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CN109495047B - High-frequency signal injection-based sensorless control method for permanent magnet synchronous motor - Google Patents

High-frequency signal injection-based sensorless control method for permanent magnet synchronous motor Download PDF

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CN109495047B
CN109495047B CN201811625584.6A CN201811625584A CN109495047B CN 109495047 B CN109495047 B CN 109495047B CN 201811625584 A CN201811625584 A CN 201811625584A CN 109495047 B CN109495047 B CN 109495047B
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coordinate system
rotor position
frequency
permanent magnet
synchronous motor
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CN109495047A (en
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王大志
李汶浍
孔德善
王海洋
周迎宾
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Northeastern University China
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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
    • H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
    • 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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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Abstract

本发明的一种基于高频信号注入的永磁同步电机无传感器控制方法，包括以下步骤：步骤1：在两相静止坐标系下建立永磁同步电机基波数学模型及高频电压信号激励下的高频激励数学模型；步骤2：在两相静止坐标系下注入高频电压激励信号，根据高频激励数学模型进行采样，得到包含转子位置信息的电流项，进而得到转子位置的显示表达式；步骤3：将估计的转子位置送入转速控制器和电流控制器，构成转速‑电流双闭环控制结构，产生控制信号。本发明可克服传统转子位置估计方法的缺点，采用补偿矩阵方法，直接得到转子位置的解析表达式，消除现有技术因使用低通滤波器和带通滤波器存在的时间延迟问题，有效估计转子位置。

Figure 201811625584

A sensorless control method of a permanent magnet synchronous motor based on high frequency signal injection of the present invention includes the following steps: Step 1: Establish a fundamental wave mathematical model of the permanent magnet synchronous motor in a two-phase static coordinate system and under the excitation of a high frequency voltage signal Step 2: Inject the high-frequency voltage excitation signal in the two-phase static coordinate system, perform sampling according to the high-frequency excitation mathematical model, obtain the current term containing the rotor position information, and then obtain the display expression of the rotor position ; Step 3: Send the estimated rotor position to the speed controller and the current controller to form a speed-current double closed-loop control structure to generate a control signal. The invention can overcome the shortcomings of the traditional rotor position estimation method, directly obtain the analytical expression of the rotor position by using the compensation matrix method, eliminate the time delay problem existing in the prior art due to the use of low-pass filters and band-pass filters, and effectively estimate the rotor. Location.

Figure 201811625584

Description

High-frequency signal injection-based sensorless control method for permanent magnet synchronous motor
Technical Field
The invention belongs to the field of permanent magnet synchronous motor control, and relates to a high-frequency signal injection-based sensorless control method for a permanent magnet synchronous motor.
Background
The permanent magnet synchronous motor speed regulating system has the advantages of fast dynamic response, strong overload capacity, good stability and the like, and is suitable for the running states of various loads. The permanent magnet synchronous motor rotor is made of permanent magnet materials, has high power density, small volume and weight and flexible appearance size design, and is widely applied to various fields of national production and life. The electric energy is a main secondary energy source for production and life of the nation, the motor is used as a main body for electromechanical energy conversion and electric energy consumption, and the application of the motor relates to a plurality of aspects such as metallurgy, mines, electric power, petroleum, chemical industry, building intelligence, municipal administration, textiles, building materials and the like. In 2013, the Ministry of industry and informatization came out motor energy efficiency improvement plan, which provides policy guarantee and support for the performance improvement of a motor control system.
At present, most permanent magnet synchronous motor control systems need to acquire real-time position information of a rotor to perform speed closed-loop control and rotation coordinate transformation, generally, the position information of the rotor is acquired by mechanical position sensors, such as a photoelectric encoder, a rotary transformer, a hall element and the like, and the mechanical sensors bring the following problems to the system: the high-precision sensor is expensive, the system cost is increased, and the volume is increased; the signal is easy to be interfered by external electromagnetic waves in the transmission process, so that the stability of the system is reduced; under severe environment, a photoelectric encoder may not be used, a hall sensor is easily affected by temperature, and an external demodulation circuit is needed for a rotary transformer, so that the reliability of the system is reduced; the sensor increases the rotational inertia, and the dynamic performance of the system is influenced; the problems of concentricity, angle deviation and the like exist in the installation process of the position sensor, so that the system precision is reduced; some special occasions cannot install and use the sensor.
In order to effectively solve the problems and practically improve the control quality of a permanent magnet synchronous motor control system, domestic and foreign scholars try to estimate the position of a rotor through parameters such as voltage, current and the like which can be directly obtained in the motor operation process so as to replace a mechanical sensor, and thoroughly solve the problem of reduction of system stability, reliability and accuracy caused by sensing, thereby forming a sensorless control method of the permanent magnet synchronous motor.
Although the existing sensorless control method can well estimate the rotor position, the existing sensorless control method has certain limitations: when the permanent magnet synchronous motor operates in a zero/low speed range, the signal-to-noise ratio of a useful signal which can be detected is very low, even cannot be extracted, but the basic idea of the methods relying on the fundamental wave mathematical model is that the back electromotive force is in direct proportion to the rotating speed of the motor, and the speed value of the permanent magnet synchronous motor during zero/low speed operation is very small and even possibly zero, so that the method finally fails at zero/low speed, and the position of a rotor cannot be effectively estimated.
Disclosure of Invention
The invention aims to overcome the defects of low estimation precision, time delay, low dynamic response speed and the like in the prior art, provides a high-frequency signal injection-based permanent magnet synchronous motor sensorless control method, can effectively overcome the defects of the traditional rotor position estimation method through mathematical analysis derivation and calculation, adopts a compensation matrix method to directly obtain an analytical expression of the rotor position, eliminates the time delay problem caused by the use of a low-pass filter and a band-pass filter in the prior art, and effectively estimates the rotor position.
The invention provides a permanent magnet synchronous motor sensorless control method based on high-frequency signal injection, which is used for motor rotor position estimation in a permanent magnet synchronous motor sensorless control system and comprises the following steps:
step 1: establishing a fundamental wave mathematical model of the permanent magnet synchronous motor and a high-frequency excitation mathematical model under the excitation of a high-frequency voltage signal under a two-phase static coordinate system (alpha beta coordinate system);
step 2: injecting a high-frequency voltage excitation signal under a two-phase static coordinate system (alpha beta coordinate system), sampling according to a high-frequency excitation mathematical model, and obtaining a current item containing rotor position information so as to obtain a display expression of the rotor position;
and step 3: and sending the estimated rotor position to a rotating speed controller and a current controller to form a rotating speed-current double closed-loop control structure and generate a control signal.
In the sensorless control method of the permanent magnet synchronous motor based on high-frequency signal injection, the step 1 specifically includes:
step 1.1: establishing a fundamental wave mathematical model of the permanent magnet synchronous motor under a two-phase static coordinate system (alpha beta coordinate system), as shown in the following formula:
Figure BDA0001927914100000031
wherein [ u ]α uβ]TAnd [ iα iβ]TStator voltage and current under a two-phase static coordinate system are respectively; rsA stator winding resistor; l issA stator winding inductance; lambda [ alpha ]fIs a rotor permanent magnet flux linkage; thetaeIs the rotor position; omegaeIs the rotor speed; l is-A half-differential inductance;
wherein, the stator winding inductance matrix is:
Figure BDA0001927914100000032
Figure BDA0001927914100000033
wherein L is+Is average inductance, L-A half-differential inductance; l isd、LqRespectively a d-axis inductor and a q-axis inductor under a two-phase rotating coordinate system (dq coordinate system);
when the sampling time is sufficiently short, the fundamental mathematical model can be expressed in the form:
Figure BDA0001927914100000034
wherein, [ Delta i [ ]αΔiβ]TIs a current variable under a two-phase static coordinate system (alpha beta coordinate system); Δ T is the sampling time;
step 1.2: the injection frequency of the high-frequency signal is far higher than the fundamental frequency, the permanent magnet synchronous motor can be regarded as a simple RL loop, the stator resistance is far smaller than the reactance in high frequency, the rotary electromotive force is very small and can be ignored, and then a high-frequency excitation mathematical model of the permanent magnet synchronous motor under high-frequency excitation can be obtained by the formula (1.1):
Figure BDA0001927914100000035
when the sampling time is short, in terms of the differential term in the discrete quantity approximation equation (2.1), equation (2.1) can be written as follows:
Figure BDA0001927914100000041
in the sensorless control method of the permanent magnet synchronous motor based on the high-frequency signal injection, the step 2 is specifically as follows:
step 2.1: injection frequency of omega in two-phase stationary coordinate system (alpha beta coordinate system)inAmplitude of UinThe high-frequency voltage excitation signal of (2) is as follows:
Figure BDA0001927914100000042
wherein [ u ]αin uβin]ΤIs a high-frequency voltage signal injected under a two-phase static coordinate system.
Step 2.2: when the sampling time is short enough, the fundamental frequency components of the voltage and the current can be regarded as constants, and only the high-frequency component is taken as a variable, so that the voltage difference is only related to the current variable, and the difference is made between the sampling values of two sampling periods of the formula (2.2), so that the following results can be obtained:
Figure BDA0001927914100000043
wherein [ u ]α1 uβ1]TAnd [ u ]α2 uβ2]TFor the voltage in each sampling period, [ u ]α21 uβ21]TIs the voltage difference in the sampling period; [ Delta iα1Δiβ1]TAnd [ Delta i [ ]α2Δiβ2]TIs a sampled current corresponding to the sampled voltage.
Step 2.3: since the inductance matrix in equation (1.2) can be divided into rotor position dependent terms and rotor position independent terms, equation (3.2) is rewritten into the following form according to equation (1.2) and equation (1.3):
Figure BDA0001927914100000044
setting:
Figure BDA0001927914100000045
then there are:
Figure BDA0001927914100000051
a compensation matrix is arranged:
Figure BDA0001927914100000052
combining the following double angles and the sum and difference formulas of the two angles:
Figure BDA0001927914100000053
simplifying the left and right ends of the expression (3.5) by the expression (3.6) and the expression (3.7) to obtain 2 thetaeReduction of terms to thetaeTerm, the compensation matrix can be derived:
Figure BDA0001927914100000054
and the results at the left and right ends of the compensation matrix multiplier (3.5) are:
Figure BDA0001927914100000055
then, a display expression of the rotor position of the permanent magnet synchronous motor can be further obtained:
Figure BDA0001927914100000056
compared with the prior art, the sensorless control method of the permanent magnet synchronous motor based on high-frequency signal injection has the following advantages:
1. the invention provides a mathematical model under high-frequency excitation on the basis of a fundamental wave mathematical model, and simultaneously provides an improved permanent magnet synchronous motor rotor position estimation method based on high-frequency voltage signal injection in a two-phase static coordinate system.
2. The method adopts the compensation matrix and the voltage and current differential equation to obtain the rotor position information, omits the low-pass and band-pass filtering links used in the prior art, successfully eliminates the hidden trouble that the estimated rotor position lags behind the actual position due to the time delay brought by the filtering link, and greatly improves the estimation precision of the rotor position of the permanent magnet synchronous motor.
3. The invention obtains the rotor position display expression of the permanent magnet synchronous motor under the condition of high-frequency signal injection through rigorous and accurate mathematical derivation and analysis, improves the technology that the prior art can only indirectly obtain the rotor position, greatly reduces the estimation error compared with the prior art when the invention is adopted to estimate the rotor position, obviously improves the dynamic response speed, has strong robustness, and does not influence the rotor position estimation precision due to the change of motor parameters.
4. In order to verify the effectiveness of the method provided by the invention, the simulation link verification is specially carried out in an MATLAB/Simulink simulation environment, and the simulation result shows that the method can greatly improve the rotor position estimation precision.
Drawings
FIG. 1 is a block diagram of a sensorless control system for a PMSM in the practice of the present invention;
FIG. 2 is a rotor position estimation method of a sensorless control system of a conventional permanent magnet synchronous motor;
FIG. 3 illustrates a rotor position estimation method for a PMSM according to the present invention;
FIG. 4 is a rotation speed fluctuation simulation verification of the existing permanent magnet synchronous motor rotor position estimation method;
FIG. 5 is a rotation speed fluctuation simulation verification of the permanent magnet synchronous motor rotor position estimation method of the present invention;
FIG. 6 is a rotor position simulation verification of a prior art PMSM rotor position estimation method;
FIG. 7 is a simulation verification of rotor position for the PMSM rotor position estimation method of the present invention;
FIG. 8 is a simulation verification of rotor position estimation error of the existing PMSM rotor position estimation method;
FIG. 9 is a simulation verification of rotor position estimation error of the PMSM rotor position estimation method of the present invention.
Detailed Description
In order to realize sensorless control in a full speed range including zero/low speed, the invention provides that a high-frequency signal injection method is applied to a permanent magnet synchronous motor control system, the accurate estimation of the position of a rotor is realized through detected parameters such as motor voltage, current and the like, the time delay problem caused by the use of a low-pass filter and a band-pass filter in the prior art is eliminated, and the estimation precision and the dynamic response speed are improved.
Fig. 1 is a block diagram of a sensorless control system of a permanent magnet synchronous motor in the specific implementation process of the present invention, and the sensorless control system is divided into the following main parts:
(1) high frequency signal injection part
High-frequency signal generator continuously injects high-frequency signal u into systemαβinThe high-frequency signal is injected after the current controller, and generates a control signal along with the current controller and transmits the control signal to the PWM module, and the PWM module generates six paths of pulse signals to drive a power switch tube of a voltage type inverter VSI and drive a PMSM (permanent magnet synchronous motor) to operateAnd (6) rows.
(2) Signal processing section
The part is to extract three-phase high-frequency induction current i from the end of the permanent magnet synchronous motorABCTransformed by rotating coordinates T3s/2sConverted to two-phase static coordinate system (alpha beta coordinate system), and converted current signal iαβOne path is transformed by coordinates
Figure BDA0001927914100000071
After being converted into a two-phase rotating coordinate system (dq coordinate system), the two-phase rotating coordinate system is filtered by a low pass filter LPF and then is sent to a current controller, and the other path of current signal iαβAnd sending the rotor position estimation algorithm module to estimate the rotor position.
(3) Rotor position estimating section
High frequency induced current i extracted from the motor endαβThe method comprises the steps of extracting a rotor position related item and a rotor position unrelated item, obtaining a rotor position value through related operation, filtering the calculated rotor position value through a Low Pass Filter (LPF) and then sending the filtered rotor position value to a position/speed observer, outputting the observed speed of a rotor by the observer and then sending the observed speed to a speed controller to further obtain a control signal as shown in figure 3
Figure BDA0001927914100000081
Fig. 2 is a rotor position estimation method of a sensorless control system of a conventional permanent magnet synchronous motor.
FIG. 3 shows a three-phase high-frequency voltage u extracted from the end of a PMSM according to the method for estimating the rotor position of a PMSM according to the present inventionABCAnd an induced current iABCTransformed by rotating coordinates T3s/2sConverting the signal from ABC coordinate system to two-phase stationary coordinate system (alpha beta coordinate system), and obtaining delta i after the difference between the sampling values of current and voltageαβ21And uαβ21The rotor position expression is calculated to obtain a rotor position value, the calculated rotor position value is filtered by a low pass filter LPF and then is sent to a position/speed observer, and the observer outputs observed values of the rotating speed and the position
Figure BDA0001927914100000082
And
Figure BDA0001927914100000083
the invention discloses a high-frequency signal injection-based sensorless control method for a permanent magnet synchronous motor, which is used for estimating the position of a motor rotor in a sensorless control system of the permanent magnet synchronous motor and specifically comprises the following steps:
step 1: establishing a fundamental wave mathematical model of the permanent magnet synchronous motor and a high-frequency excitation mathematical model under the excitation of a high-frequency voltage signal under a two-phase static coordinate system (alpha beta coordinate system); the step 1 specifically comprises:
step 1.1: establishing a fundamental wave mathematical model of the permanent magnet synchronous motor under a two-phase static coordinate system (alpha beta coordinate system), as shown in the following formula:
Figure BDA0001927914100000084
wherein [ u ]α uβ]TAnd [ iα iβ]TStator voltage and current under a two-phase static coordinate system are respectively; rsA stator winding resistor; l issA stator winding inductance; lambda [ alpha ]fIs a rotor permanent magnet flux linkage; thetaeIs the rotor position; omegaeIs the rotor speed; l is-A half-differential inductance;
wherein, the stator winding inductance matrix is:
Figure BDA0001927914100000085
Figure BDA0001927914100000086
wherein L is+Is average inductance, L-A half-differential inductance; l isd、LqRespectively two-phase rotating coordinate system(dq coordinate system) under d-axis inductance and q-axis inductance;
when the sampling time is sufficiently short, the fundamental mathematical model can be expressed in the form:
Figure BDA0001927914100000091
wherein, [ Delta i [ ]αΔiβ]TIs a current variable under a two-phase static coordinate system (alpha beta coordinate system); Δ T is the sampling time;
step 1.2: the injection frequency of the high-frequency signal is far higher than the fundamental frequency, the permanent magnet synchronous motor can be regarded as a simple RL loop, the stator resistance is far smaller than the reactance in high frequency, the rotary electromotive force is very small and can be ignored, and then a high-frequency excitation mathematical model of the permanent magnet synchronous motor under high-frequency excitation can be obtained by the formula (1.1):
Figure BDA0001927914100000092
when the sampling time is short, in terms of the differential term in the discrete quantity approximation equation (2.1), equation (2.1) can be written as follows:
Figure BDA0001927914100000093
step 2: injecting a high-frequency voltage excitation signal under a two-phase static coordinate system (alpha beta coordinate system), sampling according to a high-frequency excitation mathematical model, and obtaining a current item containing rotor position information so as to obtain a display expression of the rotor position; the step 2 specifically comprises the following steps:
step 2.1: injection frequency of omega in two-phase stationary coordinate system (alpha beta coordinate system)inAmplitude of UinThe high-frequency voltage excitation signal of (2) is as follows:
Figure BDA0001927914100000094
wherein [ u ]αin uβin]ΤInjecting a high-frequency voltage signal under a two-phase static coordinate system;
step 2.2: when the sampling time is short enough, the fundamental frequency components of the voltage and the current can be regarded as constants, and only the high-frequency component is taken as a variable, so that the voltage difference is only related to the current variable, and the difference is made between the sampling values of two sampling periods of the formula (2.2), so that the following results can be obtained:
Figure BDA0001927914100000101
wherein [ u ]α1 uβ1]TAnd [ u ]α2 uβ2]TFor the voltage in each sampling period, [ u ]α21 uβ21]TIs the voltage difference in the sampling period; [ Delta iα1Δiβ1]TAnd [ Delta i [ ]α2Δiβ2]TIs a sampling current corresponding to the sampling voltage;
step 2.3: since the inductance matrix in equation (1.2) can be divided into rotor position dependent terms and rotor position independent terms, equation (3.2) is rewritten into the following form according to equation (1.2) and equation (1.3):
Figure BDA0001927914100000102
setting:
Figure BDA0001927914100000103
then there are:
Figure BDA0001927914100000104
a compensation matrix is arranged:
Figure BDA0001927914100000105
combining the following double angles and the sum and difference formulas of the two angles:
Figure BDA0001927914100000106
simplifying the left and right ends of the expression (3.5) by the expression (3.6) and the expression (3.7) to obtain 2 thetaeReduction of terms to thetaeTerm, the compensation matrix can be derived:
Figure BDA0001927914100000107
and the results at the left and right ends of the compensation matrix multiplier (3.5) are:
Figure BDA0001927914100000111
then, a display expression of the rotor position of the permanent magnet synchronous motor can be further obtained:
Figure BDA0001927914100000112
and step 3: and sending the estimated rotor position to a rotating speed controller and a current controller to form a rotating speed-current double closed-loop control structure and generate a control signal.
Fig. 4 to 9 are simulation studies conducted in the present invention and the prior art, and a system simulation model is built in the MATLAB/Simulink environment. The parameters of the permanent magnet synchronous motor are as follows: 2 pairs of poles, 5.2 millihenry of d-axis inductance, 17.4 millihenry of q-axis inductance, 0.33 ohm of stator resistance and 0.008 Newton-meter seconds of damping coefficient. The simulation conditions are as follows: DC side voltage Udc36V; PWM switching frequency fpwm5 kHz; adopting a variable step size ode45 algorithm; the relative error is 0.001. Injection amplitude Uin20V, frequency ωin1000Hz, sinusoidal high frequency voltage signal. The motor is arranged in a simulation wayThe simulation results are shown in FIGS. 4-9 when the operation is carried out under two working conditions that the rotation speed is suddenly changed from 30rpm to 50rpm under the conditions of 40rpm, no load and 0.1 s.
The following results can be obtained by simulation:
in a steady state, the simulation results of the prior art and the invention are as follows:
(1) the fluctuation of the rotating speed of the rotor position estimation method based on the heterodyne method is 10.5rpm, and the estimation error of the rotor position is 34.4 degrees;
(2) the fluctuation of the rotating speed of the rotor position estimation method based on the compensation matrix is 5rpm, and the estimation error of the rotor position is 14.3 degrees.
In the dynamic process, the simulation results of the prior art and the invention are as follows:
(1) the transition time of the rotor position estimation method based on the heterodyne method is 25ms, the rotating speed overshoot is 9rpm, and the estimated rotor position is obviously lagged behind the actual rotor position, so that the performance of the rotor position estimation method provided by the invention is obviously superior to that of the rotor position estimation method based on the heterodyne method;
(2) the transition time of the rotor position estimation method based on the compensation matrix is 16ms, the rotating speed overshoot is 5rpm, and the estimated rotor position is basically consistent with the actual rotor position. Therefore, the rotor position estimation method provided by the invention can still show good tracking performance in the dynamic transition process.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the scope of the present invention, which is defined by the appended claims.

Claims (1)

1.一种基于高频信号注入的永磁同步电机无传感器控制方法，用于永磁同步电机无传感器控制系统中的电机转子位置估计，其特征在于，包括以下步骤：1. a permanent magnet synchronous motor sensorless control method based on high frequency signal injection, for the estimation of the rotor position of the permanent magnet synchronous motor sensorless control system, is characterized in that, comprises the following steps: 步骤1：在两相静止坐标系(αβ坐标系)下建立永磁同步电机基波数学模型及高频电压信号激励下的高频激励数学模型，具体包括：Step 1: Establish the fundamental wave mathematical model of the permanent magnet synchronous motor and the high-frequency excitation mathematical model under the excitation of the high-frequency voltage signal in the two-phase static coordinate system (αβ coordinate system), which specifically includes: 步骤1.1：在两相静止坐标系(αβ坐标系)下建立永磁同步电机基波数学模型，如下式所示：Step 1.1: Establish the fundamental wave mathematical model of the permanent magnet synchronous motor in the two-phase stationary coordinate system (αβ coordinate system), as shown in the following formula:
Figure FDA0002961363050000011
Figure FDA0002961363050000011
 其中，[uα uβ]T和[iα iβ]T分别为两相静止坐标系下的定子电压和电流；Rs为定子绕组电阻；Ls为定子绕组电感；λf为转子永磁体磁链；θe为转子位置；ωe为转子速度；L-为半差电感；Among them, [u α u β ] T and [i α i β ] T are the stator voltage and current in the two-phase stationary coordinate system, respectively; R s is the stator winding resistance; L s is the stator winding inductance; λ f is the rotor permanent magnet flux linkage; θ e is the rotor position; ω e is the rotor speed; L - is the semi-differential inductance; 其中，定子绕组电感矩阵为：Among them, the stator winding inductance matrix is:
Figure FDA0002961363050000012
Figure FDA0002961363050000012
Figure FDA0002961363050000013
Figure FDA0002961363050000013
 其中，L+为平均电感，L-为半差电感；Ld、Lq分别为两相旋转坐标系(dq坐标系)下的d轴电感和q轴电感；Among them, L + is the average inductance, L - is the semi-difference inductance; L d and L q are the d-axis inductance and the q-axis inductance in the two-phase rotating coordinate system (dq coordinate system), respectively; 当采样时间足够短时，基波数学模型可以表示成如下形式：When the sampling time is short enough, the fundamental wave mathematical model can be expressed in the following form:
Figure FDA0002961363050000014
Figure FDA0002961363050000014
 其中，[Δiα Δiβ]T为两相静止坐标系(αβ坐标系)下的电流变量；ΔT为采样时间；Among them, [Δi α Δi β ] T is the current variable in the two-phase stationary coordinate system (αβ coordinate system); ΔT is the sampling time; 步骤1.2：高频信号的注入频率远高于基频，此时可将永磁同步电机看作一个简单的RL回路，由于高频时定子电阻远小于电抗，旋转电动势非常小，可以忽略不计，则由式(1.1)可得到高频激励下的永磁同步电机的高频激励数学模型：Step 1.2: The injection frequency of the high-frequency signal is much higher than the fundamental frequency. At this time, the permanent magnet synchronous motor can be regarded as a simple RL loop. Since the stator resistance is much smaller than the reactance at high frequency, the rotating electromotive force is very small and can be ignored. Then the high-frequency excitation mathematical model of the permanent magnet synchronous motor under high-frequency excitation can be obtained by formula (1.1):
Figure FDA0002961363050000021
Figure FDA0002961363050000021
 当采样时间很短时，以离散量逼近式(2.1)中的微分项，式(2.1)可以写成如下形式：When the sampling time is very short, the differential term in equation (2.1) is approximated by discrete quantities, and equation (2.1) can be written in the following form:
Figure FDA0002961363050000022
Figure FDA0002961363050000022
 步骤2：在两相静止坐标系(αβ坐标系)下注入高频电压激励信号，根据高频激励数学模型进行采样，可以得到包含转子位置信息的电流项，进而得到转子位置的显示表达式，具体为：Step 2: Inject the high-frequency voltage excitation signal in the two-phase static coordinate system (αβ coordinate system), and perform sampling according to the high-frequency excitation mathematical model, the current term containing the rotor position information can be obtained, and then the display expression of the rotor position can be obtained, Specifically: 步骤2.1：在两相静止坐标系(αβ坐标系)下注入频率为ωin，幅值为Uin的高频电压激励信号，如下式所示：Step 2.1: Inject a high-frequency voltage excitation signal with a frequency of ω in and an amplitude of U in in the two-phase stationary coordinate system (αβ coordinate system), as shown in the following formula:
Figure FDA0002961363050000023
Figure FDA0002961363050000023
 其中，[uαin uβin]T为两相静止坐标系下注入的高频电压信号；Among them, [u αin u βin ] T is the high-frequency voltage signal injected in the two-phase stationary coordinate system; 步骤2.2：当采样时间足够短时，电压与电流的基频分量可以看作常量，而只把高频分量作为变量，则电压差只与电流变量有关，对式(2.2)两个采样周期的采样值做差，可以得到：Step 2.2: When the sampling time is short enough, the fundamental frequency components of the voltage and current can be regarded as constants, and only the high-frequency components are used as variables, then the voltage difference is only related to the current variable. By doing the difference of the sampled values, you can get:
Figure FDA0002961363050000024
Figure FDA0002961363050000024
 其中，[uα1 uβ1]T和[uα2 uβ2]T为每个采样周期内的电压，[uα21 uβ21]T为采样周期内的电压差；[Δiα1 Δiβ1]T和[Δiα2 Δiβ2]T为与采样电压对应的采样电流；Among them, [u α1 u β1 ] T and [u α2 u β2 ] T are the voltage in each sampling period, [u α21 u β21 ] T is the voltage difference in the sampling period; [Δi α1 Δi β1 ] T and [ Δi α2 Δi β2 ] T is the sampling current corresponding to the sampling voltage; 步骤2.3：由于公式(1.2)中的电感矩阵可以分为转子位置相关项和转子位置无关项，根据公式(1.2)和公式(1.3)将公式(3.2)改写成如下形式：Step 2.3: Since the inductance matrix in formula (1.2) can be divided into rotor position dependent terms and rotor position independent terms, formula (3.2) is rewritten into the following form according to formula (1.2) and formula (1.3):
Figure FDA0002961363050000031
Figure FDA0002961363050000031
 设：Assume:
Figure FDA0002961363050000032
Figure FDA0002961363050000032
 则有：Then there are:
Figure FDA0002961363050000033
Figure FDA0002961363050000033
 设有补偿矩阵：With the compensation matrix:
Figure FDA0002961363050000034
Figure FDA0002961363050000034
 结合如下倍角及两角和差公式：Combine the following double-angle and two-angle sum-difference formulas:
Figure FDA0002961363050000038
Figure FDA0002961363050000038
 以式(3.6)乘式(3.5)左右两端，采用式(3.7)对其进行化简，将2θe项化简成θe项，可得补偿矩阵：Multiplying the left and right ends of Equation (3.5) by Equation (3.6), using Equation (3.7) to simplify it, and simplifying the 2θ e term into the θ e term, the compensation matrix can be obtained:
Figure FDA0002961363050000035
Figure FDA0002961363050000035
 且以补偿矩阵乘式(3.5)左右两端的结果为：And the results of the left and right ends of the compensation matrix multiplication (3.5) are:
Figure FDA0002961363050000036
Figure FDA0002961363050000036
 则可进一步得到永磁同步电机转子位置的显示表达式：Then the display expression of the rotor position of the permanent magnet synchronous motor can be further obtained:
Figure FDA0002961363050000037
Figure FDA0002961363050000037
 步骤3：将估计的转子位置送入转速控制器和电流控制器，构成转速-电流双闭环控制结构，产生控制信号。Step 3: The estimated rotor position is sent to the speed controller and the current controller to form a speed-current double closed-loop control structure to generate a control signal.
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