CN111697886A - Permanent magnet synchronous motor speed sensorless control method based on parameter identification - Google Patents

Permanent magnet synchronous motor speed sensorless control method based on parameter identification Download PDF

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CN111697886A
CN111697886A CN202010491480.1A CN202010491480A CN111697886A CN 111697886 A CN111697886 A CN 111697886A CN 202010491480 A CN202010491480 A CN 202010491480A CN 111697886 A CN111697886 A CN 111697886A
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permanent magnet
synchronous motor
magnet synchronous
parameter
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张承宁
滕继晖
张硕
李雪萍
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Beijing Institute of Technology BIT
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0017—Model reference adaptation, e.g. MRAS or MRAC, useful for control or parameter estimation
    • 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
    • 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
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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Abstract

The invention provides a permanent magnet synchronous motor speed sensorless control method based on parameter identification, and provides improvement aiming at the existing model reference self-adaptive method based on a model and combining a parameter identification means. In the prior art, only through the implementation mode of the model reference adaptive method, although the rotor speed can be accurately estimated, the method has the defect of depending on the accuracy of a reference model, including the accuracy of the model and the accuracy of parameters. Therefore, the method combines the model reference self-adaptive method and the parameter identification method, and can improve the accuracy of the model through the identified accurate parameters, so as to improve the accuracy of the rotation speed estimation.

Description

一种基于参数辨识的永磁同步电机无速度传感器控制方法A Speed Sensorless Control Method of Permanent Magnet Synchronous Motor Based on Parameter Identification

技术领域technical field

本发明属于永磁同步电机控制技术领域，尤其涉及一种适用于电感失配情况下的基于参数辨识的无速度控制技术。The invention belongs to the technical field of permanent magnet synchronous motor control, and in particular relates to a speedless control technology based on parameter identification suitable for inductance mismatch.

背景技术Background technique

在永磁同步电机的矢量控制中，转速和位置是非常重要的反馈信息，也是实现闭环控制的关键。现有技术中多采用光电编码器作为速度传感器，通过发射光以及光栅间隔透光，最终在光的接收板上得到转子的转速和位置。但是通常来讲，机械编码器的存在对永磁同步电机的应用带来了一些问题，譬如对于车用永磁同步电机来说，机械编码器的存在使得整个电机的安装空间变大，这对车上本就稀缺的空间来说极不友好；还有因为机械编码器本身仪器的属性，使得电机的应用场景受到限制，在一些例如寒冷，颠簸的恶劣环境下不具有鲁棒性；而且由于机械编码器价格不菲，使得电机控制系统的成本加剧，不利于商业运作。In the vector control of permanent magnet synchronous motor, speed and position are very important feedback information and the key to realize closed-loop control. In the prior art, a photoelectric encoder is mostly used as a speed sensor, and the rotational speed and position of the rotor are finally obtained on the light receiving plate by emitting light and transmitting light at intervals of the grating. But generally speaking, the existence of the mechanical encoder brings some problems to the application of the permanent magnet synchronous motor. For example, for the permanent magnet synchronous motor used in the vehicle, the existence of the mechanical encoder makes the installation space of the whole motor larger, which is very important for the permanent magnet synchronous motor. The scarce space in the car is extremely unfriendly; also because of the properties of the mechanical encoder itself, the application scenarios of the motor are limited, and it is not robust in some harsh environments such as cold and bumps; and due to Mechanical encoders are expensive, which increases the cost of motor control systems and is not conducive to commercial operations.

后续发展出的针对永磁同步电机的无速度控制技术，能够有效克服机械式速度测量的上述缺陷。目前使用较为广泛的有基于反电势的滑模观测器方法，基于旋转电压注入的方法，基于模型的模型参考自适应方法等，但是这些方法本身都存在一定的不足，例如滑模控制存在震荡效应，电压注入方法引入噪声，模型参考方法依赖模型的准确度等，在实际应用中都需要结合其他方法一起使用。The subsequently developed speedless control technology for permanent magnet synchronous motors can effectively overcome the above shortcomings of mechanical speed measurement. At present, the sliding mode observer method based on back EMF, the method based on rotating voltage injection, the model based model reference adaptive method, etc. are widely used, but these methods have certain shortcomings, such as the oscillation effect of sliding mode control. , the voltage injection method introduces noise, the model reference method depends on the accuracy of the model, etc., all of which need to be combined with other methods in practical applications.

发明内容SUMMARY OF THE INVENTION

有鉴于此，本发明提供了一种基于参数辨识的永磁同步电机无速度传感器控制方法，具体包括以下步骤：In view of this, the present invention provides a speed sensorless control method for a permanent magnet synchronous motor based on parameter identification, which specifically includes the following steps:

步骤一、在线实时采集永磁同步电机的三相电流；Step 1: Collect the three-phase current of the permanent magnet synchronous motor in real time online;

步骤二、建立永磁同步电机d-q坐标系下的数学模型，并利用递归最小二乘法辨识出该坐标系下的等效电感参数；Step 2, establishing a mathematical model under the d-q coordinate system of the permanent magnet synchronous motor, and identifying the equivalent inductance parameter under the coordinate system using the recursive least squares method;

步骤三、基于模型参考自适应方法得到永磁同步电机在d-q坐标系下的数学模型，并基于Popov超稳定性设计自适应律来得到转子电角速度表达式；利用由步骤二中辨识出的等效电感参数，得到基于参数辨识的转子电角速度估计值；Step 3: Obtain the mathematical model of the permanent magnet synchronous motor in the d-q coordinate system based on the model reference adaptive method, and obtain the rotor electrical angular velocity expression based on the Popov ultra-stability design adaptive law; The effective inductance parameters are obtained, and the estimated value of rotor electrical angular velocity based on parameter identification is obtained;

步骤四、利用步骤四中得到的转子电角速度估计值，以及对其积分得到的位置信息，反馈至矢量控制并实现对永磁同步电机的控制。Step 4: Using the estimated value of the rotor electrical angular velocity obtained in the step 4 and the position information obtained by integrating it, feed back to the vector control and realize the control of the permanent magnet synchronous motor.

进一步地，所述步骤二中建立的永磁同步电机d-q坐标系下的数学模型，具体包括：Further, the mathematical model under the d-q coordinate system of the permanent magnet synchronous motor established in the step 2 specifically includes:

对由步骤一中所采集的三相电流依次进行Clark变换与Park变换，并建立如下模型：Clark transform and Park transform are performed on the three-phase current collected in step 1 in turn, and the following model is established:

Figure BDA0002521245100000021
Figure BDA0002521245100000021

式中，id、iq分别为d轴和q轴电流，Ud和Uq为d轴和q轴电压，Rs和Ls为d-q坐标系下的等效电阻和电感，We为转子的电角速度，Ψf为永磁体磁链；In the formula, i d and i q are the d-axis and q-axis currents, respectively, U d and U q are the d-axis and q-axis voltages, R s and L s are the equivalent resistance and inductance in the dq coordinate system, and We are The electrical angular velocity of the rotor, Ψ f is the permanent magnet flux linkage;

在id＝0的矢量控制方式下，可表示为以下向量相乘的形式：In the vector control mode with id = 0, it can be expressed as the following vector multiplication form:

Figure BDA0002521245100000022
Figure BDA0002521245100000022

进一步地，所述步骤二中利用递归最小二乘法辨识出该坐标系下的等效电感参数，具体包括：Further, in the second step, the equivalent inductance parameter under the coordinate system is identified by using the recursive least squares method, which specifically includes:

S2.1、给定初始参数值，观测得到m个包含待估计参数的状态方程与m个真实状态值与估计状态值的误差方程，计算m个误差的平方和，公式为：

Figure BDA0002521245100000023
E表示状态估计值与观测值的误差，Y代表真实观测的状态值向量，X表示状态变量矩阵θ表示待估计参数矩阵，Xθ为状态估计值向量；S2.1. Given the initial parameter values, observe and obtain m state equations containing the parameters to be estimated and m error equations between the real state values and the estimated state values, and calculate the sum of the squares of the m errors. The formula is:
Figure BDA0002521245100000023
E represents the error between the state estimated value and the observed value, Y represents the actual observed state value vector, X represents the state variable matrix θ represents the parameter matrix to be estimated, and Xθ represents the state estimated value vector;

S2.2、通过对上述误差平方和公式求导并令其等于零便可以得到最优的参数估计：

Figure BDA0002521245100000024
其中
Figure BDA0002521245100000025
为待估计的参数估计值，也即待估计的等效电感参数；S2.2. The optimal parameter estimation can be obtained by taking the derivation of the above-mentioned error sum of squares formula and making it equal to zero:
Figure BDA0002521245100000024
in
Figure BDA0002521245100000025
is the estimated value of the parameter to be estimated, that is, the equivalent inductance parameter to be estimated;

S2.3、然而该方法对于新增观测方程的情况并不友好，当有新的观测方程时(即第m+1个观测方程)，那么则需要重新计算所有矩阵运算，这无疑增加了计算复杂度。基于该考虑，使用递归最小二乘法，首先当有m+1个观测方程时，最优参数估计表达式为：

Figure BDA0002521245100000026
式中Xm+1表示m+1个观测方程的状态变量组成的矩阵，Ym+1表示m+1个观测值组成的矩阵。在本发明中使该式建立在前m个观测方程的基础上，因此定义两个新的变量P(m)和P(m+1)：S2.3. However, this method is not friendly to new observation equations. When there is a new observation equation (ie, the m+1th observation equation), all matrix operations need to be recalculated, which undoubtedly increases the computational cost. the complexity. Based on this consideration, using the recursive least squares method, first, when there are m+1 observation equations, the optimal parameter estimation expression is:
Figure BDA0002521245100000026
In the formula, X m+1 represents the matrix composed of the state variables of m+1 observation equations, and Y m+1 represents the matrix composed of m+1 observation values. In the present invention, this formula is based on the first m observation equations, so two new variables P(m) and P(m+1) are defined:

Figure BDA0002521245100000027
Figure BDA0002521245100000027

引入一个矩阵定理：Introduce a matrix theorem:

(A+BC)-1＝A-1-A-1B(E+CA-1B)-1CA-1，式中A、B和C分别代表非奇异矩阵。(A+BC) -1 =A -1 -A -1 B(E+CA -1 B) -1 CA -1 , where A, B and C respectively represent non-singular matrices.

将新变量应用矩阵定理可以得到Applying the matrix theorem to the new variable gives

P(m+1)＝[P-1(m)+XT(m+1)X(m+1)]-1 P(m+1)=[P -1 (m)+X T (m+1)X(m+1)] -1

＝P(m)-P(m)XT(m+1)[1+X(m+1)P(m)XT(m+1)]-1X(m+1)P(m)=P(m)-P(m)X T (m+1)[1+X(m+1)P(m)X T (m+1)] -1 X(m+1)P(m)

式中X(m+1)表示第m+1个状态方程，P(m)同上述定义；In the formula, X(m+1) represents the m+1th state equation, and P(m) is the same as the above definition;

S2.4、将S2.3得到的P(m+1)公式代入到S2.2得到的最优参数可以看到式中X(m+1)P(m)XT(m+1)为常数，因此省去了求逆矩阵的繁琐计算过程，这也正是递归最小二乘相对于传统最小二乘的优势所在。最终得到最优的参数估计为：S2.4. Substitute the P(m+1) formula obtained in S2.3 into the optimal parameters obtained in S2.2. It can be seen that X(m+1)P(m)X T (m+1) in the formula is Therefore, the tedious calculation process of inverting the matrix is omitted, which is the advantage of recursive least squares over traditional least squares. Finally, the optimal parameter estimation is obtained as:

Figure BDA0002521245100000031
Figure BDA0002521245100000031

式中

Figure BDA0002521245100000032
表示在m个观测方程之后得到的参数最优估计值，y(m+1)表示第m+1个观测值，P(m)同上定义，最终得到的就是基于m+1个状态方程的参数最优估计值。in the formula
Figure BDA0002521245100000032
Represents the optimal estimated value of the parameters obtained after m observation equations, y(m+1) represents the m+1th observation value, P(m) is defined as above, and finally obtained is the parameter based on m+1 state equations best estimate.

进一步地，所述步骤三基于模型参考自适应方法得到永磁同步电机在d-q坐标系下的数学模型，具有以下形式：Further, the step 3 obtains the mathematical model of the permanent magnet synchronous motor in the d-q coordinate system based on the model reference adaptive method, which has the following form:

Figure BDA0002521245100000033
Figure BDA0002521245100000033

模型中用估计转速

Figure BDA0002521245100000034
替换实际转速We。The estimated speed used in the model
Figure BDA0002521245100000034
Substitute actual rotational speed We .

基于Popov超稳定性设计自适应律来得到以下转子电角速度表达式：Based on the Popov superstability design adaptive law, the following expression of rotor electrical angular velocity is obtained:

Figure BDA0002521245100000035
Figure BDA0002521245100000035

将辨识出的等效电感参数代入上式，便可得到基于参数辨识的转子电角速度估计值。By substituting the identified equivalent inductance parameters into the above formula, the estimated value of the rotor electrical angular velocity based on parameter identification can be obtained.

上述本发明所提供的方法，针对基于模型的模型参考自适应方法，结合参数辨识的手段提出了改进。现有技术中仅通过模型参考自适应方法的实现方式，虽可以精确的估算出转子转速，但是缺点是依赖参考模型的准确性，包括模型准确性和参数的准确性。因此，本发明采用了将模型参考自适应方法和参数辨识方法相结合的方式，能够通过辨识到的准确参数提高模型的准确性，继而提高转速估计的准确性。通过执行本发明的方法，将得到的转速以及积分得到的位置信息反馈至矢量控制中，能够最终实现参数闭环和转速闭环的双闭环的具有一定鲁棒性的无速度传感器控制过程。The above-mentioned method provided by the present invention proposes an improvement for the model-based model reference adaptive method combined with the method of parameter identification. In the prior art, only through the implementation of the model reference adaptive method, although the rotor speed can be accurately estimated, the disadvantage is that it depends on the accuracy of the reference model, including the accuracy of the model and the accuracy of the parameters. Therefore, the present invention adopts the method of combining the model reference adaptive method and the parameter identification method, which can improve the accuracy of the model through the identified accurate parameters, thereby improving the accuracy of the rotation speed estimation. By executing the method of the present invention, the obtained rotational speed and the integrally obtained position information are fed back into the vector control, and finally a speed sensorless control process with a certain robustness of double closed loops of parameter closed loop and rotational speed closed loop can be realized.

附图说明Description of drawings

图1是本发明所提供方法所对应的控制系统总体框架；Fig. 1 is the overall framework of the control system corresponding to the method provided by the present invention;

图2是在电感参数失配时没有参数闭环时的转速估计；Figure 2 is the speed estimation without parameter closed-loop when the inductance parameters are mismatched;

图3电感参数失配时没有参数闭环时的位置估计；Figure 3. Position estimation without parameter closed-loop when inductor parameters are mismatched;

图4是递归最小二乘法辨识的电感参数；Figure 4 is the inductance parameter identified by the recursive least squares method;

图5电感失配时带有参数闭环时的转速估计；Figure 5. Speed estimation with parameter closed loop with inductor mismatch;

图6是电感失配时带有参数闭环时的位置估计。Figure 6 is a position estimate with parametric closed loop with inductor mismatch.

具体实施方式Detailed ways

下面将结合附图对本发明的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

本发明所提供的一种基于参数辨识的永磁同步电机无速度传感器控制方法，如图1所示，具体包括以下步骤：A sensorless control method for a permanent magnet synchronous motor based on parameter identification provided by the present invention, as shown in FIG. 1 , specifically includes the following steps:

步骤一、在线实时采集永磁同步电机的三相电流；Step 1: Collect the three-phase current of the permanent magnet synchronous motor in real time online;

步骤二、建立永磁同步电机d-q坐标系下的数学模型，并利用递归最小二乘法辨识出该坐标系下的等效电感参数；Step 2, establishing a mathematical model under the d-q coordinate system of the permanent magnet synchronous motor, and identifying the equivalent inductance parameter under the coordinate system using the recursive least squares method;

步骤三、基于模型参考自适应方法得到永磁同步电机在d-q坐标系下的数学模型，并基于Popov超稳定性设计自适应律来得到转子电角速度表达式；利用由步骤二中辨识出的等效电感参数，得到基于参数辨识的转子电角速度估计值；Step 3: Obtain the mathematical model of the permanent magnet synchronous motor in the d-q coordinate system based on the model reference adaptive method, and obtain the rotor electrical angular velocity expression based on the Popov ultra-stability design adaptive law; The effective inductance parameters are obtained, and the estimated value of rotor electrical angular velocity based on parameter identification is obtained;

步骤四、利用步骤四中得到的转子电角速度估计值，以及对其积分得到的位置信息，反馈至矢量控制并实现对永磁同步电机的控制。Step 4: Using the estimated value of the rotor electrical angular velocity obtained in the step 4 and the position information obtained by integrating it, feed back to the vector control and realize the control of the permanent magnet synchronous motor.

在本发明的一个优选实施方式中，所述步骤二中建立的永磁同步电机d-q坐标系下的数学模型，具体包括：In a preferred embodiment of the present invention, the mathematical model under the d-q coordinate system of the permanent magnet synchronous motor established in the second step specifically includes:

对由步骤一中所采集的三相电流依次进行Clark变换与Park变换，并建立如下模型：Clark transform and Park transform are performed on the three-phase current collected in step 1 in turn, and the following model is established:

Figure BDA0002521245100000041
Figure BDA0002521245100000041

式中，id、iq分别为d轴和q轴电流，Ud和Uq为d轴和q轴电压，Rs和Ls为d-q坐标系下的等效电阻和电感，We为转子的电角速度，Ψf为永磁体磁链；In the formula, i d and i q are the d-axis and q-axis currents, respectively, U d and U q are the d-axis and q-axis voltages, R s and L s are the equivalent resistance and inductance in the dq coordinate system, and We are The electrical angular velocity of the rotor, Ψ f is the permanent magnet flux linkage;

在id＝0的矢量控制方式下，可表示为以下向量相乘的形式：In the vector control mode with id = 0, it can be expressed as the following vector multiplication form:

Figure BDA0002521245100000042
Figure BDA0002521245100000042

在本发明的一个优选实施方式中，所述步骤二中利用递归最小二乘法辨识出该坐标系下的等效电感参数，具体包括：In a preferred embodiment of the present invention, the recursive least squares method is used to identify the equivalent inductance parameter in the coordinate system in the second step, which specifically includes:

S2.1、给定初始参数值，观测得到m个包含待估计参数的状态方程与m个真实状态值与估计状态值的误差方程，计算m个误差的平方和，公式为：

Figure BDA0002521245100000051
E表示状态估计值与观测值的误差，Y代表真实观测的状态值向量，X表示状态变量矩阵θ表示待估计参数矩阵，Xθ为状态估计值向量；S2.1. Given the initial parameter values, observe and obtain m state equations containing the parameters to be estimated and m error equations between the real state values and the estimated state values, and calculate the sum of the squares of the m errors. The formula is:
Figure BDA0002521245100000051
E represents the error between the state estimated value and the observed value, Y represents the actual observed state value vector, X represents the state variable matrix θ represents the parameter matrix to be estimated, and Xθ represents the state estimated value vector;

S2.2、通过对上述误差平方和公式求导并令其等于零便可以得到最优的参数估计：

Figure BDA0002521245100000052
其中
Figure BDA0002521245100000053
为待估计的参数估计值，也即待估计的等效电感参数；S2.2. The optimal parameter estimation can be obtained by taking the derivation of the above-mentioned error sum of squares formula and making it equal to zero:
Figure BDA0002521245100000052
in
Figure BDA0002521245100000053
is the estimated value of the parameter to be estimated, that is, the equivalent inductance parameter to be estimated;

S2.3、使用递归最小二乘法，首先当有m+1个观测方程时，最优参数估计表达式为：

Figure BDA0002521245100000054
式中Xm+1表示m+1个观测方程的状态变量组成的矩阵，Ym+1表示m+1个观测值组成的矩阵；使该式建立在前m个观测方程的基础上，定义两个新的变量P(m)和P(m+1)：S2.3. Use recursive least squares method. First, when there are m+1 observation equations, the optimal parameter estimation expression is:
Figure BDA0002521245100000054
In the formula, X m+1 represents the matrix composed of the state variables of m+1 observation equations, and Y m+1 represents the matrix composed of m+1 observation values; this formula is established on the basis of the first m observation equations, and the definition Two new variables P(m) and P(m+1):

Figure BDA0002521245100000055
Figure BDA0002521245100000055

引入一个矩阵定理：Introduce a matrix theorem:

(A+BC)-1＝A-1-A-1B(E+CA-1B)-1CA-1，式中A、B和C分别代表非奇异矩阵。(A+BC) -1 =A -1 -A -1 B(E+CA -1 B) -1 CA -1 , where A, B and C respectively represent non-singular matrices.

将新变量应用矩阵定理可以得到Applying the matrix theorem to the new variable gives

P(m+1)＝[P-1(m)+XT(m+1)X(m+1)]-1 P(m+1)=[P -1 (m)+X T (m+1)X(m+1)] -1

＝P(m)-P(m)XT(m+1)[1+X(m+1)P(m)XT(m+1)]-1X(m+1)P(m)=P(m)-P(m)X T (m+1)[1+X(m+1)P(m)X T (m+1)] -1 X(m+1)P(m)

式中，X(m+1)表示第m+1个状态方程；In the formula, X(m+1) represents the m+1th state equation;

S2.4、将S2.3得到的P(m+1)公式代入到S2.2得到最优的参数估计为：S2.4. Substitute the P(m+1) formula obtained in S2.3 into S2.2 to obtain the optimal parameter estimation as:

Figure BDA0002521245100000056
Figure BDA0002521245100000056

式中

Figure BDA0002521245100000057
表示在m个观测方程之后得到的参数最优估计值，y(m+1)表示第m+1个观测值，最终得到的就是基于m+1个状态方程的参数最优估计值。in the formula
Figure BDA0002521245100000057
Represents the optimal parameter estimation value obtained after m observation equations, y(m+1) represents the m+1th observation value, and finally obtained is the optimal parameter estimation value based on m+1 state equations.

在本发明的一个优选实施方式中，所述步骤三基于模型参考自适应方法得到永磁同步电机在d-q坐标系下的数学模型，具有以下形式：In a preferred embodiment of the present invention, the step 3 obtains the mathematical model of the permanent magnet synchronous motor in the d-q coordinate system based on the model reference adaptive method, which has the following form:

Figure BDA0002521245100000058
Figure BDA0002521245100000058

模型中用估计转速

Figure BDA0002521245100000061
替换实际转速We。The estimated speed used in the model
Figure BDA0002521245100000061
Substitute actual rotational speed We .

基于Popov超稳定性设计自适应律来得到以下转子电角速度表达式：Based on the Popov superstability design adaptive law, the following expression of rotor electrical angular velocity is obtained:

Figure BDA0002521245100000062
Figure BDA0002521245100000062

将辨识出的等效电感参数代入上式，便可得到基于参数辨识的转子电角速度估计值。By substituting the identified equivalent inductance parameters into the above formula, the estimated value of the rotor electrical angular velocity based on parameter identification can be obtained.

图2、图3示出了现有的对转子电角速度及位置在电感失配时的估计情况，可以看到在未进行本发明中的改进时，与实际值均存在较大的偏差。图4-6示出了基于本发明的一个实例中，对电感的辨识以及对电子转角速度和位置的估计情况，可以看到估计效果具有明显的改善。Figures 2 and 3 show the existing estimation of the rotor electrical angular velocity and position when the inductance is mismatched. It can be seen that there is a large deviation from the actual value without the improvement in the present invention. Figures 4-6 show the identification of the inductance and the estimation of the angular velocity and position of the electrons in an example based on the present invention, and it can be seen that the estimation effect is significantly improved.

应理解，本发明实施例中各步骤的序号的大小并不意味着执行顺序的先后，各过程的执行顺序应以其功能和内在逻辑确定，而不应对本发明实施例的实施过程构成任何限定。It should be understood that the size of the sequence numbers of the steps in the embodiments of the present invention does not imply the sequence of execution, and the execution sequence of each process should be determined by its functions and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention .

尽管已经示出和描述了本发明的实施例，对于本领域的普通技术人员而言，可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由所附权利要求及其等同物限定。Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, and substitutions can be made in these embodiments without departing from the principle and spirit of the invention and modifications, the scope of the present invention is defined by the appended claims and their equivalents.

Claims (4)

1. A permanent magnet synchronous motor speed sensorless control method based on parameter identification is characterized in that: the method specifically comprises the following steps:
firstly, acquiring three-phase current of a permanent magnet synchronous motor in real time on line;
step two, establishing a mathematical model under a d-q coordinate system of the permanent magnet synchronous motor, and identifying equivalent inductance parameters under the coordinate system by using a recursive least square method;
thirdly, obtaining a mathematical model of the permanent magnet synchronous motor under a d-q coordinate system based on a model reference self-adaptive method, and designing a self-adaptive law based on Popov super-stability to obtain a rotor electrical angular velocity expression; obtaining a rotor electrical angular velocity estimation value based on parameter identification by using the equivalent inductance parameter identified in the step two;
and step four, feeding back the rotor electric angular velocity estimated value obtained in the step four and position information obtained by integrating the rotor electric angular velocity estimated value to vector control and realizing the control of the permanent magnet synchronous motor.
2. The method of claim 1, wherein: the mathematical model under the d-q coordinate system of the permanent magnet synchronous motor established in the second step specifically comprises the following steps:
sequentially performing Clark conversion and Park conversion on the three-phase current collected in the step one, and establishing the following model:
Figure FDA0002521245090000011
in the formula id、iqD-and q-axis currents, UdAnd UqIs d-axis and q-axis voltage, RsAnd LsIs equivalent resistance and inductance in d-q coordinate system, WeIs the electrical angular velocity of the rotor, /)fIs a permanent magnet flux linkage;
at idIn the vector control method of 0, the vector control method can be expressed as a form of vector multiplication of:
Figure FDA0002521245090000012
3. the method of claim 2, wherein: identifying the equivalent inductance parameter under the coordinate system by using a recursive least square method in the second step specifically comprises the following steps:
s2.1, setting initial parameter values, observing to obtain m state equations containing parameters to be estimated and m error equations of real state values and estimated state values, and calculating the square sum of m errors, wherein the formula is as follows:
Figure FDA0002521245090000013
e represents the error between the state estimation value and the observed value, Y represents the state value vector of the real observation, X represents the state variable matrix theta represents the parameter matrix to be estimated, and X theta is the state estimation value vector;
s2.2, obtaining the optimal parameter estimation by deriving the error sum of squares formula and making the error sum of squares equal to zero:
Figure FDA0002521245090000021
wherein
Figure FDA0002521245090000022
The method comprises the steps of obtaining a parameter estimation value to be estimated, namely an equivalent inductance parameter to be estimated;
s2.3, using a recursive least square method, wherein when m +1 observation equations exist, the optimal parameter estimation expression is as follows:
Figure FDA0002521245090000023
in the formula Xm+1Matrix of state variables representing m +1 observation equations, Ym+1Representing a matrix consisting of m +1 observations; on the basis of the first m observation equations, two new variables P (m) and P (m +1) are defined:
Figure FDA0002521245090000024
introducing a matrix theorem:
(A+BC)-1＝A-1-A-1B(E+CA-1B)-1CA-1wherein A, B and C represent non-singular matrices, respectively;
applying matrix theorem to the new variables can obtain
P(m+1)＝[P-1(m)+XT(m+1)X(m+1)]-1
＝P(m)-P(m)XT(m+1)[1+X(m+1)P(m)XT(m+1)]-1X(m+1)P(m)
In the formula, X (m +1) represents the (m +1) th equation of state;
s2.4, substituting the formula P (m +1) obtained by S2.3 into S2.2 to obtain the optimal parameter estimation:
Figure FDA0002521245090000025
in the formula
Figure FDA0002521245090000026
Expressed in m observation equationsAnd finally, obtaining the optimal parameter estimation value based on m +1 state equations, wherein y (m +1) represents the m +1 th observation value.
4. The method of claim 3, wherein: the third step is to obtain a mathematical model of the permanent magnet synchronous motor under a d-q coordinate system based on a model reference self-adaptive method, and the mathematical model has the following form:
Figure FDA0002521245090000027
will be W in the modeleBy estimating the speed of rotation
Figure FDA0002521245090000028
Alternatively, the following form is obtained:
Figure FDA0002521245090000029
designing an adaptive law based on Popov hyperstability to obtain the following rotor electrical angular velocity expression:
Figure FDA0002521245090000031
and substituting the identified equivalent inductance parameters into the formula to obtain the rotor electrical angular velocity estimated value based on parameter identification.
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