time;
and carrying out discretization treatment on the model to complete the establishment of the model.
In this embodiment, when the motor is a surface-mount motor (R)d＝Rq＝R，Ld＝LqL), the current loop model can be expressed as
Figure RE-GDA0003221088590000102
Then, its nominal model is
Figure RE-GDA0003221088590000103
In the formula Ln，RnThe nominal electric group and the nominal inductance of the current loop are respectively represented and can be obtained in real time through motor testing.
Based on the foregoing embodiments, in this embodiment, in step S20, designing a robust internal model controller and a fractional order vector resonance controller to design a robust fractional order vector resonance controller includes:
designing a robust internal model controller, and controlling the stability of the robust internal model controller, wherein the robust internal model controller specifically adopts the following form:
defining a preset dynamic response transfer function of the robust internal model controller, wherein the preset dynamic response transfer function is expressed by a formula II:
Figure RE-GDA0003221088590000111
the disturbance rejection filter is represented by formula three:
Figure RE-GDA0003221088590000112
wherein tau represents a time constant, and the smaller the value of tau, the faster the dynamic response; lambda is a constant related to the bandwidth of the disturbance suppression filter, the smaller the value of lambda is, the stronger the disturbance suppression capability is, but the more sensitive the system is to noise, therefore, 1/tau < 1/lambda is preferred in parameter selection, and the controller can have good robustness to current loop interference;
designing the robust internal model controller according to the second formula and the third formula, and expressing the robust internal model controller by using the fourth formula:
Figure RE-GDA0003221088590000113
the following time-domain control law is given by equation five by the inverse laplace transform:
Figure RE-GDA0003221088590000114
in the formula
Figure RE-GDA0003221088590000115
Figure RE-GDA0003221088590000116
To avoid integration iteration errors, the following state variables are defined:
x1＝e(t)
Figure RE-GDA0003221088590000117
Figure RE-GDA0003221088590000118
Figure RE-GDA0003221088590000119
wherein the parameter satisfies
Figure RE-RE-GDA0003221088590000121
Based on the integral iterative error definition, the time domain control law is represented by a formula five conversion and a formula six:
uIMO＝(kpe+kpy)x1+(kie1+kiy1)x2+(kie2+kiy2)x8+kie8x4
the differentiated form of the current loop transfer function is represented by equation seven:
Figure RE-GDA0003221088590000122
according to the sixth formula and the seventh formula, and assuming that the reference current is slowly changed, the state equation of the current loop can be obtained as
Figure RE-GDA0003221088590000123
Wherein,
Figure RE-GDA0003221088590000125
in order to be a state variable, the state variable,
Figure RE-GDA0003221088590000124
is a constant matrix of elements
A(4，1)＝-kie8/L，A(4，2)＝-(kie2+kiy2)/L，A(4，2)＝-(kie2+kiy2)/L
A(4，3)＝-(kpe+kpy+R)/L，A(1，2)＝A(2，3)＝A(3，4)＝1
The rest is all 0, so as long as A is a Helvelz matrix, a current loop closed-loop system is stable, the current error tends to 0 in a limited time, namely the robust internal model controller is stable;
and finally, designing the robust fractional order vector resonance controller according to the designed robust internal model controller and the fractional order vector resonance controller.
Referring to fig. 3, fig. 3 is a block diagram of a fractional order vector resonance controller.
As shown in the figure, based on the above-mentioned embodiment, in order to solve the problem of the decrease of the harmonic suppression capability caused by the insufficient gain of the conventional resonant controller, the fractional calculus is introduced into the resonant controller, and specifically, in the present embodiment,
step S20, designing a robust internal model controller and a fractional order vector resonance controller for designing a robust fractional order vector resonance controller, including:
designing a fractional order vector resonance controller, and controlling the stability of the fractional order vector resonance controller, wherein the following form is adopted specifically:
and introducing the fractional calculus into the resonance controller to obtain the following control law of the fractional vector resonance controller, wherein the control law is expressed by a formula eight:
in the formula kr，ωe，α
Figure RE-GDA0003221088590000131
Respectively representing a controller gain coefficient, a damping frequency and a fractional order;
rewrite equation eight to equation nine:
Figure RE-GDA0003221088590000132
in the formula, Y(s)k，R(s)kRespectively representing fractional ordersVector resonance controller kthInput and output of time;
and designing a robust fractional order vector resonance controller according to the designed robust internal model controller and the fractional order vector resonance controller.
Further, to illustrate the parameter kr wcAnd a influence on the resonance controller frequency, whose frequency characteristics are analyzed here at a resonance frequency w of 400 π rad/s.
Referring to fig. 4, fig. 4 is a graph of the frequency response of the fractional order vector resonance controller.
In this embodiment, (a) when the damping frequency and order are fixed values of 10rad/s and 1, the frequency response of the resonance controller follows the gain coefficient krThe change curve of (2). (b) When the gain coefficient and order are fixed values 10 and 1, the frequency response of the resonance controller is along with the damping frequency parameter wcThe change curve of (2). (c) When the gain coefficient and the damping frequency are fixed values of 10 and 10rad/s, the frequency response of the resonance controller is along with the change curve of the order a.
FIG. (a) shows different krAnd fixed wcBode plots of 10rad/s and a 1. It can be observed that the peak gain of the FOVR controller is proportional to the gain factor. Increasing its value can increase the gain at the resonance point, thereby improving the harmonic rejection performance, but the bandwidth is hardly changed. Plot (b) shows the amplitude-frequency characteristic of the FOVR controller when k isrWhen 10 and a 1. It shows that reducing the damping frequency coefficient can improve the gain but reduce the bandwidth, which will result in poor robustness of the frequency variation. In the actual controller design, 5-15 rad/s is a reference design range. FIG. c illustrates the case when kr＝10rad/s、w c10, the effect of the order on the FOVR controller. It can be observed that larger orders can improve the gain, but the bandwidth remains unchanged while the frequency response curve moves above 0 °, indicating that the phase delay will be reduced in the open loop. Thus, the parameter can be considered as a parameter that can adjust the gain and phase difference of the FOVR controller.
Analysis of the above parameters shows that the peak gain, bandwidth and phase delay are smoother to adjust to the resonant controller than conventional resonant controllers. Furthermore, increasing the order may increase the degree of self-reliance of the VR controller, thereby improving harmonic rejection performance.
Referring to fig. 5, fig. 5 is a block diagram of a robust fractional order vector resonance controller.
Based on the foregoing embodiments, in this embodiment, in step S20, designing a robust internal model controller and a fractional order vector resonance controller to design a robust fractional order vector resonance controller includes:
designing a robust fractional order vector resonance controller according to the designed robust internal model controller and the fractional order vector resonance controller, wherein the robust fractional order vector resonance controller specifically adopts the following form:
F(s)，CA(s) and CB(s) is a component of the internal model controller, and the closed-loop transfer function of the robust fractional order vector resonance controller obtained as follows is expressed by a formula ten:
Figure RE-GDA0003221088590000141
in which i(s) and iref(s) represents i (t) and iref(t) a transfer function in the s-domain;
at GFOVRFractional operator s in(s)aA plurality of fractional zero poles are generated; zero point z of the resonant controller itself1-R/L and pole
Figure RE-GDA0003221088590000142
Outer, GFOVRThe transfer function of the integral order pole-zero obtained by the fractional order pole-zero in(s) through an outlaid method is formula eleven:
Figure RE-GDA0003221088590000143
and (4) carrying out importing processing on the formula to finish the design of the robust fractional order vector resonance controller.
Further, after step S20, the method for suppressing torque ripple of a permanent magnet synchronous motor further includes:
performing stability analysis on the robust fractional order vector resonance controller, wherein the following form is specifically adopted:
the stability of the robust fractional order vector resonance controller meets the following condition, and the robust fractional order vector resonance controller is expressed by a formula twelve:
Figure RE-GDA0003221088590000144
in the formula | · | non-conducting phosphor∞Table infinite norm;
obtaining a closed loop transfer function formula thirteen of the current loop according to the formula ten and the formula eleven:
Figure RE-GDA0003221088590000145
when A is a Helvelz matrix, controller CA(s) and CB(s) enabling 1+ Gp(s)(CA(s)+CB(s)) stable, i.e. 1+ Gp(s)(CA(s)+CB(s)) all feature roots fall in the left half plane of the s domain, then stability is determined by the following transfer function equation fourteen:
Figure RE-GDA0003221088590000151
from the small gain theorem, the closed loop satisfies the following condition, which is expressed by equation fifteen:
Figure RE-GDA0003221088590000152
if the formula fifteen can prove that the formula twelve, the robust fractional order vector resonance controller is stable.
Further, after step S20, the method for suppressing torque ripple of a permanent magnet synchronous motor further includes:
carrying out robust stability analysis on the robust fractional order vector resonance controller, and specifically adopting the following form:
when the mathematical model of the permanent magnet synchronous motor is mismatched, the controlled object can be represented by the formula sixteen:
Figure RE-GDA0003221088590000153
in the formula,. DELTA.Gp(s) represents a model error;
the robust stability of the robust fractional order vector resonance controller meets the following condition, and is expressed by a formula seventeen:
Figure RE-GDA0003221088590000154
when the mathematical model of the permanent magnet synchronous motor is mismatched, the current loop characteristic polynomial can be expressed by a formula eighteen:
Figure RE-GDA0003221088590000155
in the formula
Figure RE-GDA0003221088590000156
The robust stability of the current loop meets the following conditions, which can be obtained by the small gain theorem, and is expressed by a formula of nineteen:
||Q(s)ΔGp(s)||∞≤||Q(s)||∞||ΔGp(s)||∞＜1
from this, the formula twenty can be derived:
Figure RE-GDA0003221088590000161
and if the formula twenty can prove the formula seventeen, the robust fractional order vector resonance controller is stable in robustness.
In the embodiment, the advantages of robust internal model control and fractional order resonance control are combined, so that the robustness of the current loop of the permanent magnet synchronous motor is improved, and the torque pulsation of the permanent magnet synchronous motor can be effectively inhibited. The invention can effectively inhibit the current loop harmonic wave and ensure the good robustness and dynamic response performance of the control system.
Referring to fig. 6, fig. 6 is a system structure block diagram of an embodiment of the present invention of a robust fractional order vector resonance-based permanent magnet synchronous motor speed servo system.
Permanent magnet synchronous motor rotational speed servo system based on robust fractional order vector resonance includes: the system comprises a processor, a permanent magnet synchronous motor, a three-phase inverter, a speed PI controller, a space voltage vector pulse width modulation (SVPWM) and a robust fractional order vector resonance controller (current controller); the device also comprises a position sensor and a coordinate transformation module.
A robust fractional order vector resonance controller for generating a control voltage;
a speed PI controller for generating a control current;
the processor is used for controlling the on-off of the three-phase inverter power device by adopting an SVPWM control strategy so as to drive the permanent magnet synchronous motor to operate;
a processor further configured to perform the steps of the robust fractional order vector resonance based permanent magnet synchronous motor torque ripple suppression method according to any of the above.
Specifically, a PI controller is adopted by a speed loop to generate a q-axis current given value, and a robust fractional order vector resonance controller is adopted by a current loop to generate control voltage. And (3) controlling the on-off of a power device of the three-phase inverter by adopting an SVPWM control strategy, and finally driving the permanent magnet synchronous motor to operate.
Further, a computer readable storage medium having stored thereon a torque ripple suppression program which, when executed by a processor, implements the steps of the robust fractional order vector resonance based permanent magnet synchronous motor torque ripple suppression method as claimed in any of the above.
The specific embodiment of the computer-readable storage medium of the present invention is substantially the same as the embodiments of the method for suppressing torque ripple of a permanent magnet synchronous motor based on robust fractional order vector resonance, and will not be described in detail herein.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better embodiment. With this understanding, the technical solutions of the present invention may be embodied in the form of a software product, which is stored in a readable storage medium (such as ROM/RAM, magnetic disk, optical disk) and includes instructions for enabling a terminal (which may be a computer, a server, or a network device) to execute the methods according to the embodiments of the present invention.
The present invention is described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, which are only illustrative and not restrictive, and those skilled in the art can make many changes and modifications without departing from the spirit and scope of the invention as claimed, and all changes and modifications that come within the meaning and range of equivalency of the claims are intended to be embraced therein.
The above description is only a preferred embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by the contents of the present specification and drawings, or used directly or indirectly in other related fields, are included in the scope of the present invention.

Claims (9)

1. A permanent magnet synchronous motor torque ripple suppression method based on robust fractional order vector resonance is characterized by comprising the following steps:
collecting parameters of a permanent magnet synchronous motor in real time, and establishing a mathematical model of the permanent magnet synchronous motor;
designing a robust internal model controller and a fractional order vector resonance controller for designing the robust fractional order vector resonance controller;
and based on the robust fractional order vector resonance controller, driving the permanent magnet synchronous motor to operate by adopting an SVPWM control strategy.
2. The method for suppressing the torque ripple of the permanent magnet synchronous motor according to claim 1, wherein the establishing of the mathematical model of the permanent magnet synchronous motor specifically adopts the following form:
the formula I is as follows:
Figure FDA0003043031770000011
in the formula of Ud、UqD-axis voltage and q-axis voltage under a rotating coordinate system respectively; i.e. id、iqD-axis and q-axis currents, respectively; rd、RqD-axis and q-axis inductances, respectively; l isd、LqD-axis and q-axis resistors respectively; omegahIs the electrical angular frequency of the motor; ΨfIs a motor magnetic linkage; t is time;
and carrying out discretization treatment on the model to complete the establishment of the model.
3. The method for suppressing torque ripple of a permanent magnet synchronous motor according to claim 1, wherein designing the robust internal model controller and the fractional order vector resonance controller to design the robust fractional order vector resonance controller comprises:
designing a robust internal model controller, and controlling the stability of the robust internal model controller, wherein the robust internal model controller specifically adopts the following form:
defining the preset dynamic response transfer function of the robust internal model controller, wherein the preset dynamic response transfer function is expressed by a formula two:
Figure FDA0003043031770000012
the disturbance rejection filter is represented by formula three:
Figure FDA0003043031770000013
wherein τ represents a time constant; λ is a constant related to the bandwidth of the disturbance rejection filter, wherein the parameter is chosen to be 1/τ < 1/λ;
designing the robust internal model controller according to a formula II and a formula III, wherein the robust internal model controller is represented by a formula IV:
Figure FDA0003043031770000021
the following time-domain control law is given by equation five by the inverse laplace transform:
Figure FDA0003043031770000022
wherein e (t) ═ irefF(s)-i(t)，
Figure FDA0003043031770000023
Figure FDA0003043031770000024
To avoid integration iteration errors, the following state variables are defined:
x1＝e(t)
Figure FDA0003043031770000025
Figure FDA0003043031770000026
Figure FDA0003043031770000027
wherein the parameter satisfies
Figure FDA0003043031770000028
Based on the integral iterative error definition, the time domain control law is represented by a formula five conversion and a formula six:
uIMO＝(kpc+kpy)x1+(kic1+kiy1)x2+(kic2+kiy2)x3+kic3x4
the differentiated form of the current loop transfer function is represented by equation seven:
Figure FDA0003043031770000031
according to the formula six and the formula seven, the state equation of the current loop is obtained
Figure FDA0003043031770000032
When in use
Figure FDA0003043031770000033
When the state variable is A and A is a Helverz matrix, the robust internal model controller is stable;
and designing a robust fractional order vector resonance controller according to the designed robust internal model controller and the fractional order vector resonance controller.
4. The method for suppressing torque ripple of a permanent magnet synchronous motor according to claim 1, wherein designing the robust internal model controller and the fractional order vector resonance controller to design the robust fractional order vector resonance controller comprises:
designing a fractional order vector resonance controller, and controlling the stability of the fractional order vector resonance controller, wherein the following form is adopted specifically:
and introducing the fractional calculus into the resonance controller to obtain the following control law of the fractional vector resonance controller, wherein the control law is expressed by a formula eight:
Figure FDA0003043031770000034
in the formula kr，ωoAnd alpha represents the controller gain coefficient, damping frequency, and fractional order, respectively;
rewrite equation eight to equation nine:
Figure FDA0003043031770000035
in the formula, Y(s)h，R(s)kRespectively, said fractional order vector resonance controller kthInput and output of time;
and designing a robust fractional order vector resonance controller according to the designed robust internal model controller and the fractional order vector resonance controller.
5. The method for suppressing torque ripple of a permanent magnet synchronous motor according to claims 3 and 4, wherein the designing the robust internal model controller and the fractional order vector resonance controller for designing the robust fractional order vector resonance controller comprises:
designing a robust fractional order vector resonance controller according to the designed robust internal model controller and the fractional order vector resonance controller, wherein the robust fractional order vector resonance controller specifically adopts the following form:
F(s)，CA(s) and CB(s) is a component of the internal model controller, and the closed-loop transfer function of the robust fractional order vector resonance controller obtained as follows is expressed by a formula ten:
Figure FDA0003043031770000041
in which i(s) and iref(s) represents i (t) and iref(t) a transfer function in the s-domain;
at GFOVRThe transfer function of the integral order pole-zero obtained by the fractional order pole-zero in(s) through an outlaid method is formula eleven:
Figure FDA0003043031770000042
and carrying out importing treatment on the formula to finish the design of the robust fractional order vector resonance controller.
6. The PMSM torque ripple suppression method of claim 5, wherein after the designing the robust fractional order vector resonance controller, the PMSM torque ripple suppression method further comprises:
performing stability analysis on the robust fractional order vector resonance controller, wherein the following form is specifically adopted:
the stability of the robust fractional order vector resonance controller meets the following condition, and the robust fractional order vector resonance controller uses a formula of twelve:
Figure FDA0003043031770000043
in the formula | · | non-conducting phosphor∞Table infinite norm;
obtaining a closed loop transfer function formula thirteen of the current loop according to the formula ten and the formula eleven:
Figure FDA0003043031770000044
when A is a Helverz matrix, 1+ Gp(s)(CA(s)+CB(s)) all feature roots fall in the left half plane of the s domain, then stability is determined by the following transfer function equation fourteen:
Figure FDA0003043031770000045
from the small gain theorem, the closed loop satisfies the following condition, which is expressed by equation fifteen:
Figure FDA0003043031770000051
if the formula fifteen can prove that the formula twelve, the robust fractional order vector resonance controller is stable.
7. The PMSM torque ripple suppression method of claim 6, wherein after the designing the robust fractional order vector resonance controller, the PMSM torque ripple suppression method further comprises:
performing robust stability analysis on the robust fractional order vector resonance controller, wherein the robust stability analysis specifically adopts the following form:
when the mathematical model of the permanent magnet synchronous motor is mismatched, the controlled object can be represented by the formula sixteen:
Figure FDA0003043031770000052
in the formula,. DELTA.Gp(s) represents a model error;
the robust stability of the robust fractional order vector resonance controller meets the following conditions, and is represented by a formula seventeen:
Figure FDA0003043031770000053
when the mathematical model of the permanent magnet synchronous motor is mismatched, the current loop characteristic polynomial can be expressed by a formula eighteen:
Figure FDA0003043031770000054
in the formula
Figure FDA0003043031770000055
The robust stability of the current loop meets the following conditions, which can be obtained by the small gain theorem, and is expressed by a formula of nineteen:
||Q(s)ΔGp(s)||∞≤||Q(s)||∞||ΔGp(s)||∞＜1
from this, the formula twenty can be derived:
Figure FDA0003043031770000061
and if the formula twenty can prove the formula seventeen, the robust fractional order vector resonance controller is robust and stable.
8. A permanent magnet synchronous motor rotating speed servo system based on robust fractional order vector resonance is characterized by comprising: the system comprises a processor, a permanent magnet synchronous motor, a three-phase inverter, a speed PI controller, a space voltage vector pulse width modulation (SVPWM) and a robust fractional order vector resonance controller;
the robust fractional order vector resonance controller is used for generating a control voltage;
the speed PI controller is used for generating control current;
the processor is used for controlling the on-off of the three-phase inverter power device by adopting an SVPWM control strategy so as to drive the permanent magnet synchronous motor to operate;
the processor is further configured to execute the steps of the robust fractional order vector resonance-based permanent magnet synchronous motor torque ripple suppression method according to any one of claims 1 to 7.
9. A computer readable storage medium, characterized in that the computer readable storage medium has stored thereon a torque ripple suppression program, which when executed by a processor implements the steps of the robust fractional order vector resonance based permanent magnet synchronous motor torque ripple suppression method according to any one of claims 1 to 7.
CN202110469036.4A 2021-04-28 2021-04-28 Torque ripple suppression method for permanent magnet synchronous motor, servo system and storage medium Pending CN114039519A (en)

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104104297A (en) * 2014-07-16 2014-10-15 东南大学 Flux-switching linear motor based rail transit velocity fluctuation inhibition method
CN107070341A (en) * 2017-03-24 2017-08-18 中国科学院长春光学精密机械与物理研究所 Permagnetic synchronous motor method for suppressing torque ripple based on Robust Iterative Learning Control

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104104297A (en) * 2014-07-16 2014-10-15 东南大学 Flux-switching linear motor based rail transit velocity fluctuation inhibition method
CN107070341A (en) * 2017-03-24 2017-08-18 中国科学院长春光学精密机械与物理研究所 Permagnetic synchronous motor method for suppressing torque ripple based on Robust Iterative Learning Control

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
MINGFEI HUANG: "Torque Ripple Suppression of PMSM Using Fractional-Order Vector Resonant and Robust Internal Model Control", IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION, vol. 7, no. 3, 20 January 2021 (2021-01-20), pages 1437 - 1453, XP011873005, DOI: 10.1109/TTE.2021.3053063 *

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