阅读说明：本技术 一种感应电机转子磁链的观测方法 (Method for observing rotor flux linkage of induction motor ) 是由 董蕊 于 2021-08-25 设计创作，主要内容包括：一种感应电机转子磁链的观测方法,涉及电机控制技术领域。本发明是为了解决现有对磁链观测器进行离散化时,离散化误差大,导致磁链观测精度低的问题。本发明所述的一种感应电机转子磁链的观测方法,采集感应电机定子电流,建立转子磁链观测器,利用改进欧拉法对转子磁链观测器进行离散化并获得观测值,所述观测值用于对感应电机进行控制,所述改进欧拉法为前向欧拉法与梯形离散法的结合离散化方法。本发明适用于感应电机控制中的转子磁链观测部分,以提高磁链观测精度。(An observation method for a rotor flux linkage of an induction motor relates to the technical field of motor control. The invention aims to solve the problem that the existing discretization method of the flux linkage observer has large discretization error and low flux linkage observation precision. The invention relates to an observation method of induction motor rotor flux linkage, which comprises the steps of collecting induction motor stator current, establishing a rotor flux linkage observer, discretizing the rotor flux linkage observer by utilizing an improved Euler method and obtaining an observed value, wherein the observed value is used for controlling an induction motor, and the improved Euler method is a combined discretization method of a forward Euler method and a trapezoidal discretization method. The invention is suitable for the rotor flux linkage observation part in induction motor control so as to improve the flux linkage observation precision.)

1. A method for observing the flux linkage of the rotor of an induction motor is characterized in that,

collecting the stator current of the induction motor, establishing a rotor flux linkage observer,

discretizing the rotor flux linkage observer by using an improved Euler method, obtaining an observed value of the discretized rotor flux linkage observer,

the observations are used to control the induction machine,

the improved Euler method is a combined discretization method of a forward Euler method and a trapezoidal discretization method.

2. The method of claim 1, wherein the rotor flux linkage observer is a rotor flux linkage current model of the induction machine in an α β coordinate system.

3. An observation method of a rotor flux linkage of an induction machine according to claim 1, characterized in that a differential expression of said rotor flux linkage observer is as follows:

wherein the content of the first and second substances,B＝λL_m，ω_ras angular speed of the rotor, L_mIs mutual inductance, R_rIs rotor resistance, L_rIs the rotor inductance, x is the flux linkage,as an observed value of flux linkage, i_sIs the stator current, t is the time.

4. An observation method of rotor flux linkage of an induction machine according to claim 3, wherein the expression of the continuous domain of the rotor flux linkage observer in the α β coordinate system is:

wherein the content of the first and second substances,andalpha-axis component and beta-axis component, i, of rotor flux linkage observed value_sαAnd i_sβThe stator current alpha-axis component and the stator current beta-axis component, respectively.

5. The method of claim 3, wherein discretizing the rotor flux linkage observer by using the modified Euler method comprises:

discretizing the rotor flux linkage observer by using a forward Euler method to obtain a primary discretization result:

wherein, T_sK is a discrete step size, k is 0,1,2, k (k) is kT_sTime magnetic linkage observed valueThe differential of (a) is determined,when K is 0, K (0) is 0;

and obtaining the discrete induction motor rotor flux linkage observer based on the primary discrete result.

6. The method for observing rotor flux linkage of an induction machine according to claim 5, wherein the obtaining a discretized rotor flux linkage observer of an induction machine based on a primary discretization result comprises:

discretizing the primary discrete result again by using a trapezoidal discrete method to obtain the discrete induction motor rotor flux linkage observer:

wherein K (K +1) is (K +1) T_sTime magnetic linkage observed valueThe differential of (a) is determined,

7. the method for observing the rotor flux linkage of the induction machine according to claim 6, wherein the expression of the discretized rotor flux linkage observer of the induction machine in an α β coordinate system is as follows:

wherein the content of the first and second substances,andare each kT_sThe alpha-axis component and the beta-axis component of the rotor flux linkage observations at the time,andare respectively (k +1) T_sAlpha-axis component and beta-axis component, K, of the moment rotor flux linkage observed value_α(k) And K_β(k) Are each kT_sDifferential, K, of the alpha-axis component and the beta-axis component of the time rotor flux linkage observed value_α(K +1) and K_β(k +1) are (k +1) T respectively_sAnd the time rotor flux linkage observed value is the differential of the alpha axis component and the beta axis component.

8. Method for observing the flux linkage of the rotor of an induction machine according to claim 7, characterised in that K_α(k) And K_β(k) The specific expression of (a) is as follows:

wherein i_sα(k) And i_sβ(k) Are each kT_sThe time stator current alpha-axis component and beta-axis component, omega_r(k) Is kT_sThe rotor angular velocity is at that moment.

9. Method for observing the flux linkage of the rotor of an induction machine according to claim 7 or 8, characterised in that K_α(K +1) and K_βThe specific expression of (k +1) is as follows:

wherein i_sα(k +1) and i_sβ(k +1) are (k +1) T respectively_sThe time stator current alpha-axis component and beta-axis component, omega_r(k +1) is (k +1) T_sThe rotor angular velocity is at that moment.

10. The method for observing the rotor flux linkage of the induction machine according to claim 6, wherein the discrete error epsilon expression of the discrete observer of the rotor flux linkage of the induction machine is as follows:

wherein phi is a state transition matrix of the discrete rear rotor flux linkage observer.

Technical Field

The invention belongs to the technical field of motor control.

Background

The induction motor is widely applied to a variable frequency speed control system due to the advantages of simple structure, strong durability, high reliability, low cost and the like. Flux linkage is the magnetic flux of a conductive coil or link of a current loop. Since the flux linkage can not be controlled in the high-precision control process of the induction motor, the acquisition of high-precision flux linkage information is a crucial part in the control of the induction motor.

In a practical digital driving system of the induction motor, a rotor flux linkage observation current model (continuous domain) in an alpha beta coordinate system of the induction motor is as follows:

in the formula (I), the compound is shown in the specification,andrespectively representing the observed values, omega, of the flux linkages of the alpha and beta axes of the rotor_rIndicating the motor speed, i_sαAnd i_sβRepresenting stator alpha and beta axis currents, lambda and L, respectively_mRespectively motor parameters.

Since the induction motor control signals are discrete, the flux linkage observer is discretized to approximately fit its continuous domain observed current model.

Specifically, the method comprises the following steps: the rotor flux linkage observation current model shown in formula (1) is written as follows:

wherein the content of the first and second substances,B＝λL_m，ω_ras angular speed of the rotor, L_mIs mutual inductance, R_rIs rotor resistance, L_rIs the rotor inductance.

Definition of T_sIs discrete step size, and let T be (k +1) T_sEquation (2) can be discretized according to the theorem of the nonhomogeneous matrix equation as:

in the formula (I), the compound is shown in the specification,andrespectively, the state transition matrix and the input matrix of the equation.

Solving equation (3) can obtain:

it is also possible to obtain:

multiplying both sides of the formula (5) byAnd then subtracting the formula (4) to obtain:

if the input signal is assumed to be constant during the iteration cycle, equation (6) can be equivalent to:

the precise discrete model of the rotor flux linkage current model is stable in the whole rotating speed range, but according to the formula (7), the matrix exponential function is required when the discrete model is discreteThe real-time operation and the large calculation amount cannot be applied to an actual digital control system.

In order to discretize a flux linkage observer in an actual digital control system, a discrete rotor flux linkage current model based on a forward euler method, a discrete rotor flux linkage current model based on a backward euler method, and a discrete rotor flux linkage current model based on a bilinear method are commonly used in the prior art.

1. Discrete rotor flux linkage current model based on forward euler method (most commonly adopted).

The forward Eulerian method has simple structure and easy programming realization, and is the most widely applied discretization method. First, assume that there is a first order ordinary differential equation:

dx/dt＝f(x,y) (1-1)

where f (x, y) is a function of x and y, a and b are real numbers and a ≦ x ≦ b. According to the forward Euler method, equation (1-1) can be discretized into:

x(k+1)≈x(k)+T_sf[x(k),y(k)] (1-2)

wherein k is 0,1,2.

According to the formula (3) and the formula (1-2), the flux linkage current model observer based on the forward euler method discretization can be obtained as follows:

as can be seen from the equations (1-3), the forward Euler method has small calculation amount and is easy to realize digitally, but has the problem that the discrete error increases with the increase of the rotating speed.

2. And (3) a discrete rotor flux linkage current model based on a backward Euler method.

According to the backward euler method, equation (1-1) can be discretized into:

x(k+1)≈x(k)+T_sf[x(k+1),y(k+1)] (2-1)

according to the formula (2) and the formula (2-1), a flux linkage current model observer based on the backward euler method discretization can be obtained as follows:

the complete form of formula (2-2) can be represented as:

wherein a is 1+ λ T_s，b＝ω_r(k)T_s，C＝λL_mT_s。

It can be seen that there is matrix inversion operation in the backward euler method-based discrete process, so the discrete method is accompanied by a large number of multiplication-division operations in each iteration period, which obviously increases the burden of the processor, and the physical significance of each coefficient is not clear, so that the actual debugging is difficult, and is not beneficial to the practical application.

3. A discrete rotor flux linkage current model based on a bilinear method.

According to the bilinear approach, equation (1-1) can be discretized into:

according to the formula (1) and the formula (3-1), the flux linkage current model observer based on bilinear discretization can be obtained as follows:

the complete form of formula (3-2) can be represented as:

in the formula

As can be seen from the above formula, the inverse operation of the matrix also exists in the discrete process based on the bilinear method, and the discrete process is more complex and more computationally intensive than the backward Euler method, so that the discrete process is also less practical.

In summary, when the prior magnetic linkage observer is discretized, the backward eulerian method and the bilinear method have huge calculation amount, which is not beneficial to practical application. The forward eulerian method has a small calculation amount and is easy to implement digitally, but the discretization error is large, so that the magnetic linkage observation precision is low.

Disclosure of Invention

The invention provides an observation method for a flux linkage of an induction motor rotor, aiming at solving the problem that the existing flux linkage observer has low flux linkage observation precision due to large discretization error when discretizing the flux linkage observer.

The method comprises the steps of collecting stator current of an induction motor, establishing a rotor flux observer, discretizing the rotor flux observer by using an improved Euler method, and obtaining an observed value of the discretized rotor flux observer, wherein the observed value is used for controlling the induction motor, and the improved Euler method is a discretization method combining a forward Euler method and a trapezoidal discretization method.

Further, the rotor flux linkage observer is a rotor flux linkage current model of the induction machine in an α β coordinate system.

Further, the differential expression of the rotor flux linkage observer is as follows:

wherein the content of the first and second substances,B＝λL_m，ω_ras angular speed of the rotor, L_mIs mutual inductance, R_rIs rotor resistance, L_rIs the rotor inductance, x is the flux linkage,as an observed value of flux linkage, i_sIs the stator current, t is the time.

Further, the expression of the rotor flux linkage observer in the α β coordinate system is:

wherein the content of the first and second substances,andalpha-axis component and beta-axis component, i, of rotor flux linkage observed value_sαAnd i_sβThe stator current alpha-axis component and the stator current beta-axis component, respectively.

Further, the discretizing the rotor flux linkage observer by using the modified euler method includes:

discretizing the rotor flux linkage observer by using a forward Euler method to obtain a primary discretization result:

wherein, T_sK is a discrete step size, k is 0,1,2, k (k) is kT_sTime magnetic linkage observed valueThe differential of (a) is determined,when K is 0, K (0) is 0;

and obtaining the discrete induction motor rotor flux linkage observer based on the primary discrete result.

Further, the obtaining a discrete flux linkage observer of the rotor of the induction machine based on the primary discrete result includes:

discretizing the primary discrete result again by using a trapezoidal discrete method to obtain the discrete induction motor rotor flux linkage observer:

wherein K (K +1) is (K +1) T_sTime magnetic linkage observed valueThe differential of (a) is determined,

further, the expression of the discrete induction machine rotor flux linkage observer in an α β coordinate system is as follows:

wherein the content of the first and second substances,andare each kT_sThe alpha-axis component and the beta-axis component of the rotor flux linkage observations at the time,andare respectively (k +1) T_sAlpha-axis component and beta-axis component, K, of the moment rotor flux linkage observed value_α(k) And K_β(k) Are each kT_sDifferential, K, of the alpha-axis component and the beta-axis component of the time rotor flux linkage observed value_α(k+1) And K_β(k +1) are (k +1) T respectively_sAnd the time rotor flux linkage observed value is the differential of the alpha axis component and the beta axis component.

Further, K is as defined above_α(k) And K_β(k) The specific expression of (a) is as follows:

wherein i_sα(k) And i_sβ(k) Are each kT_sThe time stator current alpha-axis component and beta-axis component, omega_r(k) Is kT_sThe rotor angular velocity is at that moment.

Further, K is as defined above_α(K +1) and K_βThe specific expression of (k +1) is as follows:

wherein i_sα(k +1) and i_sβ(k +1) are (k +1) T respectively_sThe time stator current alpha-axis component and beta-axis component, omega_r(k +1) is (k +1) T_sThe rotor angular velocity is at that moment.

Further, the discrete error of the discrete induction machine rotor flux linkage observer is obtained_εThe expression is as follows:

wherein phi is a state transition matrix of the discrete rear rotor flux linkage observer.

The invention has the beneficial effects that:

1. the discretization complexity is low, and the digitization is easy to realize;

2. the operation times in the iteration process are less, and the requirement on a processor is not high;

3. the discretization precision is very high, and almost no error exists in flux linkage observation in the full-speed range of the induction motor;

4. each physical meaning in the discretization equation is clear, and the debugging of the actual process is facilitated.

In summary, the observation method for the rotor flux linkage of the induction motor, provided by the invention, adopts the improved euler method to discretize the rotor flux linkage observer, and compared with the existing discretization method, the method has the advantages of simplicity in digital implementation and high discretization precision, and can obtain the balance between the discretization complexity and the discretization error, so that the discretization precision can be ensured, and the control precision of the induction motor can be further improved. The invention is suitable for the rotor flux linkage observation part in induction motor control so as to improve the flux linkage observation precision.

Drawings

FIG. 1 is a graph of the variation of the dispersion error of four discretization methods with the operation frequency of the motor;

FIG. 2 is a graph of a flux linkage observation result of an induction motor rotor based on a forward Euler method;

FIG. 3 is a graph of an observed flux linkage of an induction motor rotor based on the modified Euler method.

Detailed Description

In order to take the discrete error and the discrete complexity into consideration and further improve the control precision of the induction motor, the embodiment improves the discretization method of the rotor flux linkage observer, so that the observation of the rotor flux linkage of the induction motor is more accurate, and the embodiment is specifically as follows.

The first embodiment is as follows: in the method for observing the rotor flux linkage of the induction motor according to the present embodiment,

firstly, collecting stator current of an induction motor, and establishing a rotor flux linkage observer; and then, discretizing the rotor flux linkage observer by using an improved Euler method, and obtaining an observed value according to the discretized rotor flux linkage observer. The improved Euler method is a combined discretization method of a forward Euler method and a trapezoidal discretization method. The observed value is used for controlling the induction motor.

Under the condition that the motor is accelerated from 0 speed to 50Hz of rated rotating speed in a stepped mode, the magnetic linkage observation results of the induction motor rotor based on the forward Euler method and the improved Euler method are compared, and are shown in figures 2 and 3. It can be seen from both figures: the improved Euler discretization method can realize accurate observation of the rotor flux linkage in a full-speed range, and almost has no error. The rotor flux linkage error observed by the traditional forward Euler discretization method is increased along with the increase of the rotating speed, the maximum observation error exceeds 100 percent, and a motor control system cannot normally operate.

The method and the device can be used in the driving control of the AGV in the field of bullet train fault detection in practical application. Specifically, collecting stator current of an induction motor in an AGV, and establishing a rotor flux linkage observer; discretizing the rotor flux linkage observer by using an improved Euler method, and obtaining an accurate flux linkage observation value according to the discretized rotor flux linkage observer; and then, obtaining a flux linkage angle by using the flux linkage observation value, and accurately controlling the motor of the AGV by using the voltage and the current after coordinate transformation according to the coordinates of the voltage and the current of the transformed motor.

The second embodiment is as follows: in this embodiment, a rotor flux linkage observer is a rotor flux linkage current model of the induction machine in an α β coordinate system.

The third concrete implementation mode: in this embodiment, a differential expression of a rotor flux linkage observer is as follows:

wherein the content of the first and second substances,B＝λL_m，ω_ras angular speed of the rotor, L_mIs mutual inductance, R_rIs rotor resistance, L_rIs the rotor inductance, x is the flux linkage,as an observed value of flux linkage, i_sIs the stator current, t is the time.

The fourth concrete implementation mode: in this embodiment, the method for observing a rotor flux linkage of an induction motor according to the third embodiment is further described, and in this embodiment, an expression of a rotor flux linkage observer in an α β coordinate system is as follows:

wherein the content of the first and second substances,andalpha-axis component and beta-axis component, i, of rotor flux linkage observed value_sαAnd i_sβThe stator current alpha-axis component and the stator current beta-axis component, respectively.

The fifth concrete implementation mode: in this embodiment, the method for observing a rotor flux linkage of an induction motor according to the third embodiment further includes:

discretizing the rotor flux linkage observer by using a forward Euler method to obtain a primary discretization result:

wherein, T_sK is a discrete step size, k is 0,1,2, k (k) is kT_sTime magnetic linkage observed valueThe differential of (a) is determined,when K is 0, K (0) is 0;

and obtaining the discrete induction motor rotor flux linkage observer based on the primary discrete result.

The sixth specific implementation mode: in this embodiment, the method for observing a rotor flux linkage of an induction motor according to the fifth embodiment is further described, and the observer for obtaining a discrete rotor flux linkage of an induction motor based on a primary discrete result includes:

discretizing the primary discrete result again by using a trapezoidal discrete method to obtain the discrete induction motor rotor flux linkage observer:

wherein K (K +1) is (K +1) T_sTime magnetic linkage observed valueThe differential of (a) is determined,

the seventh embodiment: in this embodiment, an expression of the discrete rotor flux linkage observer for the induction machine in an α β coordinate system is as follows:

wherein the content of the first and second substances,andare each kT_sThe alpha-axis component and the beta-axis component of the rotor flux linkage observations at the time,andare respectively (k +1) T_sAlpha-axis component and beta-axis component, K, of the moment rotor flux linkage observed value_α(k) And K_β(k) Are each kT_sDifferential, K, of the alpha-axis component and the beta-axis component of the time rotor flux linkage observed value_α(K +1) and K_β(k +1) are (k +1) T respectively_sAnd the time rotor flux linkage observed value is the differential of the alpha axis component and the beta axis component.

The specific implementation mode is eight: in this embodiment, a method for observing a flux linkage of a rotor of an induction motor according to a seventh embodiment is further described_α(k) And K_β(k) The specific expression of (a) is as follows:

wherein i_sα(k) And i_sβ(k) Are each kT_sThe time stator current alpha-axis component and beta-axis component, omega_r(k) Is kT_sThe rotor angular velocity is at that moment.

The specific implementation method nine: this embodiment mode is further described with respect to a method for observing a rotor flux linkage of an induction motor according to the seventh or eighth embodiment modes, where K is_α(K +1) and K_βThe specific expression of (k +1) is as follows:

wherein i_sα(k +1) and i_sβ(k +1) are (k +1) T respectively_sThe time stator current alpha-axis component and beta-axis component, omega_r(k +1) is (k +1) T_sThe rotor angular velocity is at that moment.

The detailed implementation mode is ten: in this embodiment, a discrete error epsilon expression of the discrete observer of the rotor flux linkage of the induction motor is as follows:

wherein phi is a state transition matrix of the discrete rear rotor flux linkage observer.

The discrete steps are respectively 1/3000 seconds and 1/6000 seconds, and the running frequency of the motor is 0-200 Hz. The existing three discretization methods and the discretization method (modified euler method) in the embodiment have a graph of discretization error varying with the increase of the motor rotation speed, as shown in fig. 1, it can be seen:

the discretization errors of the four methods are increased along with the increase of the running frequency of the motor and the increase of the discretization step length. And when the dispersion step length is the same, the discretization errors of the bilinear method and the improved Eulerian method are obviously smaller than those of the forward Eulerian method and the backward Eulerian method. When the discretization step length is 1/3000 seconds and the motor running frequency is 200Hz, the discretization error of the forward Eulerian method and the backward Eulerian method reaches more than 7 percent; and the discretization error of the improved Eulerian method and the bilinear method is always kept within 2 percent. Therefore, the improved eulerian method in the embodiment effectively reduces the discrete error without increasing the discrete operation too much, balances the discrete error and the discrete complexity, and is suitable for the digital control system of the induction motor.