CN107872178B - Rotor position error estimation method of permanent magnet synchronous motor without position sensor - Google Patents

Rotor position error estimation method of permanent magnet synchronous motor without position sensor Download PDF

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CN107872178B
CN107872178B CN201711349302.XA CN201711349302A CN107872178B CN 107872178 B CN107872178 B CN 107872178B CN 201711349302 A CN201711349302 A CN 201711349302A CN 107872178 B CN107872178 B CN 107872178B
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axis
sliding mode
gamma
rotor position
delta
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CN107872178A (en
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浦蓉杰
高翔
林利
蔡良生
赵艳
吴佳祥
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Shanghai Zhongke Shenjiang Electric Vehicle Co Ltd
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Shanghai Zhongke Shenjiang Electric Vehicle Co Ltd
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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
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode 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
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2203/00—Indexing scheme relating to controlling arrangements characterised by the means for detecting the position of the rotor
    • H02P2203/03—Determination of the rotor position, e.g. initial rotor position, during standstill or low speed operation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2203/00—Indexing scheme relating to controlling arrangements characterised by the means for detecting the position of the rotor
    • H02P2203/09—Motor speed determination based on the current and/or voltage without using a tachogenerator or a physical encoder

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Abstract

The invention relates to a rotor position error estimation method of a permanent magnet synchronous motor without a position sensor, which comprises the following steps: (1) constructing a sliding-mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor, and acquiring a rotor position error; (2) measuring corresponding rotor position errors of the permanent magnet synchronous motor at different rotating speeds according to different rotating speeds, and manufacturing a one-dimensional table of the rotor position errors relative to the rotating speeds; (3) and looking up a table according to the rotating speed of the motor to obtain a rotor position error, and summing the estimated rotor position and the rotor position error to obtain a rotor position, wherein the rotor position participates in the operation of a control system of the permanent magnet synchronous motor. The rotor position error estimation method of the permanent magnet synchronous motor sensorless can obviously improve the accuracy of rotor position estimation of a traditional permanent magnet synchronous motor sensorless algorithm.

Description

Rotor position error estimation method of permanent magnet synchronous motor without position sensor
Technical Field
The invention relates to the technical field of electric transmission, in particular to a rotor position compensation problem of permanent magnet synchronous motor sensorless control, and specifically relates to a rotor position error estimation method of a permanent magnet synchronous motor sensorless.
Background
In pump loads, position sensorless permanent magnet synchronous motor control systems are increasingly used. The motor rotor position estimation algorithm in the motor control system without the position sensor is in a core position, and the sliding-mode observer is a relatively common and practical rotor position estimation algorithm.
Because of the inherent bucket vibration phenomenon of the sliding mode, high-frequency burrs and fluctuation exist in the αβ axis component of the back electromotive force, low-pass filtering needs to be introduced to filter the back electromotive force, and then the position of the rotor is estimated according to the back electromotive force, so that filtering delay is brought, the estimated rotor position is delayed, and the estimated rotor position is usually required to be compensated to overcome the delay.
The estimation of the rotor position in this type of sliding-mode observer requires α shaft voltage vαβ Axis Voltage vβ，vα、vβBy vd、vqThe rotor position is obtained through park inverse transformation, the park inverse transformation needs the last algorithm period to estimate the rotor position, namely the estimation of the rotor position in the current algorithm period depends on the correlation value of the last algorithm period and is supplied to the next algorithm period for use, and the iteration process of the digital algorithm causes the estimated rotor position to lag behind the real rotor position. Furthermore, i is used in the observer due to the delay in current samplingα、iβLagging in phase with the true current.
Summarizing the reasons for the lag in rotor position estimation:
1. using the rotor position of the last algorithm period to participate in the estimation of the rotor position of the algorithm period;
2. the delay in estimating the rotor position due to current sampling delay, the delay due to the introduction of low-pass filtering in the observer.
How to provide a method for estimating the position of a rotor more accurately and conveniently is a problem to be solved in the field.
Disclosure of Invention
The invention aims to provide a rotor position error estimation method of a permanent magnet synchronous motor sensorless, which overcomes the defects of the prior art and adopts a novel sliding-mode observer and a traditional sliding-mode observer to be combined to obtain a more accurate estimated rotor position.
In order to achieve the above object, the method for estimating rotor position error of a permanent magnet synchronous motor without a position sensor according to the present invention comprises:
the method for estimating the rotor position error of the permanent magnet synchronous motor without the position sensor is mainly characterized by comprising the following steps of:
(1) constructing a sliding-mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor, and acquiring a rotor position error;
(2) controlling the permanent magnet synchronous motor to work at different rotating speeds, and constructing a rotating speed-rotor position error one-dimensional table;
(3) and according to the one-dimensional table of the rotating speed and the rotor position error, obtaining the rotor position error at the corresponding rotating speed, and eliminating the rotor position error.
Preferably, the step (1) is based on iteration of a plurality of calculation cycles, each calculation cycle comprising the steps of:
(1.1) applying the d-axis reference voltage u of the permanent magnet synchronous motor of the sliding-mode observer based on αβ axis coordinate system of the permanent magnet synchronous motord_refQ-axis reference voltage uq_refD axis current idQ-axis current iqGamma-axis voltage v in sliding mode observer correspondingly given to gamma-delta-axis coordinate system based on permanent magnet synchronous motorγDelta axis voltage vδGamma axis current iγDelta axis current iδ；
(1.2) according to the gamma-axis estimated current observed by the sliding-mode observer of the gamma-delta-axis coordinate system based on the permanent magnet synchronous motor, which is acquired in the last calculation period
Figure GDA0002428209630000021
And estimating the current using the gamma axis
Figure GDA0002428209630000022
And a gamma axis current iγSubtracting to obtain a first difference s between the twoγ(ii) a According to delta axis estimated current observed by a sliding mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor and acquired in the previous calculation period
Figure GDA0002428209630000023
And estimating the current using the delta axis
Figure GDA0002428209630000024
And delta axis current iδSubtracting the two to obtain the differenceA second difference S therebetweenδConstructing a sliding mode surface of the sliding mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor;
(1.3) based on the first difference sγAnd a second difference SδObtaining a first sliding mode coefficient ZγAnd a second sliding mode coefficient ZδBy a first sliding mode coefficient ZγAnd a second sliding mode coefficient ZδConstructing a saturation function of the sliding-mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor;
(1.4) sliding mode coefficient Z to be obtainedγAnd ZδPerforming first-order low-pass filtering to obtain a first sliding mode coefficient Z after filteringeγAnd a second sliding mode coefficient Zeδ；
(1.5) estimating the Current from the Gamma-axis
Figure GDA0002428209630000025
Delta axis estimated current
Figure GDA0002428209630000026
The resistance of the stator of the permanent magnet synchronous motor obtains the resistance voltage drop of a gamma axis and the resistance voltage drop of a delta axis; according to the electric angular speed of the rotor of the permanent magnet synchronous motor and the q-axis inductance LqGamma axis estimated current
Figure GDA0002428209630000027
Delta axis estimated current
Figure GDA0002428209630000028
Obtaining the inductance voltage drop of a gamma axis and the inductance voltage drop of a delta axis;
(1.6) according to the gamma-axis voltage vγFirst sliding mode coefficient ZγSecond sliding mode coefficient ZδFirst sliding mode coefficient Z after filteringeγAnd a second sliding mode coefficient ZeδGamma axis resistance drop, delta axis resistance drop, gamma axis inductance drop, delta axis inductance drop, and d axis inductance LdObtaining gamma-axis estimated current
Figure GDA0002428209630000031
Sum delta axis estimated current
Figure GDA0002428209630000032
(1.7) according to the obtained filtered first sliding mode coefficient ZeγAnd a second sliding mode coefficient ZeδObtaining a rotor position error thetae；
In the first calculation period, the gamma-axis estimated current observed by the sliding-mode observer based on the gamma-delta-axis coordinate system of the permanent magnet synchronous motor, which is acquired in the previous calculation period
Figure GDA0002428209630000033
Initial value and delta axis estimated current
Figure GDA0002428209630000034
Are all 0.
More preferably, said step (1.2) is based on the first difference sγAnd a second difference SδThe sliding mode surface S for constructing the sliding mode observer is as follows:
Figure GDA0002428209630000035
preferably, in step (1.3), the first sliding mode coefficient and the second sliding mode coefficient are determined by defining a saturation function, and the saturation function is:
Figure GDA0002428209630000036
wherein S isγδComprising SγAnd SδAnd delta is a sliding mode boundary, and delta is larger than zero, S is a sliding mode surface, and k is a sliding mode gain.
More preferably, the sliding mode coefficient Z to be obtained in the step (1.4)γAnd ZδPerforming first-order low-pass filtering to obtain a first sliding mode coefficient Z after filteringeγAnd a second sliding mode coefficient ZeδThe method comprises the following steps:
Figure GDA0002428209630000037
wherein Z iseγIs the first sliding mode coefficient after filtering, ZeδIs the second sliding mode coefficient after filtering, ZγIs the first sliding mode coefficient, ZδIs the second sliding mode coefficient, s is Laplace operator, ωeThe cut-off frequency of the low-pass filter.
Preferably, in the step (1.5), the gamma axis resistance voltage drop, the delta axis resistance voltage drop, the gamma axis inductance voltage drop and the delta axis inductance voltage drop are obtained by the following formulas:
Figure GDA0002428209630000038
Figure GDA0002428209630000039
Figure GDA00024282096300000310
Figure GDA00024282096300000311
wherein, the U isγRaFor gamma-axis resistive voltage drop, UδRaIs delta axis resistance drop; u shapeγLFor gamma axis inductive voltage drop, UδLIs delta axis inductance voltage drop, omega is rotor electrical angular velocity, LqIs a q-axis inductor;
Figure GDA0002428209630000041
the current is estimated for the gamma axis acquired in the last calculation cycle,
Figure GDA0002428209630000042
estimating the current, R, for the delta axis obtained in the previous calculation cycleaIs the stator resistance.
More preferably, in the step (1.6), the γ -axis estimated current and the δ -axis estimated current are obtained by the following formulas:
Figure GDA0002428209630000043
Figure GDA0002428209630000044
wherein the content of the first and second substances,
Figure GDA0002428209630000045
the current is estimated for the gamma axis,
Figure GDA0002428209630000046
the current is estimated for the delta axis.
Preferably, the model of the sliding-mode observer constructed under the γ δ axis coordinate system of the permanent magnet synchronous motor is as follows:
Figure GDA0002428209630000047
wherein L isdIs d-axis inductance, LqIs q-axis inductance, RaIs the stator resistance, ω is the rotor electrical angular velocity,
Figure GDA0002428209630000048
for the permanent magnet effective flux linkage, p is the differential operator, vγVoltage of gamma axis, vδVoltage of delta axis, ZγIs the first sliding mode coefficient, ZδIs the second sliding mode coefficient, ZeγIs the first sliding mode coefficient after filtering, ZeδIs the filtered second sliding mode coefficient.
More preferably, the step (1.7) obtains the rotor position error θ according to the following formulae：
Figure GDA0002428209630000049
Wherein, E isexTo expand the electromotive force, eγFor expanding the electromotive force EexComponent on the gamma axis, said eγTo spread the component of the electromotive force on the delta axis, theta iseIs the rotor position error.
More preferably, the step (2) comprises:
the rotor position of the permanent magnet synchronous motor is estimated through a sliding mode observer based on an αβ axial coordinate system and a sliding mode observer based on a gamma delta coordinate system, an estimated position obtained by the sliding mode observer based on a αβ axial coordinate system and an estimated position error obtained by the sliding mode observer based on the gamma delta coordinate system are obtained, the estimated position is also used for forming a closed loop of the permanent magnet synchronous motor, therefore, the error of the rotor position when the permanent magnet synchronous motor works at different rotating speeds is obtained, the error of the rotor position corresponds to the rotating speed, and a one-dimensional table about the rotating speed and the rotor position error is constructed.
Preferably, the step (3) is:
the rotor position is obtained through a sliding mode observer based on an αβ shaft coordinate system, the rotor position error corresponding to the rotor speed of the permanent magnet synchronous motor to which the sliding mode observer based on the αβ shaft coordinate system is applied is obtained through a rotating speed-rotor position error one-dimensional table, and the rotor position with the rotor position error removed is obtained through addition.
The rotor position error estimation method of the permanent magnet synchronous motor without the position sensor can obviously improve the accuracy of rotor position estimation of the traditional permanent magnet synchronous motor without the position sensor algorithm.
Drawings
Fig. 1 is a block diagram of a permanent magnet synchronous motor coordinate system of a rotor position error estimation method of a permanent magnet synchronous motor sensorless according to the present invention.
Fig. 2 is a control schematic block diagram of a position sensorless permanent magnet synchronous motor using the position error estimation method of a position sensorless rotor of a permanent magnet synchronous motor according to the present invention.
Fig. 3 is a schematic block diagram of a sliding-mode observer based on an extended back emf model in a γ δ coordinate system of the permanent magnet synchronous motor sensorless rotor position error estimation method of the present invention.
Fig. 4 shows an actual rotor position error and a rotor position error estimated by a sliding mode observer of a γ δ coordinate system, which are obtained by using the rotor position error estimation method without a position sensor of a permanent magnet synchronous motor according to the present invention.
Detailed Description
In order to more clearly describe the technical contents of the present invention, the following further description is given in conjunction with specific embodiments.
The method for estimating the rotor position error of the permanent magnet synchronous motor without the position sensor is mainly characterized by comprising the following steps of:
(1) constructing a sliding-mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor, and acquiring a rotor position error;
(2) controlling the permanent magnet synchronous motor to work at different rotating speeds, and constructing a rotating speed-rotor position error one-dimensional table;
(3) and according to the one-dimensional table of the rotating speed and the rotor position error, obtaining the rotor position error at the corresponding rotating speed, and eliminating the rotor position error.
In a preferred embodiment, the step (1) is based on iteration of a plurality of calculation cycles, each calculation cycle comprising the steps of:
(1.1) applying the d-axis reference voltage u of the permanent magnet synchronous motor of the sliding-mode observer based on αβ axis coordinate system of the permanent magnet synchronous motord_refQ-axis reference voltage uq_refD axis current idQ-axis current iqGamma-axis voltage v in sliding mode observer correspondingly given to gamma-delta-axis coordinate system based on permanent magnet synchronous motorγDelta axis voltage vδGamma axis current iγDelta axis current iδ；
(1.2) according to the gamma-axis estimated current observed by the sliding-mode observer of the gamma-delta-axis coordinate system based on the permanent magnet synchronous motor, which is acquired in the last calculation period
Figure GDA0002428209630000051
And estimating the current using the gamma axis
Figure GDA0002428209630000052
And a gamma axis current iγSubtracting to obtain the difference between the twoFirst difference sγ(ii) a According to delta axis estimated current observed by a sliding mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor and acquired in the previous calculation period
Figure GDA0002428209630000061
And estimating the current using the delta axis
Figure GDA0002428209630000062
And delta axis current iδSubtracting to obtain a second difference S between the twoδConstructing a sliding mode surface of the sliding mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor;
(1.3) based on the first difference sγAnd a second difference SδObtaining a first sliding mode coefficient ZγAnd a second sliding mode coefficient ZδBy a first sliding mode coefficient ZγAnd a second sliding mode coefficient ZδConstructing a saturation function of the sliding-mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor;
(1.4) sliding mode coefficient Z to be obtainedγAnd ZδPerforming first-order low-pass filtering to obtain a first sliding mode coefficient Z after filteringeγAnd a second sliding mode coefficient Zeδ；
(1.5) estimating the Current from the Gamma-axis
Figure GDA0002428209630000063
Delta axis estimated current
Figure GDA0002428209630000064
The resistance of the stator of the permanent magnet synchronous motor obtains the resistance voltage drop of a gamma axis and the resistance voltage drop of a delta axis; according to the electric angular speed of the rotor of the permanent magnet synchronous motor and the q-axis inductance LqGamma axis estimated current
Figure GDA0002428209630000065
Delta axis estimated current
Figure GDA0002428209630000066
Obtaining the inductance voltage drop of a gamma axis and the inductance voltage drop of a delta axis;
(1.6) root ofAccording to the gamma axis voltage vγFirst sliding mode coefficient ZγSecond sliding mode coefficient ZδFirst sliding mode coefficient Z after filteringeγAnd a second sliding mode coefficient ZeδGamma axis resistance drop, delta axis resistance drop, gamma axis inductance drop, delta axis inductance drop, and d axis inductance LdObtaining gamma-axis estimated current
Figure GDA0002428209630000067
Sum delta axis estimated current
Figure GDA0002428209630000068
(1.7) according to the obtained filtered first sliding mode coefficient ZeγAnd a second sliding mode coefficient ZeδObtaining a rotor position error thetae；
In the first calculation period, the gamma-axis estimated current observed by the sliding-mode observer based on the gamma-delta-axis coordinate system of the permanent magnet synchronous motor, which is acquired in the previous calculation period
Figure GDA0002428209630000069
Initial value and delta axis estimated current
Figure GDA00024282096300000610
Are all 0.
In a more preferred embodiment, said step (1.2) is based on the first difference sγAnd a second difference SδThe sliding mode surface S for constructing the sliding mode observer is as follows:
Figure GDA00024282096300000611
in a more preferred embodiment, the first sliding mode coefficient and the second sliding mode coefficient are determined in step (1.3) by defining a saturation function, and the saturation function is:
Figure GDA00024282096300000612
wherein S isγδComprising SγAnd SδAnd delta is a sliding mode boundary, and delta is larger than zero, S is a sliding mode surface, and k is a sliding mode gain.
In a more preferred embodiment, the sliding mode coefficient Z to be obtained in step (1.4) isγAnd ZδPerforming first-order low-pass filtering to obtain a first sliding mode coefficient Z after filteringeγAnd a second sliding mode coefficient ZeδThe method comprises the following steps:
Figure GDA0002428209630000071
wherein Z iseγIs the first sliding mode coefficient after filtering, ZeδIs the second sliding mode coefficient after filtering, ZγIs the first sliding mode coefficient, ZδIs the second sliding mode coefficient, s is Laplace operator, ωeThe cut-off frequency of the low-pass filter.
In a more preferred embodiment, in the step (1.5), the γ -axis resistance voltage drop, the δ -axis resistance voltage drop, the γ -axis inductance voltage drop and the δ -axis inductance voltage drop are obtained by the following formulas:
Figure GDA0002428209630000072
Figure GDA0002428209630000073
Figure GDA0002428209630000074
Figure GDA0002428209630000075
wherein, the U isγRaFor gamma-axis resistive voltage drop, UδRaIs delta axis resistance drop; u shapeγLFor gamma axis inductive voltage drop, UδLIs delta axis inductance voltage drop, omega is rotor electrical angular velocity, LqIs a q-axis inductor;
Figure GDA0002428209630000076
the current is estimated for the gamma axis acquired in the last calculation cycle,
Figure GDA0002428209630000077
estimating the current, R, for the delta axis obtained in the previous calculation cycleaIs the stator resistance.
In a more preferred embodiment, the step (1.6) obtains the γ -axis estimated current and the δ -axis estimated current by the following formulas:
Figure GDA0002428209630000078
Figure GDA0002428209630000079
wherein the content of the first and second substances,
Figure GDA00024282096300000710
the current is estimated for the gamma axis,
Figure GDA00024282096300000711
the current is estimated for the delta axis.
In a more preferred embodiment, the model of the sliding-mode observer constructed based on the γ δ axis coordinate system of the permanent magnet synchronous motor is:
Figure GDA00024282096300000712
wherein L isdIs d-axis inductance, LqIs q-axis inductance, RaIs the stator resistance, ω is the rotor electrical angular velocity,
Figure GDA00024282096300000713
for the permanent magnet effective flux linkage, p is the differential operator, vγVoltage of gamma axis, vδVoltage of delta axis, ZγIs the first sliding mode coefficient, ZδIs the second sliding mode coefficient, ZeγIs the first sliding mode coefficient after filtering, ZeδIs the filtered second sliding mode coefficient.
In a more preferred embodiment, the step (1.7) obtains the rotor position error θ according to the following formulae：
Figure GDA0002428209630000081
Wherein, E isexTo expand the electromotive force, eγFor expanding the electromotive force EexComponent on the gamma axis, said eγTo spread the component of the electromotive force on the delta axis, theta iseIs the rotor position error.
In a more preferred embodiment, the step (2) comprises:
the rotor position of the permanent magnet synchronous motor is estimated through a sliding mode observer based on an αβ axial coordinate system and a sliding mode observer based on a gamma delta coordinate system, an estimated position obtained by the sliding mode observer based on a αβ axial coordinate system and an estimated position error obtained by the sliding mode observer based on the gamma delta coordinate system are obtained, the estimated position is also used for forming a closed loop of the permanent magnet synchronous motor, therefore, the error of the rotor position when the permanent magnet synchronous motor works at different rotating speeds is obtained, the error of the rotor position corresponds to the rotating speed, and a one-dimensional table about the rotating speed and the rotor position error is constructed.
In a preferred embodiment, the step (3) is:
the rotor position is obtained through a sliding mode observer based on an αβ shaft coordinate system, the rotor position error corresponding to the rotor speed of the permanent magnet synchronous motor to which the sliding mode observer based on the αβ shaft coordinate system is applied is obtained through a rotating speed-rotor position error one-dimensional table, and the rotor position with the rotor position error removed is obtained through addition.
In a particular embodiment of the present invention,
Figure GDA0002428209630000082
estimating current, delta, for the gamma axis acquired in the last calculation cycleThe axis estimates the current, both with an initial value of 0, i.e.
Figure GDA0002428209630000083
The initial value is 0, after a number of algorithm cycles,
Figure GDA0002428209630000084
approximating actual gamma axis current
Figure GDA0002428209630000085
Delta axis current
Figure GDA0002428209630000086
The rotor position error estimation method of the permanent magnet synchronous motor without the position sensor comprises the following steps:
(1) constructing a sliding-mode observer under a gamma delta axis coordinate system of the permanent magnet synchronous motor, and estimating the position error of the rotor;
(2) measuring corresponding rotor position errors under different rotating speeds according to different rotating speeds, and manufacturing a one-dimensional table of the rotor position errors relative to the rotating speeds;
(3) and looking up a table according to the motor to obtain a rotor position error, wherein the sum of the rotor position error and the rotor position estimated by the traditional sliding-mode observer is a new rotor position, and the new rotor position is used for participating in the operation of the control system.
The correlation equation for obtaining the voltages about the d-axis and the q-axis in the permanent magnet synchronous motor is shown in the following formula 1:
Figure GDA0002428209630000087
in the formula 1, vd、vqD-axis voltage and q-axis voltage, id、iqD-axis current and q-axis current, L, respectivelyd、LqD-axis inductance and q-axis inductance, R, respectivelyaIs the stator resistance, ω is the rotor electrical angular velocity,
Figure GDA0002428209630000088
for effective flux linkage of permanent magnetsAnd p is a differential operator.
Rewrite equation 1 to an extended back-emf model, as shown in equation 2:
Figure GDA0002428209630000091
wherein E isexTo expand the back emf, the definition of the expanded back emf is as follows:
Figure GDA0002428209630000092
the expanded counter potential model is not only specific to the embedded permanent magnet synchronous motor (L)d≠LqThe case where the d-axis inductance and the q-axis inductance are not equal) is satisfied, for a surface-mount permanent magnet synchronous motor (L)d＝LqAnd the d-axis inductance and the q-axis inductance are equal) are also established, and the extended counter potential model of the surface-mounted permanent magnet synchronous motor is simplified into the formula (4).
Figure GDA0002428209630000093
And (5) deriving a correlation equation about the gamma axis and the delta axis in the gamma-delta coordinate system. As shown in formulas (5) and (6):
Figure GDA0002428209630000094
Figure GDA0002428209630000095
angular velocity of rotation assuming gamma-delta coordinate system
Figure GDA0002428209630000096
The rotation angular velocity ω is almost equal to the rotation angular velocity ω of the dq axis coordinate system, the error between the rotation angular velocity and the rotation angular velocity ω is negligible, and the second term on the right side of the equation (6) can be omitted.
E in formulae (5) and (6)γ、eδV is a component of the expanded counter-electromotive force on the gamma axis and a component on the delta axis of the gamma delta coordinate system respectivelyγ、vδVoltages of the gamma axis and delta axis, iγ、iδThe gamma axis current and the delta axis current, respectively.
Rewrite equation (5) to an equation of state, as shown in equation (7):
Figure GDA0002428209630000097
designing a sliding-mode observer:
Figure GDA0002428209630000098
in formula (8):
Figure GDA0002428209630000099
wherein, ω iseS is the laplacian operator for the cut-off frequency of the low-pass filter.
Defining a slip form surface:
Figure GDA0002428209630000101
defining a saturation function:
Figure GDA0002428209630000102
in the formula (11), k is a sliding mode gain and is a coefficient larger than zero, and Δ is a sliding mode boundary and is also a coefficient larger than zero.
The gamma-delta coordinate system lags behind the actual rotor angle thetaeIs represented by equation (12):
Figure GDA0002428209630000103
FIG. 2 is a schematic block diagram of the control principle of a permanent magnet synchronous motor without a position sensor according to the present invention, and fig. 3 is a schematic block diagram of a sliding mode observer based on an extended back emf model in a γ δ coordinate system in FIG. 2Referring now to FIGS. 2 and 3, a rotor position estimation algorithm used in a typical position sensorless motor control system estimates the rotor position based on the αβ axis coordinate system of the motor
Figure GDA0002428209630000104
There is some error from the true motor rotor position, so the dq axis in fig. 2 is not actually the true dq axis, but the γ δ axis, based on the recognition that u in fig. 2d_ref、uq_ref、id、iqI.e. v in fig. 3, respectivelyγ、vδ、iγ、iδ。
Based on a gamma delta axis coordinate system, a PMSM (permanent magnet synchronous motor) is utilized to expand a counter-electromotive force model, and a novel sliding-mode observer is constructed, and can estimate an angle error between a gamma delta coordinate system and an αβ axis coordinate system, namely an error between a rotor position estimated by the observer and a real rotor position under a traditional αβ axis coordinate system.
In one embodiment, the rotor position error estimation method comprises the steps of:
step (1): a sliding mode observer based on an extended back electromotive force model under a gamma delta axis coordinate system is constructed according to the formulas (8) to (12), and the specific process is as follows:
(1.1) adding ud_ref、uq_ref、id、iqAre respectively assigned to vγ、vδ、iγ、iδ；
(1.2) estimating the current with the gamma axis acquired in the last calculation cycle
Figure GDA00024282096300001013
Minus the gamma-axis current iγLet the difference be Sγ(ii) a Estimating current with delta axis
Figure GDA0002428209630000105
Minus the gamma-axis current iδLet the difference be Sδ. With SγMultiplying by a sliding mode gain k and dividing by a sliding mode boundary delta if
Figure GDA0002428209630000106
Figure GDA0002428209630000107
Then let ZγK is; if it is
Figure GDA0002428209630000108
Then let Zδ-k; if it is
Figure GDA0002428209630000109
Then order
Figure GDA00024282096300001010
By the same token, obtain Zδ；
(1.3) to Zγ、ZδPerforming a first-order low-pass filtering to obtain Zeγ、Zeδ；
(1.4) mixing
Figure GDA00024282096300001011
And a motor stator resistor RaMultiplying, called gamma-axis resistance drop; will be provided with
Figure GDA00024282096300001012
And a motor stator resistor RaMultiplying, called delta axis resistance drop; the electric angular speed w and q axes of the rotor are induced by an inductor Lq、
Figure GDA0002428209630000111
Multiplying the three, namely gamma axis inductance voltage drop; the electric angular speed w and q axes of the rotor are induced by an inductor Lq、
Figure GDA0002428209630000112
Multiplying the three, namely delta axis inductance voltage drop; using gamma-axis voltage vγMinus ZγSubtracting Z fromeγThe value obtained by subtracting the resistance voltage drop of the gamma axis and adding the inductance voltage drop of the gamma axis is divided by the inductance L of the d axisdThen, the quotient is integrated to obtain the gamma-axis estimated current
Figure GDA0002428209630000113
This operation is represented by equation (13):
Figure GDA0002428209630000114
using delta-axis voltage vδMinus ZδSubtracting Z fromeδThe d-axis inductance L is divided by the value obtained by subtracting the delta-axis resistance voltage drop and subtracting the delta-axis inductance voltage dropdThen, the quotient is integrated to obtain the delta axis estimated current
Figure GDA0002428209630000115
This operation is expressed by equation (14):
Figure GDA0002428209630000116
(1.5) calculating a rotor position error:
Figure GDA0002428209630000117
step (2) measuring the corresponding rotor position error theta under different rotating speeds according to different rotating speedse
In this step, a conventional αβ -based axial coordinate system observer and the sliding mode observer based on the extended back emf model in the γ δ axial coordinate system of the present invention work simultaneously, and the rotor position estimated by the observer based on the αβ axial coordinate system
Figure GDA0002428209630000118
Participating in Park transformation and Park inverse transformation, and estimating a rotation angular velocity w for a rotating speed closed loopeIn this step, the closed loop operation of the control system is not directly involved. Measuring the rotor position error theta when the motor works at different rotating speedseWill thetaeA one-dimensional table is made about the rotational speed.
Simulation model construction under Matlab/Simulink environmentThe main parameters of the motor are as follows: stator resistance Ld＝8.5mH，Lq12.5mH, 2.875 Ω, rotor effective flux linkage is 0.175 Wb. Theta in FIG. 4eFor true rotor position error, θe_estiFor the rotor position error estimated by the sliding mode observer under the gamma-delta coordinate system, 1780rpm of the motor is obtained before 1.3s, and the motor is gradually accelerated to 2280rpm after 1.3s, so that the rotor position error estimated by the novel sliding mode observer can accurately track the actual position error.
Removing the sliding-mode observer based on the extended back emf model in the gamma delta axis coordinate system in the invention in fig. 2, wherein only one traditional observer based on an αβ axis coordinate system is arranged in a motor control system, and the rotor position error theta of the motor working at different rotating speeds is differenteThe rotor position error theta is obtained by looking up the one-dimensional table in step 2eRotor position obtained based on αβ axial coordinate system observer
Figure GDA0002428209630000119
The sum theta is the new rotor position and participates in Park transformation and Park inverse transformation in the control system.
The rotor position error estimation method of the permanent magnet synchronous motor without the position sensor can obviously improve the accuracy of rotor position estimation of the traditional permanent magnet synchronous motor without the position sensor algorithm.
In this specification, the invention has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense.

Claims (10)

1. A rotor position error estimation method of a permanent magnet synchronous motor without a position sensor is characterized by comprising the following steps:
(1) constructing a sliding-mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor, and acquiring a rotor position error;
(2) controlling the permanent magnet synchronous motor to work at different rotating speeds, and constructing a rotating speed-rotor position error one-dimensional table;
(3) according to the one-dimensional table of the rotating speed and the rotor position error, the rotor position error under the corresponding rotating speed is obtained, and the rotor position error is eliminated;
the step (1) is based on iteration of a plurality of calculation cycles, each calculation cycle comprising the steps of:
(1.1) applying the d-axis reference voltage u of the permanent magnet synchronous motor of the sliding-mode observer based on αβ axis coordinate system of the permanent magnet synchronous motord_refQ-axis reference voltage uq_refD axis current idQ-axis current iqGamma-axis voltage v in sliding mode observer correspondingly given to gamma-delta-axis coordinate system based on permanent magnet synchronous motorγDelta axis voltage vδGamma axis current iγDelta axis current iδ；
(1.2) according to the gamma-axis estimated current observed by the sliding-mode observer of the gamma-delta-axis coordinate system based on the permanent magnet synchronous motor, which is acquired in the last calculation period
Figure FDA0002428209620000011
And estimating the current using the gamma axis
Figure FDA0002428209620000012
And a gamma axis current iγSubtracting to obtain a first difference s between the twoγ(ii) a According to delta axis estimated current observed by a sliding mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor and acquired in the previous calculation period
Figure FDA0002428209620000013
And estimating the current using the delta axis
Figure FDA0002428209620000014
And delta axis current iδSubtracting to obtain a second difference S between the twoδConstructing a sliding mode surface of the sliding mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor;
(1.3) based on the first difference sγAnd a second difference SδObtaining a first sliding mode coefficient ZγAnd a second sliding mode coefficient ZδBy a first sliding mode coefficient ZγAnd a second sliding mode coefficient ZδConstructing a saturation function of the sliding-mode observer based on a gamma delta axis coordinate system of the permanent magnet synchronous motor;
(1.4) sliding mode coefficient Z to be obtainedγAnd ZδPerforming first-order low-pass filtering to obtain a first sliding mode coefficient Z after filteringeγAnd a second sliding mode coefficient Zeδ；
(1.5) estimating the Current from the Gamma-axis
Figure FDA0002428209620000015
Delta axis estimated current
Figure FDA0002428209620000016
The resistance of the stator of the permanent magnet synchronous motor obtains the resistance voltage drop of a gamma axis and the resistance voltage drop of a delta axis; according to the electric angular speed of the rotor of the permanent magnet synchronous motor and the q-axis inductance LqGamma axis estimated current
Figure FDA0002428209620000017
Delta axis estimated current
Figure FDA0002428209620000018
Obtaining the inductance voltage drop of a gamma axis and the inductance voltage drop of a delta axis;
(1.6) according to the gamma-axis voltage vγFirst sliding mode coefficient ZγSecond sliding mode coefficient ZδFirst sliding mode coefficient Z after filteringeγAnd a second sliding mode coefficient ZeδGamma axis resistance drop, delta axis resistance drop, gamma axis inductance drop, delta axis inductance drop, and d axis inductance LdObtaining gamma-axis estimated current
Figure FDA0002428209620000021
Sum delta axis estimated current
Figure FDA0002428209620000022
(1.7) according to the obtained filtered first sliding mode coefficient ZeγAnd a second sliding mode coefficient ZeδObtaining a rotor position error thetae；
In the first calculation period, the gamma-axis estimated current observed by the sliding-mode observer based on the gamma-delta-axis coordinate system of the permanent magnet synchronous motor, which is acquired in the previous calculation period
Figure FDA0002428209620000023
Initial value and delta axis estimated current
Figure FDA0002428209620000024
Are all 0.
2. The sensorless rotor position error estimation method of a PMSM according to claim 1, wherein step (1.2) is based on the first difference sγAnd a second difference SδThe sliding mode surface S for constructing the sliding mode observer is as follows:
Figure FDA0002428209620000025
3. the sensorless rotor position error estimation method of a permanent magnet synchronous motor according to claim 1, wherein the step (1.3) determines the first sliding mode coefficient and the second sliding mode coefficient by defining a saturation function, and the saturation function is:
Figure FDA0002428209620000026
wherein S isγδComprising SγAnd SδAnd delta is a sliding mode boundary, and delta is larger than zero, S is a sliding mode surface, and k is a sliding mode gain.
4. The PMSM position-less sensing of claim 1Method for estimating rotor position error of machine, characterized in that, the sliding mode coefficient Z obtained in step (1.4)γAnd ZδPerforming first-order low-pass filtering to obtain a first sliding mode coefficient Z after filteringeγAnd a second sliding mode coefficient ZeδThe method comprises the following steps:
Figure FDA0002428209620000027
wherein Z iseγIs the first sliding mode coefficient after filtering, ZeδIs the second sliding mode coefficient after filtering, ZγIs the first sliding mode coefficient, ZδIs the second sliding mode coefficient, s is Laplace operator, ωeThe cut-off frequency of the low-pass filter.
5. The method for estimating rotor position error of a permanent magnet synchronous motor sensorless according to claim 1, wherein in step (1.5), the gamma axis resistance voltage drop, the delta axis resistance voltage drop, the gamma axis inductance voltage drop and the delta axis inductance voltage drop are obtained by the following formulas:
Figure FDA0002428209620000028
Figure FDA0002428209620000029
Figure FDA00024282096200000210
Figure FDA0002428209620000031
wherein, the U isγRaFor gamma-axis resistive voltage drop, UδRaIs delta axis resistance drop; u shapeγLFor gamma axis inductive voltage drop, UδLIs delta axis inductance voltage drop, omega is rotor electrical angular velocity, LqIs a q-axis inductor;
Figure FDA0002428209620000032
the current is estimated for the gamma axis acquired in the last calculation cycle,
Figure FDA0002428209620000033
estimating the current, R, for the delta axis obtained in the previous calculation cycleaIs the stator resistance.
6. The sensorless rotor position error estimation method of the permanent magnet synchronous motor according to claim 1, wherein the step (1.6) obtains the γ -axis estimated current and the δ -axis estimated current by the following formulas:
Figure FDA0002428209620000034
Figure FDA0002428209620000035
wherein the content of the first and second substances,
Figure FDA0002428209620000036
the current is estimated for the gamma axis,
Figure FDA0002428209620000037
the current is estimated for the delta axis.
7. The method for estimating the rotor position error of the permanent magnet synchronous motor without the position sensor according to claim 1, wherein the model of the sliding-mode observer constructed under the gamma-delta axis coordinate system based on the permanent magnet synchronous motor is as follows:
Figure FDA0002428209620000038
wherein L isdIs d-axis inductance, LqIs q-axis inductance, RaAs the resistance of the stator,omega is the electrical angular velocity of the rotor,
Figure FDA00024282096200000310
for the permanent magnet effective flux linkage, p is the differential operator, vγVoltage of gamma axis, vδVoltage of delta axis, ZγIs the first sliding mode coefficient, ZδIs the second sliding mode coefficient, ZeγIs the first sliding mode coefficient after filtering, ZeδIs the filtered second sliding mode coefficient.
8. The sensorless rotor position error estimation method of the PMSM according to claim 1, wherein in step (1.7), the rotor position error θ is obtained according to the following formulae：
Figure FDA0002428209620000039
Wherein, E isexTo expand the electromotive force, eγFor expanding the electromotive force EexComponent on the gamma axis, said eγTo spread the component of the electromotive force on the delta axis, theta iseIs the rotor position error.
9. The sensorless rotor position error estimation method of a permanent magnet synchronous motor according to claim 1, wherein the step (2) comprises:
the rotor position of the permanent magnet synchronous motor is estimated through a sliding mode observer based on an αβ axial coordinate system and a sliding mode observer based on a gamma delta coordinate system, an estimated position obtained by the sliding mode observer based on a αβ axial coordinate system and an estimated position error obtained by the sliding mode observer based on the gamma delta coordinate system are obtained, the estimated position is also used for forming a closed loop of the permanent magnet synchronous motor, therefore, the error of the rotor position when the permanent magnet synchronous motor works at different rotating speeds is obtained, the error of the rotor position corresponds to the rotating speed, and a one-dimensional table about the rotating speed and the rotor position error is constructed.
10. The sensorless rotor position error estimation method of the permanent magnet synchronous motor according to claim 1, wherein the step (3) is:
the rotor position is obtained through a sliding mode observer based on an αβ shaft coordinate system, the rotor position error corresponding to the rotor speed of the permanent magnet synchronous motor to which the sliding mode observer based on the αβ shaft coordinate system is applied is obtained through a rotating speed-rotor position error one-dimensional table, and the rotor position with the rotor position error removed is obtained through addition.
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