CN115347840A - Current harmonic suppression method for permanent magnet synchronous motor - Google Patents

Current harmonic suppression method for permanent magnet synchronous motor Download PDF

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CN115347840A
CN115347840A CN202211038214.9A CN202211038214A CN115347840A CN 115347840 A CN115347840 A CN 115347840A CN 202211038214 A CN202211038214 A CN 202211038214A CN 115347840 A CN115347840 A CN 115347840A
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current
controller
disturbance
resonance
permanent magnet
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邓永停
曹海洋
王建立
李洪文
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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
    • H02P21/22—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
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

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Abstract

The invention discloses a method for suppressing current harmonic waves of a permanent magnet synchronous motor, which comprises the following steps: establishing a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q; arranging a reduced order vector resonance controller, and connecting the reduced order vector resonance controller on a current loop in parallel; the method comprises the steps of setting a current loop controller based on reduced order vector resonance and a generalized active disturbance rejection controller, wherein the reduced order vector resonance and the generalized active disturbance rejection controller are connected in parallel and serve as the current loop controller. The method for suppressing the current harmonic wave of the permanent magnet synchronous motor reduces the harmonic wave component and can well suppress the current harmonic wave of the permanent magnet synchronous motor.

Description

Current harmonic suppression method for permanent magnet synchronous motor
Technical Field
The invention relates to the technical field of motor control, in particular to a method for suppressing current harmonic waves of a permanent magnet synchronous motor.
Background
The permanent magnet synchronous motor has the advantages of high efficiency, high power density, large torque inertia ratio, low noise, convenience in maintenance and the like, so that the permanent magnet synchronous motor is widely applied to a servo system, particularly the fields requiring higher motor performance and control precision, such as equipment industries of a photoelectric stable platform, a precise numerical control machine tool, a new energy electric automobile and the like. At present, the harmonic influence is mainly weakened by improving the structure of the motor and adopting an advanced control strategy, but the first method increases the manufacturing cost of the motor, so that a plurality of scholars propose algorithms such as repeated control and the like to suppress current harmonics. However, these algorithms have significant disadvantages, such as the repetitive control including a delay element, and slow adjustment speed. Therefore, it is necessary to research and design a new current harmonic suppression method so as to improve the control accuracy of the motor current.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and adopts the following technical scheme:
the invention provides a method for suppressing current harmonic waves of a permanent magnet synchronous motor.
A method for suppressing current harmonics of a permanent magnet synchronous motor comprises a current loop, and comprises the following steps:
establishing a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q;
arranging a reduced order vector resonance controller, connecting the reduced order vector resonance controller on a current loop in parallel, tracking a sinusoidal signal of a specified resonance frequency by the reduced order vector resonance controller, and suppressing current harmonics through compensation;
the method comprises the steps of setting a controller based on reduced order vector resonance and generalized active disturbance rejection, wherein the reduced order vector resonance and the generalized active disturbance rejection are connected in parallel and serve as a current loop controller, and the controller based on the reduced order vector resonance and the generalized active disturbance rejection is used for eliminating alternating current periodic disturbance and direct current non-periodic disturbance.
In some embodiments, the stator voltage equation of the permanent magnet synchronous motor may be expressed as follows:
Figure BDA0003819438220000021
in the formula, # d ＝ψ f +L d i dc And psi q ＝L q i qc Respectively represent stator magnetsD-axis and q-axis components of the chain;
i dc and u dv Respectively representing d-axis stator current and voltage, i qc And u qv Representing q-axis stator current and voltage, respectively, L d And L q Respectively representing the d-and q-axis inductances of the stator windings, R 1 Representing a stator phase resistance, n p Is the number of pole pairs, omega, of the motor m Is the mechanical angular velocity of the motor, # f Is a permanent magnet flux linkage.
In some embodiments, the permanent magnet synchronous machine is a surface-mounted permanent magnet synchronous machine.
In some embodiments, the L d ＝L q ＝L s 。
In some embodiments, the reduced order vector resonance controller expression is as follows:
Figure BDA0003819438220000022
wherein k is pr And k ir Respectively, the ratio and the resonance coefficient, j is an imaginary unit, s represents a Laplace operator, and omega h Representing the resonance frequency, ω c The cut-off frequency is indicated.
In some embodiments, the reduced order vector resonance controller is used for suppressing 5 th and 7 th harmonics in three-phase current of the permanent magnet synchronous motor.
In some embodiments, the direct current aperiodic perturbation comprises a parametric perturbation.
In some embodiments, the reduced order vector resonance-based and generalized auto-disturbance-rejection controller is a parallel connection of a reduced order resonance controller and a generalized auto-disturbance-rejection controller.
In some embodiments, the disturbance compensation based on the reduced order vector resonance and the generalized control law of the generalized auto-disturbance-rejection controller comprises: the compensation of coupled disturbances, the compensation of reference current change disturbances, which is based on step disturbance compensation, the compensation of direct current disturbances, and the compensation of alternating current harmonic disturbances are known.
In some embodiments, the permanent magnet synchronous motor further comprises a speed loop, and the speed loop adopts proportional-integral control.
The invention has the technical effects that: the invention discloses a method for suppressing current harmonic waves of a permanent magnet synchronous motor, which comprises the steps of establishing a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q; arranging a reduced order vector resonance controller, and connecting the reduced order vector resonance controller on a current loop in parallel to compensate and suppress current harmonics; the method is characterized in that an alternating current periodic disturbance and a direct current non-periodic disturbance are eliminated by arranging a controller based on reduced order vector resonance and generalized active disturbance rejection, and the reduced order vector resonance and the generalized active disturbance rejection are connected in parallel and are used as a current loop controller. The current harmonic suppression method for the permanent magnet synchronous motor reduces harmonic components, can well suppress the harmonic of the current of the permanent magnet synchronous motor, and ensures the control precision and quality of the current.
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In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a block diagram of a PMSM control based on reduced order vector resonance and generalized active-disturbance-rejection control according to an embodiment of the present invention;
FIG. 2 is a schematic block diagram of a reduced order vector resonance based current closed loop control according to an embodiment of the present invention;
FIG. 3 is a block diagram of a reduced order vector resonance structure according to one embodiment of the present invention;
FIG. 4 is a Bode diagram of a reduced order vector resonator controller according to one embodiment of the invention; wherein ω is in graph (a) c Fixed, k r Variation wherein k in graph (b) r Fixed, ω c Changing;
FIG. 5 is a Bode plot of the current loop closed loop transfer function under the action of a reduced order vector only resonant controller in accordance with one embodiment of the present invention; wherein ω is in graph (a) c Fixed, k r Variation, k in graph (b) r Fixed, ω c (ii) a change;
FIG. 6 is a three-dimensional graph of steady-state maximum interference estimation error of the generalized auto-disturbance-rejection controller according to one embodiment of the present invention;
fig. 7 is a bode plot of interference estimation and interference estimation error transfer functions for different orders of the generalized auto-disturbance rejection controller according to an embodiment of the present invention;
FIG. 8 is a structural diagram of a PMSM current harmonic suppression method based on reduced order vector resonance and generalized active-disturbance-rejection control according to an embodiment of the present invention;
FIG. 9 is a graph of three-phase current waveforms and fast Fourier transform results for different algorithms at 100rpm and 5 N.m load according to one embodiment of the present invention;
FIG. 10 is a graph of the q-axis current waveform and the FFT results for different algorithms at 100rpm and 5N m load according to an embodiment of the present invention;
fig. 11 is a schematic diagram of a method for suppressing current harmonics of a permanent magnet synchronous motor 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 will be described in further detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not to be construed as limiting the invention.
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the present application. It will be apparent, however, to one skilled in the art that the present application may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.
It will be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It should also be understood that the term "and/or" as used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.
As used in this specification and the appended claims, the term "if" may be interpreted contextually as "when", "upon" or "in response to" determining "or" in response to detecting ". Similarly, the phrase "if it is determined" or "if a [ described condition or event ] is detected" may be interpreted contextually to mean "upon determining" or "in response to determining" or "upon detecting [ described condition or event ]" or "in response to detecting [ described condition or event ]".
Furthermore, in the description of the present application and the appended claims, the terms "first," "second," "third," and the like are used for distinguishing between descriptions and not necessarily for describing or implying relative importance.
Reference throughout this specification to "one embodiment" or "some embodiments," or the like, means that a particular feature, structure, or characteristic described in connection with the embodiment is included in one or more embodiments of the present application. Thus, appearances of the phrases "in one embodiment," "in some embodiments," "in other embodiments," or the like, in various places throughout this specification are not necessarily all referring to the same embodiment, but rather "one or more but not all embodiments" unless specifically stated otherwise. The terms "comprising," "including," "having," and variations thereof mean "including, but not limited to," unless expressly specified otherwise.
The present invention will be described in detail below with reference to embodiments shown in the drawings. The embodiments are not intended to limit the present invention, and structural, methodological, or functional changes made by those skilled in the art according to the embodiments are included in the scope of the present invention.
At present, the permanent magnet synchronous motor mainly reduces the harmonic influence by improving the motor structure and adopting an advanced control strategy, but the first method increases the manufacturing cost of the motor, so that a plurality of scholars propose to inhibit current harmonics by adopting methods such as repetitive control, resonance control, iterative learning control and the like. However, these algorithms have obvious disadvantages, such as the fact that the repetitive control includes a delay link, the adjustment speed is slow, the iterative learning robustness is poor, and the convergence speed is slow. The inventors of the embodiments of the present invention found that: under the space vector control framework, a current loop is the innermost loop no matter the permanent magnet synchronous motor is in three-loop control including a position loop or double-loop control including a speed loop, so that the current loop is the key for realizing high-performance and high-precision control of the permanent magnet synchronous motor. However, there are various disturbances in the current loop, including internal parametric perturbations, external disturbances due to reference current step changes, and current harmonics due to inverter nonlinearities and motor cogging, among which the lower harmonics are dominant in the three-phase current. Therefore, it is necessary to research and design a current harmonic suppression strategy to overcome the influence of internal and external disturbances, especially current harmonics, on the current, so as to improve the control accuracy of the motor current.
The embodiment of the invention provides a method for suppressing current harmonics of a permanent magnet synchronous motor. A method schematic diagram of the current harmonic suppression method of the permanent magnet synchronous motor is shown in fig. 11.
Referring to fig. 11, an embodiment of the present invention provides a method for suppressing current harmonics of a permanent magnet synchronous motor, where the permanent magnet synchronous motor includes a current loop, and the method for suppressing current harmonics of the permanent magnet synchronous motor includes:
s1, establishing a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q;
s2, setting a reduced order vector resonance controller, connecting the reduced order vector resonance controller on a current loop in parallel, tracking a sinusoidal signal of a specified resonance frequency by the reduced order vector resonance controller, and suppressing current harmonics through compensation;
and S3, setting a reduced order vector resonance and generalized active disturbance rejection controller, connecting the reduced order vector resonance and the generalized active disturbance rejection controller in parallel and using the reduced order vector resonance and the generalized active disturbance rejection controller as a current loop controller, wherein the reduced order vector resonance and generalized active disturbance rejection controller are used for eliminating alternating current periodic disturbance and direct current non-periodic disturbance.
In the space vector control framework, the current loop is the innermost loop, whether it is a three-loop control including a position loop or a two-loop control including a speed loop. Therefore, in some embodiments, the permanent magnet synchronous motor includes a current loop and speed loop dual loop control, and in some embodiments, the permanent magnet synchronous motor includes a current loop, speed loop and position loop triple loop control.
In some embodiments, the stator voltage equation for the permanent magnet synchronous machine may be expressed as follows:
Figure BDA0003819438220000071
in the formula, /) d ＝ψ f +L d i dc And psi q ＝L q i qc Representing the d-axis and q-axis components of the stator flux linkage, respectively;
i dc and u dv Representing d-axis stator current and voltage, i qc And u qv Representing q-axis stator current and voltage, respectively, L d And L q Respectively representing the d-and q-axis inductances of the stator windings, R 1 Representing the stator one-phase resistance, n p Is the number of pole pairs, omega, of the motor m Is the mechanical angular velocity of the motor, # f Is a permanent magnet flux linkage.
In some embodiments, the permanent magnet synchronous machine is a surface-mounted permanent magnet synchronous machine.
In some embodiments, for a surface-mount PMSM, the quadrature-direct axis magnetic circuit is substantially symmetrical, thus the L d ＝L q ＝L s 。
In some embodiments, the reduced order vector resonance controller expression is as follows:
Figure BDA0003819438220000081
wherein k is pr And k ir Respectively, the ratio and the resonance coefficient, j is an imaginary unit, s represents a Laplace operator, and omega h Representing the resonance frequency, ω c The cut-off frequency is indicated.
In some embodiments, the reduced order vector resonance controller is used for suppressing 5 th and 7 th harmonics in three-phase current of the permanent magnet synchronous motor. In order to suppress low-order harmonics of 5 th order, 7 th order, and the like in three-phase current of the permanent magnet synchronous motor, a control strategy of resonance control is generally adopted. Various disturbances exist in the current loop, including internal parameter perturbation, external disturbance mainly caused by reference current step change, current harmonics caused by inverter nonlinearity, motor cogging and the like, wherein low harmonics are mainly contained in three-phase current, especially 5 th order and 7 th order harmonics.
In some embodiments, the direct current aperiodic perturbation comprises a parametric perturbation.
In some embodiments, the reduced order vector resonance-based and generalized auto-disturbance-rejection controller is a parallel connection of a reduced order resonance controller and a generalized auto-disturbance-rejection controller.
In some embodiments, the disturbance compensation based on the reduced order vector resonance and the generalized control law of the generalized auto-disturbance-rejection controller comprises: the compensation of coupled disturbances, the compensation of reference current change disturbances, which is based on step disturbance compensation, the compensation of direct current disturbances, and the compensation of alternating current harmonic disturbances are known.
In some embodiments, the permanent magnet synchronous motor further comprises a speed loop, and the speed loop adopts proportional-integral control.
The embodiment of the invention discloses a method for suppressing current harmonics of a permanent magnet synchronous motor, which comprises the steps of establishing a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q; arranging a reduced order vector resonance controller, and connecting the reduced order vector resonance controller on a current loop in parallel to compensate and suppress current harmonics; the method is characterized in that an alternating current periodic disturbance and a direct current non-periodic disturbance are eliminated by arranging a controller based on reduced order vector resonance and generalized active disturbance rejection, and the reduced order vector resonance and the generalized active disturbance rejection are connected in parallel and are used as a current loop controller. The current harmonic suppression method for the permanent magnet synchronous motor reduces harmonic components, can well suppress the harmonic of the current of the permanent magnet synchronous motor, and ensures the control precision and quality of the current. Compared with the current harmonic suppression method in the prior art: (1) The reduced order vector resonance controllers with different resonance frequencies are connected in parallel, so that unit gain and zero phase shift can be realized, and current harmonics with different resonance frequencies can be suppressed. (2) Under the condition of the same observation bandwidth and control gain, the generalized active disturbance rejection control has the advantages of being capable of estimating disturbance more quickly and reducing steady-state disturbance estimation errors. Therefore, harmonic interference can be inhibited based on reduced vector resonance and the generalized active disturbance rejection controller, and the inhibiting capability on direct current non-periodic disturbance and alternating current periodic disturbance is improved.
The following examples are provided for further details.
Referring to fig. 1, fig. 1 is a structural block diagram of a permanent magnet synchronous motor double closed loop servo system under space vector control. The permanent magnet synchronous motor comprises a current ring, a rotating speed ring, a PI controller, a space vector SVPWM, a three-phase inverter, a permanent magnet synchronous motor, clark conversion and Park conversion; the reduced order vector resonance controller is connected in parallel on the current loop, tracks a sinusoidal signal of a specified resonance frequency, and suppresses current harmonics through compensation; the reduced order vector resonance controller and the generalized auto-disturbance-rejection controller are connected in parallel and are used as a current loop controller.
In the embodiment, the rotation speed loop adopts the traditional proportional-integral control, and the proposed control based on reduced order vector resonance and generalized active disturbance rejection acts on the current loop. The proposed controller can compensate for non-periodic dc interference and suppress non-periodic ac harmonics.
The invention is realized by the following technical scheme:
firstly, establishing a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q. Neglecting motor core saturation, eddy current and hysteresis loss, the stator voltage equation can be expressed as follows:
Figure BDA0003819438220000101
in the formula, # d ＝ψ f +L d i dc And psi q ＝L q i qc Representing the d-axis and q-axis components of the stator flux linkage, respectively. i all right angle dc And u dv Respectively representing d-axis stator current and voltage, i qc And u pv Representing q-axis stator current and voltage, respectively, L d And L q Representing d-axis and q-axis inductances of the stator windings, R, respectively 1 Representing a stator phase resistance, n p Is the number of pole pairs, omega, of the motor m Is the mechanical angular velocity of the motor, # f Is a permanent magnet flux linkage. For the surface-mounted permanent magnet synchronous motor, the AC-DC axis magnetic circuits are basically symmetrical, so L d ＝L q ＝L s 。
In the case of considering external interference such as perturbation of internal parameters of the motor, current harmonics and the like, in order to facilitate the design of subsequent steps, the formula (1) can be rewritten into the following form:
Figure BDA0003819438220000102
wherein, b 0 ＝1/L s0 ,f dk And f qk Respectively representing known coupling interference, f d And f q Internal disturbances f representing unknown total disturbances of d-and q-axes, respectively, including perturbation of parameters di 、f qi And external disturbances f dominated by harmonics and current jumps de 、f qe I.e. f d ＝f di +f de ，f q ＝f qi +f qe . Thus, f dk 、f qk And f di 、f qi Respectively as follows:
Figure BDA0003819438220000111
Figure BDA0003819438220000112
in the formula,. DELTA.L s ＝L s -L s0 ，ΔR 1 ＝R 1 -R 10 ，Δψ f ＝ψ f -ψ f0 ，L s0 、R 10 And psi f0 Is the corresponding nominal value.
Secondly, a reduced order vector resonance controller is provided. In order to suppress the low harmonics of 5 th order, 7 th order, etc. in the three-phase current of the permanent magnet synchronous motor, a control strategy of resonance control is generally adopted. Thus, the present invention provides a reduced order vector resonance controller, whose expression is as follows:
Figure BDA0003819438220000113
wherein k is pr And k ir Respectively, the ratio and the resonance coefficient, j is an imaginary unit, s represents a Laplace operator, and omega h Representing the resonance frequency, ω c The cut-off frequency is indicated. In order to realize the offset of the pole of the zero-point permanent magnet synchronous motor equivalent model of the reduced order vector resonance controller, k is made pr ＝k r ω c L s0 ，k ir ＝k r ω c R 10 Wherein k is r The resonant gain is a closed loop control block diagram of d-axis and q-axis currents using reduced order vector resonance, as shown in fig. 2.
In order to realize the imaginary number j in the digital controller, the invention fully utilizes the orthogonality of a d axis and a q axis, namely u dv ＝ju qv ，u qv ＝-ju dr . Thus, the d-axis and q-axis output quantity u of the reduced order vector resonance controller is obtained by carrying out the transformation according to the formula (5) dr 、u qr Deviation from current input e dc 、e qc The relationship between them is as follows:
Figure BDA0003819438220000114
fig. 3 is a control block diagram of the reduced order vector controller according to the present invention, which is drawn according to equation (6).
To further illustrate the effect of each parameter in the controller on the reduced order vector controller, there is L according to the actual motor parameter s0 ＝0.0085H，R 10 =0.675 Ω. Thus, the bode diagram of the reduced order vector resonator controller is shown in fig. 4. As can be seen from FIG. 4 (a), when w c Constant time of constant, k r The larger the resonant gain of the reduced order vector resonant controller, the more the resonant bandwidth is substantially constant. Thus, k r Affecting the resonant gain and not the resonant bandwidth. Similarly, as shown in FIG. 4 (b), when k is r At constant time, w c The larger the resonance bandwidth of the reduced order vector resonance controller is, the better the robustness to the change of the resonance frequency of the motor is, and the resonance gain is basically unchanged. Thus, w c The resonance bandwidth is influenced, and the resonance gain is not influenced.
Under ideal conditions, L s ＝L s0 ，R 1 ＝R 10 . From FIG. 2, the actual output i is found d(q)c Ratio reference input
Figure BDA0003819438220000121
The closed loop transfer function of (a) is as follows:
Figure BDA0003819438220000122
according to the equation (7), the current closed loop transfer function Bode diagram under the action of the reduced order vector resonance controller is drawn as shown in FIG. 5, and it can be seen that when the parameter k is r And w c When varied, neither the amplitude nor the phase at a given resonant frequency will change, achieving unity gain and zero phase shift, in other words, a reduced order vector resonant controller and enabling i d(q)c Real-time tracking
Figure BDA0003819438220000123
And substantially no static error. Therefore, the proposed reduced order vector resonance controller can track the sinusoidal signal of the specified resonance frequency, and the purpose of suppressing the current harmonics is achieved through compensation.
Third, the setup is based on reduced order vector resonance and generalized auto-disturbance rejection controller. In order to eliminate direct current non-periodic disturbance such as parameter perturbation and further inhibit periodic disturbance of current harmonics, the invention designs a generalized auto-disturbance-rejection controller. Since the d-axis and q-axis design methods are similar, only the q-axis design method is given here. Adding n additional states to the original model equation according to equation (2) can obtain the following equation:
Figure BDA0003819438220000131
wherein the state matrix
Figure BDA0003819438220000132
Input matrix
Figure BDA0003819438220000133
Figure BDA0003819438220000134
Unknown interference matrix
Figure BDA0003819438220000135
Known interference matrix
Figure BDA0003819438220000136
In addition, the system matrix is expressed as
Figure BDA0003819438220000137
Figure BDA0003819438220000138
Figure BDA0003819438220000139
Is f q The n-1 order derivative of.
Thus, a generalized extended state observer is obtained as follows:
Figure BDA00038194382200001310
in the form of matrix
Figure BDA00038194382200001311
Representing an estimate of the matrix x, e q1 ＝z 1 -x 1 ，
Figure BDA00038194382200001312
The error equation of the observer can then be expressed as:
Figure BDA00038194382200001313
in the above formula, e q = z-x, C stands for output matrix, C = [ 10 … 0] n+1 . According to a general observer bandwidth setting strategy, the following are selected:
Figure BDA00038194382200001314
wherein, ω is 0 Representing the bandwidth of the generalized extended state observer, m =1,2, …, n +1. Thus, the eigenvalues of the matrix (A-LC) are all negative real numbers and all are configured to- ω 0 Thus, the matrix (A-LC) is a Helvelz matrix. At this time, if
Figure BDA00038194382200001315
Then the observation error e q Is progressively stable; if it is
Figure BDA00038194382200001316
And is bounded, then the observation error e q The bounded input and bounded output are stable. Therefore, if f q Is a constant disturbance with a first derivative of 0, then a second order dilated state viewThe detector can be free of tracking constant disturbance of the dead center at steady state. In the same way, if f q Is slope disturbance, the second derivative is 0, so the observation error of the third-order extended state observer
Figure BDA0003819438220000141
I.e. to achieve a non-static tracking ramp signal. However, for harmonic disturbances, assume f q ＝H sin(ω h t) with nth derivative not 0 and bounded, then the observation error e, no matter how many orders the observer expands to q The bounded input and bounded output are stable. From mclau Lin Gongshi, taylor unfolding of harmonic interference is performed as follows:
Figure BDA0003819438220000142
as can be seen from the above equation, the more the order of the extended state observer is, the better the Taylor expansion term can be tracked, and the maximum limit of the observation error is also reduced.
To further illustrate the performance of the generalized extended state observer, the following analysis is performed from a frequency domain perspective. Transfer function z of disturbance estimation of second, third and fourth order extended state observers can be obtained from (8) and (9) 2 /f q The following were used:
Figure BDA0003819438220000143
meanwhile, an interference estimation error transfer function can also be obtained:
Figure BDA0003819438220000144
at f q ＝H sin(ω h t), the general form of the steady-state maximum interference estimation error under different expansion orders can be obtained according to equation (14) as follows:
Figure BDA0003819438220000151
wherein e is q2 ＝z 2 -x 2 N is the order of the extended state observer and n ≧ 2,g = ω h /ω 0 Representing the ratio of the harmonic disturbance frequency to the observer bandwidth, g is generally chosen<1. Thus, taking the harmonic amplitude H =1, a steady-state maximum interference estimation error three-dimensional graph is drawn according to equation (15) as shown in fig. 6, from which, | e q2 | max Decreasing with increasing order n and decreasing with decreasing g. In other words, | e q2 | max Inversely proportional to the order n, to the harmonic frequency omega h Proportional to the observer bandwidth ω 0 In inverse proportion. Therefore, if at the harmonic frequency ω h In the case of fixation, | e q2 | max The reduction is accomplished by raising the order and increasing the observer bandwidth, but taking into account the effects of measurement noise, n and ω 0 It may not be chosen too large. According to the equation (13) and the equation (14), under the condition that the observer bandwidth is fixed, the interference estimation and interference estimation error transfer functions of the extended state observer at different orders are shown in fig. 7, and it can be seen that as the extension order increases, the anti-interference capability of the extended state observer increases, and the noise suppression capability decreases. Therefore, it is not desirable to expand too high orders, where a third order generalized extended state observer is chosen, expressed as equation (9)
Figure BDA0003819438220000152
In the formula, z 1 ,z 2 ,z 3 Are respectively to the current i qc Unknown total disturbance f q And the first derivative of the total disturbance
Figure BDA0003819438220000153
The estimation of (2) is to connect the reduced-order resonance controller and the generalized auto-disturbance rejection controller in parallel to obtain a generalized control law of
Figure BDA0003819438220000154
In the formula (I), the compound is shown in the specification,
Figure BDA0003819438220000155
Figure BDA0003819438220000156
reference current, k, representing the q-axis pq The control gain of q-axis is represented, and similarly, the d-axis correlation expression can be obtained from equations (16) and (17). According to equation (17), disturbance compensation of the generalized control law comprises four parts, first f qk For compensation of known coupling disturbances, secondly
Figure BDA0003819438220000161
For disturbance compensation of reference current variations based on step disturbance compensation, third part z 2 Is the disturbance observed by the generalized extended state observer, and can mainly realize the compensation of the direct current interference, and the fourth part b 0 u qr And compensation of alternating current harmonic disturbance is realized. As can be seen from this, it is,
Figure BDA0003819438220000162
z 2 and b 0 u qr Representing external disturbances of the system, i.e.
Figure BDA0003819438220000163
By substituting equation (17) back to equation (2), the q-axis system can be simplified to a single integrator system, i.e.
Figure BDA0003819438220000164
From the above, a controller based on reduced order vector resonance and generalized auto-disturbance-rejection is obtained by the following equations (6), (16) and (17), the structure diagram of which is shown in fig. 8, and ω is f Representing the fundamental frequency, N + Representing a positive natural number. As can be seen from FIG. 8, based on reduced order vector resonance and generalized auto-disturbance-rejection controller in conventional auto-disturbance-rejection controlOn the basis of which the estimation term of the interference derivative, i.e. z, is added 3 And a novel reduced order vector resonance controller is connected in parallel.
Compared with the traditional current harmonic suppression method, (1) the unit gain and the zero phase shift can be realized by simultaneously connecting the reduced order vector resonance controllers with different resonance frequencies in parallel so as to suppress the current harmonics with different resonance frequencies. (2) Under the condition of the same observation bandwidth and control gain, the generalized active disturbance rejection control has the advantages of being capable of estimating disturbance more quickly and reducing steady-state disturbance estimation errors. Therefore, harmonic interference can be inhibited based on reduced vector resonance and the generalized active disturbance rejection controller, and the inhibiting capability on direct current non-periodic disturbance and alternating current periodic disturbance is improved.
In order to verify the effectiveness of the current harmonic suppression method provided by the invention, the q-axis current i is simulated by respectively adopting the traditional PI algorithm and the algorithm provided by the invention under the condition of the same load and injected harmonic, and qc and comparing and analyzing the three-phase current, performing fast Fourier transform and calculating total harmonic distortion. The simulation structure is shown in fig. 9 and fig. 10, and it can be seen that the harmonic component is relatively greatly reduced based on the reduced vector resonance and generalized auto-disturbance rejection method, the harmonic of the current of the permanent magnet synchronous motor can be well suppressed, and the control accuracy and quality of the current are ensured.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, a software module executed by a processor, or a combination of the two. A software module may reside in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
In the description of the present invention, it should be understood that the symbols of the parameters, variables, program names, etc. mentioned in the embodiments of the present invention may be replaced with any other symbols that will not be confused.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, and are not intended to indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and are therefore not to be considered limiting of the invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless expressly stated or limited otherwise, the first feature "on" or "under" the second feature may be directly contacting the second feature or the first and second features may be indirectly contacting each other through intervening media. Also, a first feature "on," "over," and "above" a second feature may be directly or diagonally above the second feature, or may simply indicate that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
In the description of the specification, reference to the description of "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" or the like means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
The above-described embodiments of the present invention should not be construed as limiting the scope of the present invention. Any other corresponding changes and modifications made according to the technical idea of the present invention should be included in the protection scope of the claims of the present invention.

Claims (10)

1. A method for suppressing current harmonics of a permanent magnet synchronous motor comprises a current loop, and is characterized in that the method comprises the following steps:
establishing a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system d-q;
arranging a reduced order vector resonance controller, connecting the reduced order vector resonance controller on a current loop in parallel, tracking a sinusoidal signal of a specified resonance frequency by the reduced order vector resonance controller, and inhibiting current harmonics by compensation;
the method comprises the steps of setting a controller based on reduced order vector resonance and generalized active disturbance rejection, wherein the reduced order vector resonance and the generalized active disturbance rejection are connected in parallel and serve as a current loop controller, and the controller based on the reduced order vector resonance and the generalized active disturbance rejection is used for eliminating alternating current periodic disturbance and direct current non-periodic disturbance.
2. The method for suppressing the current harmonics of the PMSM according to claim 1, wherein the stator voltage equation of the PMSM can be expressed as follows:
Figure FDA0003819438210000011
in the formula, # d ＝ψ f +L d i dc And psi q ＝L q i qc Representing the d-axis and q-axis components of the stator flux linkage, respectively; i.e. i dc And u dv Respectively representing d-axis stator current and voltage, i qc And u qv Representing q-axis stator current and voltage, respectively, L d And L q Representing d-axis and q-axis inductances of the stator windings, R, respectively 1 Representing a stator phase resistance, n p Is the number of pole pairs, omega, of the motor m Is the mechanical angular velocity of the motor, # f Is a permanent magnet flux linkage.
3. The method for suppressing the current harmonics of the PMSM of claim 2, wherein the PMSM is a surface-mounted PMSM.
4. The PMSM current harmonic suppression method of claim 3, wherein L d ＝L q ＝L s 。
5. The method of suppressing current harmonics of a permanent magnet synchronous motor according to claim 1, wherein the reduced order vector resonance controller expression is as follows:
Figure FDA0003819438210000021
wherein k is pr And k ir Respectively, the ratio and the resonance coefficient, j is an imaginary unit, s represents a Laplace operator, and omega h Representing the resonance frequency, ω c The cut-off frequency is indicated.
6. The method for suppressing the current harmonics of the PMSM according to claim 5, wherein the reduced order vector resonance controller is used for suppressing 5 th and 7 th harmonics in the three-phase current of the PMSM.
7. The pm synchronous motor current harmonic suppression method of claim 1, wherein the dc non-periodic disturbances include parametric perturbations.
8. The method of claim 1, wherein the step-down vector resonance and generalized auto-disturbance-rejection controller is based on a parallel connection of a step-down resonance controller and a generalized auto-disturbance-rejection controller.
9. The pm synchronous motor current harmonic suppression method of claim 8, wherein the disturbance compensation based on reduced order vector resonance and generalized control law of generalized auto-disturbance-rejection controller comprises:
the compensation of coupled disturbance, the compensation of reference current change disturbance based on step disturbance compensation, the compensation of direct current interference, and the compensation of alternating current harmonic disturbance are known.
10. The method for suppressing the current harmonic waves of the permanent magnet synchronous motor is characterized by further comprising a rotating speed ring, wherein the rotating speed ring is controlled by proportional integral.
CN202211038214.9A 2022-08-29 2022-08-29 Current harmonic suppression method for permanent magnet synchronous motor Pending CN115347840A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115913017A (en) * 2023-02-16 2023-04-04 中国科学院宁波材料技术与工程研究所 Underwater propulsion motor current loop proportional integral resonance parameter self-adaption device

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115913017A (en) * 2023-02-16 2023-04-04 中国科学院宁波材料技术与工程研究所 Underwater propulsion motor current loop proportional integral resonance parameter self-adaption device

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