CN109120191B - Position sensing method of brushless DC motor based on LSSVM hierarchical classification - Google Patents

Abstract

Aiming at the problem of rotor position detection of the brushless DC motor, the invention proposes a position sensing method of the brushless DC motor based on the least squares support vector machine (LSSVM) hierarchical classification. The method proposed by the present invention takes the stator voltage and current of the brushless DC motor as the input of the decision-making LSSVM, and the rotor position information as the output, divides the DC motor rotor position into 6 regions, and each LSSVM outputs the combination of the corresponding region class, and gradually divides it into six regions. Layer decision-making until the corresponding area of the rotor is distinguished; the LSSVM network is trained by the grid optimization method to determine the optimal parameters of the LSSVM, and then the trained network model is applied to the motor operation, and the motor stator voltage and current are collected as the input of the LSSVM , the final rotor position information is determined through hierarchical decision-making, and the logical commutation signal is calculated by the rotor position to determine the on-off of the corresponding switch tube corresponding to each area, that is, the commutation logic signal.

Description

Position sensing method of brushless DC motor based on LSSVM hierarchical classification

technical field

The invention relates to a rotor position sensing method in the field of brushless direct current motors, in particular to a brushless direct current motor position sensing method based on Least Squares Support Vector Machine (LSSVM) hierarchical classification.

Background technique

The brushless DC motor controls the electronic commutation circuit through the rotor position signal, so that each winding of the stator armature is continuously commutated and energized, so that the stator magnetic field and the rotor permanent magnetic field always maintain a space angle of about 90, and generate torque to drive the rotor to run.

The rotor position information of the traditional brushless DC motor is measured by a position sensor, and a position detection device needs to be installed. However, the brushless DC motor with a position detection device has the following disadvantages: increasing the size of the motor is not conducive to the miniaturization of the motor; the installation of the position sensor In the limited space inside the motor, it is difficult to install and maintain; it is difficult to adapt to harsh environments; the wiring of the sensor is complicated, and it is easy to introduce interference. Therefore, the position sensorless brushless DC motor has become a research hotspot.

At present, the position measurement technology of the rotor position sensorless device mainly includes the back EMF method, the current detection method and the intelligent algorithm. The back EMF is proportional to the speed, so the zero-crossing signal cannot be obtained by detecting the back EMF when the rotational speed is very low or even zero; and the implementation of the current method mainly depends on the accuracy of the current sensor. Signals of the magnitude of the current, while small changes in the phase and waveform of the current are difficult to detect. Therefore, the back EMF method and the current method have their limitations when used alone.

SUMMARY OF THE INVENTION

Technical problem: Rotor signal detection methods with position sensors and various position sensor-less devices have their limitations, so it is difficult to apply to occasions with relatively high requirements for motor operation.

Technical solution: In order to solve the above problems, the LSSVM hierarchical classification is used in the rotor position detection, and the current speed control enables the motor to run stably as required. For the brushless DC motor, the mapping model between the rotor position signal and the motor voltage and current is established, and the LSSVM hierarchical classification is used to realize the mapping. The motor voltage and current are used as the input of LSSVM, and the rotor position information is used as the output, so as to realize the determination of the rotor position of the motor.

The present invention is a rotor position detection system based on LSSVM. From the working principle of the brushless motor, it can be known that the induced flux linkage of the windings A, B, and C phases is a function of the electrical angle θ, while the There is a certain relationship between the induced flux linkage and the three-phase terminal voltage and current, so the electrical angle θ, that is, the rotor position signal, can be predicted from the three-phase terminal voltage and current.

i＝1,2,…,N表示LSSVM分类预测模型的输入量，y_i表示模型目标输出量。映射函数Φ(x_i):

使用核函数将原始输入空间的样本映射到高维特征空间Ω中，在特征空间中利用映射函数对样本数据进行线性分类。LSSVM is a binary classification model. Its purpose is to find a hyperplane to segment the samples. The principle of segmentation is to maximize the interval. The general form of describing the multivariate nonlinear classification model is: y _i =sgn(g(x _i )) where

i=1,2,...,N represents the input of the LSSVM classification prediction model, and y _i represents the target output of the model. Mapping function Φ(x _i ):

The samples in the original input space are mapped into the high-dimensional feature space Ω using the kernel function, and the sample data is linearly classified by the mapping function in the feature space.

The LSSVM classification function can be expressed as: g(x)=(ω·Φ(x))+b(1)

where the vector ^ω∈Rn and the bias b∈R. While minimizing the sample error, SVM uses the principle of structural risk minimization, and the function fitting problem can be described as an optimization problem:

是将输入数据映射到高维特征空间的函数；ω∈Rⁿ，e_i为误差，e_i，b∈R，C>0为惩罚系数，用于控制解的光滑度，其值越大代表对误差的惩罚力度越强，T为转置。in the formula

is the function that maps the input data to the high-dimensional feature space; ω∈R ⁿ , e _i is the error, e _i , b∈R, C>0 is the penalty coefficient, which is used to control the smoothness of the solution, and the larger the value, the representative The stronger the penalty for error, T is the transpose.

According to formula (1), the model is converted to the dual space to solve, and the following Lagrange function is obtained:

where α _i ∈ R is the Lagrange multiplier, and the partial derivatives are obtained for ω, e _i , b, and α _i respectively, and the partial derivatives are set to 0:

Eliminate ω, e _i to get linear equation system (4):

where y=[y ₁ ...y _N ], α=[α ₁ ...α _N ], E ^T =[1...1], Ω is the kernel matrix, G is the kernel function satisfying Mercer's theorem:

Solve equation (5) to get α, b, and the obtained nonlinear regression function is:

The classification result is determined according to the sign of g(x), where: the optimal Lagrange multiplier α _i ; b is the bias term.

LSSVM is a kernel-based learning method, and the selection of kernel function has an important impact on the performance of LSSVM. To this end, the present invention uses the three kernel functions shown in Table 1 to establish a classifier.

Table 1 Three kernel functions used

the name of the kernel function The expression of the kernel function Polynomial Kernel Function G_P(x_i,x)=(x^Tx_i+1)<sup>u< /sup>(u∈N) RBF kernel function G_R(x_i,x)=exp(-‖x-x_i‖²/σ²)(σ≠0∈R) Sigmoid kernel function G_S(x_i,x)=tanh(a(x^Tx_i)+c)( a, c∈R)

In Table 1, G _P , G _R , and G _S represent the polynomial kernel function, the RBF kernel function, and the Sigmoid kernel function, respectively. In the polynomial kernel function, u is used to set the highest degree of the polynomial kernel function; in the RBF kernel function, σ is the width parameter of the function, which controls the radial range of the function; a and c in the Sigmoid kernel function are used to set the parameters in the kernel function .

The brushless DC motor position sensing method based on LSSVM (SVM) hierarchical classification proposed by the present invention, A, B phase voltage u _a (k), u _b (k), current i _a (k), i _b (k ), i _a (k-1), i _b (k-1) are used as the input of LSSVM, S(K) is the rotor position signal, and it is used as the output of LSSVM. Layer decision-making until the position of the corresponding region of the rotor is distinguished. G _j (x _i ,x) is the kernel function, j=1,2,...,L are L classifiers respectively, k is the time series, and K is the rotor position.

A position detection algorithm based on SVM hierarchical classification proposed by the present invention mainly includes LSSVM hierarchical classification modeling and model running parts.

1. The main implementation steps of the hierarchical classification modeling part of LSSVM are as follows:

Step1: Collect the input and output detection signals of the brushless DC motor with the same type of position sensor: A and B phase voltage u _a (k), u _b (k), current i _a (k), i _b (k), i _a (k-1), i _b (k-1) are used as the input of LSSVM, S(K) is the rotor position signal, which is used as the output of LSSVM, divide the 0-360 degree electrical angle θ of the rotor of the DC motor It is an area every 60 degrees, a total of 6 areas, the rotor position is represented by the area number 1-6, and the measured training data and test data are normalized;

Step2: A total of 5 LSSVM2 classifiers are set. The first layer of 1 classifier will set the samples of the selected two categories (such as 1-2) as positive samples, and the samples of the remaining 4 categories (such as 3-6 categories) Set as negative samples, the second layer has 2 classifiers, and the first layer is determined as 2 categories (such as 1-2 categories). and category 2), the data determined as 4 categories in the first layer are applied to the second classifier, and divided into 2 categories (such as 3-4 category and 4-5 category), and the 2 classifiers in the third layer The two categories of the second layer continue to be distinguished, and so on, we can get five such two-class classifiers, one of which is shown in Table 2.

Table 2 Examples of hierarchical classifiers

Determine the kernel function G _j , and the kernel function selects one of polynomial, radial basis and other functions, and sig functions.

Step3: According to the classifier output, select the training samples of the corresponding class, the positive sample is +1, and the negative sample is -1. The Vapnik algorithm is used to train the 5 LSSVM models respectively, and the grid optimization method is used to verify and test to obtain the optimal model parameters. Penalty coefficient C and kernel function parameters are used to obtain 5 optimal LSSVM binary classifiers.

2. The main implementation steps of the LSSVM hierarchical classification operation part are as follows:

Step1: Collect relevant voltage and current input signals in real time and normalize them;

Step2: Input the relevant voltage and current input signals into the established LSSVM classifier to obtain the Ki classification result of the area where the rotor is located;

When there are two or more results in categories 1, 2, ..., 6, the last classification result remains unchanged; when there are no results in categories 1, 2, ..., 6, the last classification result remains unchanged.

Step 3 performs real-time control according to the rotor position obtained by classification. Through the rotor position estimation logic commutation signal, the on-off of the corresponding switch tube corresponding to each area is determined, that is, the commutation logic signal. The transformation relationship between the rotor position information and the commutation logic signal is shown in Table 3, where 1 means turn on, and 0 means turn off.

Table 3 Transformation relationship between rotor position information and commutation logic signal

Beneficial effects: the position sensing method of the present invention has the advantages of good dynamic performance and high robustness. The running speed of the algorithm is fast, which improves the response speed of the controller.

Description of drawings

Figure 1 is a structural diagram of the position sensing structure of a brushless DC motor based on LSSVM hierarchical classification.

Detailed ways:

The brushless DC motor position sensing method based on the LSSVM hierarchical classification proposed by the present invention is described in detail as follows in conjunction with the specific implementation of the system structure diagram:

Step1: Collect the input and output detection signals of the brushless DC motor with the same type of position sensor: A and B phase voltage u _a (k), u _b (k), current i _a (k), i _b (k), i _a (k-1), i _b (k-1) are used as the input of LSSVM, S(K) is the rotor position signal, which is used as the output of LSSVM, divide the 0-360 degree electrical angle θ of the rotor of the DC motor It is an area every 60 degrees, a total of 6 areas, and the rotor position is represented by the area number 1-6.

Step2: A total of 5 LSSVM2 classifiers are set. The first layer of 1 classifier sets the selected samples of the two categories 1-2 as positive samples, and the remaining 4 types of samples of categories 3-6 are set as negative samples. There are two classifiers in the second layer. The first layer is determined as 1-2 category data. The samples of categories 1 and 2 are determined as positive samples and negative samples respectively, so as to distinguish and identify category 1 and category 2. The first layer is determined as 3- The data of 6 categories is applied to the second classifier and divided into two categories: 3-4 and 5-6. The second layer of 2 classifiers continue to distinguish the second layer of 2 categories, and so on, we can get 5 The structure of such two types of classifiers is shown in Table 4.

Table 4 Hierarchical classifier

The training data and test data are measured by a brushless DC motor with a position sensor, and the measured 5000 sets of training data and 2500 sets of test data are normalized; the excitation function is determined as G is the radial basis function

Where x is the input data, x _i is the center of the radial base, σ _i is the radius of the radial base, i=1, 2, ... m, m is the number of center vectors. j is the serial number of the corresponding classifier, j=1,2,...,5.

Step3: According to the output of the classifier, select the training samples of the corresponding class, the positive sample is +1, the negative sample is -1, the Vapnik algorithm is used to train the 5 LSSVM models, and the grid optimization method and the leave-one-out cross-validation test are used to obtain the most The optimal model parameter penalty coefficient C, radial basis radius σ _i , and five optimal LSSVM binary classifiers are obtained. The parameter grid is selected according to the exponential change as follows:

Penalty coefficient C: 10 ⁶ -10 ^-1 ; radial base radius σ _i : 10 ^-5 -10 ^-1

The second part: The main implementation steps of the LSSVM hierarchical classification model operation part are as follows:

Step1: Collect relevant voltage and current input signals in real time and normalize them;

Step2: Input the relevant voltage and current input signals into the established LSSVM hierarchical classifier to obtain the K _i classification result of the region where the rotor is located;

When there are two or more results in categories 1, 2, ..., 6, the last classification result remains unchanged; when there are no results in categories 1, 2, ..., 6, the last classification result remains unchanged.

Step3: Determine the rotor position S(K) through the LSSVM classification network, that is, the area K _i where the rotor is located, and perform real-time control according to the rotor position. Through the rotor position estimation logic commutation signal, the on-off of the corresponding switch tube corresponding to each area is determined, that is, the commutation logic signal.

The above-mentioned specific implementations are only the preferred implementations of the present invention. Of course, the present invention can also have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make according to the present invention. Various corresponding changes and deformations, but these corresponding changes and deformations should all belong to the protection scope of the claims of the present invention.

Claims (1)

1. a brushless DC motor position sensing method based on least squares support vector machine (LSSVM) hierarchical classification, it is characterized in that, obtain the position signal of brushless DC motor rotor by LSSVM hierarchical classifier, reduce the motor factor. The error caused by the existence of the position sensor and the reduction of the motor volume; the method adopts the LSSVM binary classification structure, and determines the final classification output through hierarchical decision-making, mainly including the LSSVM hierarchical classification modeling and model operation parts: 1) The main implementation steps of the LSSVM hierarchical classification modeling part are as follows: Step1: Collect the input and output detection signals of the brushless DC motor with the same type of position sensor, and compare the A and B-phase voltages ua(k), ub(k) and currents ia(k), ib(k), ia(k- 1), ib(k-1) is used as the input of LSSVM, and the rotor position signal S(K) is used as the output of LSSVM. Each LSSVM output corresponds to a set of regional samples, where k is the time series, K is the rotor position, and the decision is made continuously. , until each category is divided; the 0-360 degree electrical angle of the rotor rotation of the DC motor is divided into 6 areas, one area every 60 degrees, the area where the rotor position is represented by the category number 1-6, the measured training Data and test data are normalized; Step2: A total of 5 LSSVM binary classifiers are set, the first layer is a binary classifier, including six categories from category 1 to category 6, the samples of the selected two categories are set as positive samples, and the samples of the remaining four categories are set as Negative samples; two two-classifiers in the second layer, the first two-classifier in the second layer defines the two categories of positive samples in the first layer as positive samples and negative samples respectively, so as to distinguish the above two categories; the second The second two-classifier of the layer divides the four categories in the negative samples of the first layer into two groups, each group contains two categories, and obtains two two-classifiers in the third layer, and the two two-classifiers in the third layer are respectively Continue to distinguish the two categories included to distinguish the remaining four categories, and obtain a total of 5 binary classifiers; determine the kernel function Gj, and the kernel function selects one of the polynomial, radial basis, and sig functions; Step3: Select the training samples of the corresponding class according to the classifier output, positive samples are +1, negative samples are -1, use Vapnik algorithm to train 5 LSSVM binary classifiers, use grid optimization method to verify and test to obtain the optimal model The parameter penalty coefficient C and kernel function parameters are used to obtain 5 optimal LSSVM binary classifiers; 2) The main implementation steps of the running part of the LSSVM hierarchical classification model are as follows: Step1: Collect relevant voltage and current input signals in real time and normalize them; Step2: Input the relevant voltage and current input signals into the established LSSVM classifier to obtain the classification result of the region where the rotor is located; When there are two or more results in categories 1, 2, ..., 6, the last classification result remains unchanged; when there are no results in categories 1, 2, ..., 6, the last classification result remains unchanged; Step3: Carry out real-time control according to the rotor position obtained by classification; determine the on-off of the switch tube corresponding to each area through the rotor position reckoning logic commutation signal.

Images