阅读说明：本技术 基于改进ladrc的异步电机电流内环解耦控制方法 (Asynchronous motor current inner ring decoupling control method based on improved LADRC ) 是由 周雪松 王成龙 马幼捷 吴博宁 刘茂 陶珑 于 2020-06-18 设计创作，主要内容包括：本发明公开基于改进LADRC的异步电机电流内环解耦控制方法,包括如下步骤：步骤S1、建立异步电机在ABC三相静止坐标系下的动态数学模型；步骤S2、将转子磁链定向,通过派克变换得到异步电机在d-q旋转坐标系下的动态数学模型；步骤S3、根据异步电机在d-q旋转坐标系下的动态数学模型,确定线性自抗扰控制器的阶数与控制器增益,并构建改进线性自抗扰控制器；步骤S4、对改进后的线性自抗扰控制器进行参数整定,通过改进的线性自抗扰控制器完成对异步电机的电流内环解耦控制。本发明能够有效降低励磁子系统与转矩子系统间的耦合关系,具有优异的鲁棒性和适应性,提高了电机的调速效果。(The invention discloses an improved LADRC-based asynchronous motor current inner ring decoupling control method, which comprises the following steps: step S1, establishing a dynamic mathematical model of the asynchronous motor under an ABC three-phase static coordinate system; s2, orienting the rotor flux linkage, and obtaining a dynamic mathematical model of the asynchronous motor under a d-q rotating coordinate system through park transformation; step S3, determining the order and the controller gain of the linear active disturbance rejection controller according to the dynamic mathematical model of the asynchronous motor under the d-q rotating coordinate system, and constructing an improved linear active disturbance rejection controller; and step S4, performing parameter setting on the improved linear active disturbance rejection controller, and completing current inner loop decoupling control on the asynchronous motor through the improved linear active disturbance rejection controller. The invention can effectively reduce the coupling relation between the excitation subsystem and the torque subsystem, has excellent robustness and adaptability, and improves the speed regulation effect of the motor.)

1. An improved LADRC-based asynchronous motor current inner ring decoupling control method is characterized by comprising the following steps:

step S1, establishing a dynamic mathematical model of the asynchronous motor under an ABC three-phase static coordinate system;

s2, orienting the rotor flux linkage, and obtaining a dynamic mathematical model of the asynchronous motor under a d-q rotating coordinate system through park transformation;

step S3, determining the order and the controller gain of the linear active disturbance rejection controller according to the dynamic mathematical model of the asynchronous motor under the d-q rotating coordinate system, and constructing an improved linear active disturbance rejection controller;

and step S4, performing parameter setting on the improved linear active disturbance rejection controller, and completing current inner loop decoupling control on the asynchronous motor through the improved linear active disturbance rejection controller.

2. The improved LADRC-based asynchronous motor current inner ring decoupling control method according to claim 1, wherein the flux linkage of the asynchronous motor rotor is downward, and a dynamic mathematical model of the asynchronous motor in a d-q rotating coordinate system is shown as formula 1:

in the formula i_sd、i_sqThe components of the stator current in the time domain, u, on the d and q axes, respectively_sd、u_sqThe components of the stator voltage in the time domain in the d and q axes, R_sIs stator resistance, L_s、L_rRespectively stator, rotor inductance, L_mIs the mutual inductance of the stator and the rotor, sigma is the magnetic leakage coefficient,

and performing Laplace transform on the formula 1 to obtain a frequency domain description of the current loop control object, as shown in a formula 2:

in the formula of U_sd、U_sqThe stator voltage in the complex frequency domain is respectively the d-axis component and the q-axis component, I_sd、I_sqThe stator current in the complex frequency domain has d and q axis components, s represents complex number, omega₁σL_sI_sq、ω₁σL_sI_sdThe current coupling terms between the d-axis lower torque excitation system and the q-axis lower torque excitation system and the current coupling terms between the q-axis lower torque excitation system and the excitation system are respectively.

3. The improved LADRC-based asynchronous motor current inner-loop decoupling control method according to claim 1, wherein the linear active disturbance rejection controller comprises a linear extended observer, a linear error feedback control law; the improved linear active disturbance rejection controller is obtained by modifying the linear extended observer.

4. The improved LADRC-based asynchronous motor current inner loop decoupling control method according to claim 3, characterized in that the improved linear extended observer is shown in equation 8:

where e is the system output estimation error, u is the controller output, x₁As system output, b₀In order to control the gain of the controller,

5. The improved LADRC based asynchronous motor current inner loop decoupling control method of claim 4, wherein said improved linear active disturbance rejection controller further comprises a linear tracking differentiator.

6. The improved LADRC-based decoupling control method for the current inner ring of the asynchronous motor according to claim 1, wherein a stator exciting current component regulator and a stator torque component regulator in a vector control structure of the asynchronous motor are replaced by improved linear active disturbance rejection controllers, so that decoupling control over the current inner ring of the asynchronous motor is realized.

Technical Field

The invention relates to the technical field of alternating current motor speed regulation, in particular to an improved LADRC-based asynchronous motor current inner ring decoupling control method.

Background

The asynchronous motor is widely applied to the industrial and agricultural fields due to the reasons of simple structure, low manufacturing cost, durability and the like. The vector control enables the asynchronous motor to have good speed regulation effect like a direct current motor. At present, the control modes of the asynchronous motor are mainly divided into two types, one type depends on an accurate mathematical model and is assisted by the traditional PI control, but the robustness and the adaptability of the controller are poor and sensitive to the change of system parameters. The motor is used as a complex system with high order, multivariable, nonlinearity and strong coupling, and modeling errors, parameter perturbation and coupling between systems exist, so that the control effect of the method is not ideal. The other type of controller does not depend on an accurate mathematical model, such as a controller combined with intelligent algorithms such as fuzzy control and artificial neural networks, and the like, the algorithms have good robustness and adaptability, but also have some problems, such as the design of the fuzzy controller has no systematic theoretical guidance, and the contradiction between control accuracy and instantaneity exists. The neural network algorithm needs a large amount of data for training, the quality of the data has great influence on the training result, and the data required by training is difficult to obtain in some occasions.

The linear active disturbance rejection controller LADRC is used as a second type of control mode, has good robustness and adaptability, and can well solve the problems of nonlinearity and uncertainty. The linear extended observer is used as a core in the linear active disturbance rejection controller, and the observation precision of the linear extended observer has great influence on the effect of the controller. The controller takes factors such as unknown disturbance, unmodeled parts, system parameter perturbation, coupling between the excitation subsystem and the torque subsystem and the like as total disturbance, and estimates and compensates the total disturbance of the system through the linear extended observer. The LADRC comprises a linear extended observer LESO and a linear error feedback control law LESF, the traditional LADRC adopts the traditional LESO, differential peak values exist in both high-order and low-order LESOs, overshoot cannot be reduced by adjusting the gain of the observer, meanwhile, the traditional LESO has contradiction in overshoot, noise suppression, response speed and observation precision, the performance of the traditional LEDRC is rapidly reduced along with the increase of disturbance frequency, and the high-order LESO has certain restriction on parameter setting, so that the coupling relation between an excitation subsystem and a torque subsystem cannot be effectively reduced, and the robustness and the engineering applicability are poor.

Disclosure of Invention

The invention aims to provide an improved LADRC-based asynchronous motor current inner ring decoupling control method, which is used for solving the problems in the prior art, effectively reducing the coupling relation between an excitation subsystem and a torque subsystem, has excellent robustness and adaptability and improves the speed regulation effect of a motor.

In order to achieve the purpose, the invention provides the following scheme: the invention provides an improved LADRC-based asynchronous motor current inner ring decoupling control method, which comprises the following steps:

step S1, establishing a dynamic mathematical model of the asynchronous motor under an ABC three-phase static coordinate system;

s2, orienting the rotor flux linkage, and obtaining a dynamic mathematical model of the asynchronous motor under a d-q rotating coordinate system through park transformation;

step S3, determining the order and the controller gain of the linear active disturbance rejection controller according to the dynamic mathematical model of the asynchronous motor under the d-q rotating coordinate system, and constructing an improved linear active disturbance rejection controller;

and step S4, performing parameter setting on the improved linear active disturbance rejection controller, and completing current inner loop decoupling control on the asynchronous motor through the improved linear active disturbance rejection controller.

Preferably, the flux linkage of the rotor of the asynchronous motor is downward, and a dynamic mathematical model of the asynchronous motor in a d-q rotating coordinate system is shown as formula 1:

in the formula i_sd、i_sqOf stator currents in d, q axes in the time domain, respectivelyComponent u_sd、u_sqThe components of the stator voltage in the time domain in the d and q axes, R_sIs stator resistance, L_s、L_rRespectively stator, rotor inductance, L_mIs the mutual inductance of the stator and the rotor, sigma is the magnetic leakage coefficient,ω₁for synchronizing the electrical angular velocity, #_rRepresenting the flux linkage of the rotor;

and performing Laplace transform on the formula 1 to obtain a frequency domain description of the current loop control object, as shown in a formula 2:

in the formula of U_sd、U_sqThe stator voltage in the complex frequency domain is respectively the d-axis component and the q-axis component, I_sd、I_sqThe stator current in the complex frequency domain has d and q axis components, s represents complex number, omega₁σL_sI_sq、ω₁σL_sI_sdThe current coupling terms between the d-axis lower torque excitation system and the q-axis lower torque excitation system and the current coupling terms between the q-axis lower torque excitation system and the excitation system are respectively.

Preferably, the linear active disturbance rejection controller comprises a linear extended observer and a linear error feedback control law; the improved linear active disturbance rejection controller is obtained by modifying the linear extended observer.

Preferably, the modified linear expansion observer is as shown in equation 8:

where e is the system output estimation error, u is the controller output, x₁As system output, b₀In order to control the gain of the controller,x₂for total disturbances of the system requiring compensation, z₁For outputting x to the system₁Carry out an estimation of z₂Is a pair systemTotal disturbance x₂Make an estimate, β₁、β₂The gain of the LESO.

Preferably, the improved linear active disturbance rejection controller further comprises a linear tracking differentiator.

Preferably, a stator exciting current component regulator and a stator torque component regulator in the vector control structure of the asynchronous motor are replaced by improved linear active disturbance rejection controllers, so that decoupling control of the current inner ring of the asynchronous motor is realized.

The invention discloses the following technical effects:

(1) according to the invention, the linear extended observer LESO in the linear active disturbance rejection controller is improved, so that the improved LESO has higher observation accuracy compared with the traditional LESO; unknown disturbance, unmodeled parts, system parameter perturbation and coupling factors between the excitation subsystem and the torque subsystem are regarded as total disturbance through the expanded state variables, and the total disturbance of the system is estimated and compensated through the LESO, so that the coupling between the excitation subsystem and the torque subsystem can be effectively reduced.

(2) The invention improves the linear active disturbance rejection controller and adds the linear tracking differentiator, effectively avoids the problem of noise amplification caused by differentiation and improves the precision of decoupling control on the current inner loop of the asynchronous motor.

(3) The improved linear active disturbance rejection controller is convenient for parameter setting, theoretical analysis and engineering application and has higher engineering application value.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.

FIG. 1 is a block diagram of the vector control of an asynchronous motor according to the present invention;

FIG. 2 is a coupling structure diagram of an asynchronous motor according to the present invention;

FIG. 3 is a frequency domain diagram of the first order LADRC improvement of the present invention;

FIG. 4 is a diagram of a modified LADRC structure incorporating LTD according to the present invention;

FIG. 5 is a comparison graph of simulation of rotation speed during no-load starting of the asynchronous motor in the embodiment of the present invention;

fig. 6 is a simulation comparison diagram of electromagnetic torque during no-load starting of the asynchronous motor in the embodiment of the invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.

Referring to fig. 1 to 6, the present embodiment provides an asynchronous motor current inner loop decoupling control method based on improved LADRC, including the following steps:

step S1, regarding the asynchronous motor as an ideal motor, and establishing a dynamic mathematical model of the asynchronous motor under an ABC three-phase static coordinate system;

the ideal motor is as follows:

1) three-phase windings of the asynchronous motor are symmetrically distributed, and magnetomotive force space is in sinusoidal distribution;

2) the magnetic circuit saturation of the asynchronous motor is not considered;

3) the surfaces of the stator and the rotor of the asynchronous motor are assumed to be smooth.

Step S2, orienting the rotor flux linkage, and obtaining a dynamic mathematical model of the asynchronous motor under a d-q rotating coordinate system through park transformation;

the asynchronous motor vector control block diagram is shown in FIG. 1; the vector control structure of the asynchronous motor comprises a rotation speed regulator ASR and a stator exciting current component regulator ACMR, stator torque component regulator ACTR, modified LADRC for ACMR, ACTR. k is a radical of_p、b₀Is a constant, wherein b₀The value of the space vector control is obtained through system parameter calculation, a superscript band represents given reference input, SVPWM represents space vector control, ABC and αβ represent an ABC three-phase static coordinate system and a αβ two-phase static coordinate system, DQ represents a two-phase synchronous rotating coordinate system, three alternating currents with the mutual difference of 120 degrees in the ABC three-phase static coordinate system are converted into two alternating currents with the mutual difference of 90 degrees in the αβ two-phase static coordinate system, and the two alternating currents are converted into two direct currents when the alternating currents are converted into the DQ two-phase synchronous rotating coordinate system.

After the rotor flux linkage is oriented, the rotor flux linkage is completely projected on a d-axis of a d-q coordinate system, and then psi exists_rd＝ψ_rWherein ψ_rdShowing the flux linkage of the rotor in the d-axis,. psi_rShowing the flux linkage of the rotor.

When the flux linkage of the rotor of the asynchronous motor is oriented, a stator voltage equation under a d-q coordinate system is shown as a formula (1):

in the formula i_sd、i_sqThe components of the stator current in the time domain, u, on the d and q axes, respectively_sd、u_sqThe components of the stator voltage in the time domain in the d and q axes, R_sIs stator resistance, L_s、L_rRespectively stator, rotor inductance, L_mIs the mutual inductance of the stator and the rotor, sigma is the magnetic leakage coefficient,

ω₁to synchronize the electrical angular velocity.

And (3) performing Laplace transform on the formula (1) to obtain a frequency domain description of the current loop control object, wherein the formula (2) is as follows:

in the formula of U_sd、U_sqAre respectively fixed in complex frequency domainComponent of sub-voltages in d and q axes, I_sd、I_sqThe stator current in the complex frequency domain has d and q axis components, s represents complex number, omega₁σL_sI_sq、ω₁σL_sI_sdThe current coupling terms between the d-axis lower torque subsystem and the q-axis lower torque subsystem and the excitation subsystem are respectively.

In the formula (1), the coupling relationship between the excitation subsystem and the torque subsystem is graphically represented as shown in fig. 2, so that the speed regulation effect of the asynchronous motor is reduced.

For simplicity of presentation, the torque subsystem and the field subsystem are collectively referred to as a system.

Step S3, determining the order and the controller gain of the linear active disturbance rejection controller according to the differential equation of the asynchronous motor in a d-q rotating coordinate system;

the linear active disturbance rejection controller LADRC comprises a linear extended observer LESO and a linear error feedback control law LESF; the LADRC is applied to a current inner ring of an asynchronous motor, namely a stator torque component controller and a stator excitation component controller realize decoupling control between subsystems.

As can be seen from equation (1), the controlled object system is a first-order system, and therefore, the first-order LADRC is constructed.

The construction of a conventional first-order LADRC includes:

the continuous state space after system expansion is described as formula (3):

where u is the controller output, x₁Is the output of the system, and is,

is to x₁Derivation, b₀In order to control the gain of the controller,

x₂in order to compensate for the total disturbance of the system,

is to x₂Derivative, w is x₂Y is the reference output of the system.

The construction of the LESO is shown in formula (4):

in the formula, β₁、β₂Gain of LESO, z₁For outputting x to the system₁(corresponds to i)_sd) Carry out an estimation of z₂Total disturbance x to the system₂(the unmodeled part of the system, the perturbation of the parameters and the coupling among subsystems) are estimated and further compensated, and e is the estimation error of the system output.

The construction of the feedback control law is shown in formula (5):

in the formula, k_pIs the controller gain.

β Pole assignment of LESO and controller parameters₁＝2ω₀，k_p＝ω_cWherein, LESO bandwidth ω₀Is 3-5 times of controller bandwidth omega_c. The gain b of the excitation subsystem controller and the torque subsystem controller₀Same, therefore, only the controller gain k needs to be adjusted_pWith LESO bandwidth omega₀Make an adjustment to β₁、β₂And k_pBecomes the bandwidth omega of the LESO₀And controller bandwidth ω_cAnd (4) adjusting.

The invention improves the construction of the LESO:

from formula (4):

and then finishing to obtain:

from the formula (7), z is₂And x₂Error betweenAs correction amount, for z₂The adjustment is carried out, and the convergence speed of the observer can be accelerated without increasing the gain of the observer obviously. Thus, an improvement is made to the conventional LESO, as shown in equation (8):

equations (5) and (8) form an improved linear active disturbance rejection controller of the system (1), and the structure thereof is shown in fig. 3.

To further demonstrate the stability of the improved LESO of the present invention, the observed error of the improved LESO of the present invention was compared to that of the conventional LESO.

The calculation process for improving the observation error of the LESO comprises the following steps:

let e₁＝z₁-x₁，e₂＝z₂-x₂The formula (3) and the formula (8) can obtain:

wherein e is₁Representing the internal state variable z of the LESO₁(i.e. x)₁Estimate of) and system output (i.e., i)_sd、i_sq) Error in the true value; e.g. of the type₂Representing the internal state variable z of the LESO₂(i.e., total disturbance x of the system)₂Estimated value of) and the total disturbance x of the system₂To the error between.

Let Y₁＝e₁，Y₂＝e₂-β₁e₁And obtaining an equation of an LESO error system, wherein the equation is shown as the formula (10):

wherein, Y₁、Y₂The method is only used for variable substitution and has no special meaning.

The characteristic equation of equation (7) is shown in equation (11):

λ²+(β₁+β₂)λ+β₁β₂＝0 (11)

wherein, λ is a coefficient for measuring the output response attenuation speed of the system, and is used for judging the stability of the system, when λ <0, the system is stable, and when λ >0, the system is unstable. Because the formula (10) is in the form of a time-domain differential equation, the stability of the system is difficult to judge by solving the equation, therefore, the stability of the system is judged by performing the Laplace transform on the formula (10) and converting the time domain into the frequency domain.

The essential condition for the second-order system stability known from the Goerweiz theorem is β₁+β₂、β₁β₂>0, because of ω₀、ω_cThe system is stable with > 0. Therefore, the zero solution (e) of the second order constant coefficient differential equation shown in equation (10)₁＝0，e₂0) is globally asymptotically stable.

When the disturbance w is considered, the system has a steady-state error. Stipulate | w | < w₀，w₀Const > 0. When the system reaches a steady state, the following can be obtained:

then, according to the formula (9), calculating the steady state error as shown in the formula (13):

the calculation process of the observation error of the conventional first-order LESO includes:

stability and error analysis were performed on the conventional first order LESO represented by formula (4). Let Y₁＝e₁，Y₂＝e₂-β₁e₁To obtain an equation of the ESO error system, as shown in equation (14):

the characteristic equation of equation (14) is shown in equation (15):

λ²+β₁λ+β₂＝0 (15)

the essential condition for the second-order system stability known from the Goerweiz theorem is β₁＞0、β₂Is greater than 0. Because of omega₀、ω_cThe system is stable with > 0. Therefore, the zero solution (e) of the second order constant coefficient differential equation shown in equation (14)₁＝0，e₂0) is globally asymptotically stable.

When disturbance w is considered, the system has steady-state error, and the absolute value of w is regulated to be less than or equal to w₀，w₀Const > 0. When the system reaches a steady state, the following can be obtained:

calculating the steady state error as shown in equation (17):

from this, it is understood that the improved LESO represented by the formula (8) can be obtained at the parameter β₁、β₂And the dynamic regulation performance and the steady-state observation error are better than those of the traditional LESO under the condition of a smaller selected value.

Comparing the formula (13) with the formula (17), it can be seen that the improved LESO has higher observation accuracy than the conventional LESO under the same observer bandwidth and controller bandwidth; unknown disturbance, unmodeled parts, system parameter perturbation and coupling factors between the excitation subsystem and the torque subsystem are regarded as total disturbance through the expanded state variables, and the total disturbance of the system is estimated and compensated through the LESO, so that the coupling between the excitation subsystem and the torque subsystem can be effectively reduced.

Improving LESO Presence

e＝z₁-y，

E, which results in noise mixing in the system output y, and to avoid the noise amplification problem caused by differentiation, a linear tracking differentiator LTD is added to the modified LADRC, as shown in fig. 4.

In FIG. 4, v is a given reference input, corresponding to FIG. 1y is the system output, corresponding to i in FIG. 1_sd、i_sqThe linear tracking differentiator LTD filters the system output y, filters noise mixed in the system output y, and avoids noise amplification caused by derivation of e in the LESO. y' is the low pass filtered output of system output y,

the differential signal of the system output y is output after band-pass filtering.

In the active disturbance rejection controller, a tracking differentiator is responsible for arranging a transition process of a target signal and generating a differentiated signal of the target signal. The transfer function of the reference signal differentiation is a band-pass filter, which can suppress noise well, so this process is implemented by using a linear tracking differentiator.

The second-order linear tracking differentiator LTD is shown as equation (20):

in the formula, x₁Tracking the input signal v, x for a reference signal₂Is a reference signal x₁Approximate differentiation of (d). For x₁In other words, the transfer function of the low-pass filter is a low-pass filter with better filtering effect than that of a first-order inertia element, and the low-pass filter plays a role in arranging a transition process. x is the number of₂The transfer function of (2) is a band-pass filter for low frequency sumsThe high-frequency noise has a good suppression effect and plays a role in extracting differential signals. And the fast tracking of the input signal is realized by adjusting the speed factor r. Where v corresponds to the system output y, x₁Corresponding to y', x in FIG. 4₂Corresponding to that in FIG. 4Therefore, the modified LESO of equation (8) is modified as shown in equation (21):

wherein the content of the first and second substances,

e＝z₁-y′。

and step S4, performing parameter setting on the improved linear active disturbance rejection controller, and completing current inner loop decoupling control on the asynchronous motor through the improved linear active disturbance rejection controller.

A stator exciting current component regulator and a stator torque component regulator in the vector control structure of the asynchronous motor are replaced by improved linear active disturbance rejection controllers, so that decoupling control of an inner current ring of the asynchronous motor is realized.

To further verify the effectiveness of the current inner loop decoupling control method for the improved lamac of the present invention, this embodiment compares the control effects of the conventional lamac and the improved lamac of the present invention:

the reference rotating speed of the asynchronous motor is 800r/min, the rotating speed simulation pair in the no-load starting process of the asynchronous motor is shown in figure 5, and the electromagnetic torque simulation pair in the no-load starting process of the asynchronous motor is shown in figure 6. As can be seen from fig. 5, the idle start time of the asynchronous motor with the improved LADRC control is significantly shorter than the conventional LADRC; as can be seen from fig. 6, the key of the speed regulation of the asynchronous motor is the control of the electromagnetic torque, and the improved lacrc has higher precision and can better realize the decoupling between the excitation subsystem and the torque subsystem, so that the electromagnetic torque can be better controlled, and the motor can reach a given rotating speed faster than that under the control of the conventional lacrc when being started in an idle state.

In the description of the present invention, it is to be understood that the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, are merely for convenience of description of the present invention, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention.

The above-described embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solutions of the present invention can be made by those skilled in the art without departing from the spirit of the present invention, and the technical solutions of the present invention are within the scope of the present invention defined by the claims.