CN116526912A - Super-rotating algorithm-based asynchronous motor rotor flux linkage observation method - Google Patents

Abstract

The invention relates to the technical field of motor control, in particular to a Super-rotating algorithm-based asynchronous motor rotor flux linkage observation method, which comprises a speed loop controller and a current loop controller design module; the pulse width modulation module is used for realizing inversion by controlling the on-off of six switching devices in the three-phase full-bridge circuit; the rotor flux linkage identification module is used for realizing rotor flux linkage closed-loop observation by utilizing a second-order synovial membrane observer. The scheme can solve the pure integral problem of the pure existence of the traditional voltage type flux linkage observer, and the special second-order synovial membrane observer is used, so that the advantages of the traditional synovial membrane are maintained, and only the information of a sliding mode surface s is needed. Meanwhile, shake of the system is restrained, the limit of relative orders is removed, the control precision of the system is improved, a speed sensor is not needed, and therefore cost is reduced.

Description

A Method for Observing the Flux Linkage of Asynchronous Motor Rotor Based on Super-twisting Algorithm

technical field

The invention relates to the technical field of motor control, in particular to a method for observing the flux linkage of an asynchronous motor rotor based on a Super-twisting algorithm.

Background technique

Asynchronous motors have become the most widely used motors in various industries and people's daily life because of their advantages such as simple structure, reliable operation, and convenient maintenance. With the development of power electronics technology and the innovation of motor control theory, the application of asynchronous motors has also developed from the original non-adjustable speed drive system to the current adjustable speed drive system. The speed control technology of asynchronous motor has changed from the early constant voltage frequency ratio control to the current trend of vector control as the main and direct torque control as the auxiliary.

The traditional method uses sensors to obtain the position of the rotor, high-precision sensors are expensive, and low-quality sensors will seriously affect the control performance. In addition, sensors require regular maintenance, and sensors in some applications even require diagnostic algorithms, making control complex. Therefore, in the sensorless technology of induction motors, rotor flux linkage is usually used as an intermediate variable to estimate the rotor speed, and the method of rotor field orientation is often used in vector control, so the identification of rotor flux linkage is very important for rotor field oriented control. Particularly important. The synovial film observer is widely used in the field of motor control because of its simple structure and strong robustness to motor parameter changes and external disturbances. Most of the existing synovial film observers are first-order observers, which have the problem of system chatter and low control precision.

Contents of the invention

The purpose of the present invention is to overcome the above-mentioned problems in the prior art, and provide a method for observing the flux linkage of an asynchronous motor rotor based on a Super-twisting algorithm. It is used to solve the chattering of the traditional system, remove the limitation of the relative order, and the technical problems of low control precision of the system.

Above-mentioned purpose is to realize through following technical scheme:

A method for observing the rotor flux linkage of an asynchronous motor based on the Super-twisting algorithm includes:

A controller design module, the controller design module includes a speed loop design and a current loop design, the speed loop adopts a pi controller, and the current loop adopts decoupling control;

A pulse width modulation module, the pulse width modulation module realizes inverter by controlling the on-off of six switching devices in the three-phase full-bridge circuit;

A rotor speed estimation module, the rotor speed estimation module adopts a model reference adaptive method, uses the voltage model as a reference model, uses the current model as an adjustable model, and uses the error of the reference model and the output of the adjustable model to form an automatic Adaptive law to realize the speed tracking reference model;

The rotor flux identification module adopts the Super-twisting synovial film algorithm, constructs the sliding mode surface through the known stator voltage and current information, and inputs the designed control rate into the observer model to obtain the rotor flux observation value.

Further, the described asynchronous motor rotor flux observation method based on the Super-twisting algorithm is characterized in that it adopts a second-order synovial film observer design, including:

Step (1) Obtain the fourth-order nonlinear differential equation of the squirrel-cage asynchronous motor under the two-phase stationary coordinate system according to the motor model;

Step (2) according to the fourth-order differential equation described in the step (1) with the current error as the sliding mode surface, design the sliding film observer;

In step (3), the designed synovial film control rate is brought into the observer model to obtain the rotor flux open-loop estimation expression based on the helical synovial film observer.

Further, the step (1) is specifically:

According to the motor model, the fourth-order nonlinear differential equation of the squirrel-cage asynchronous motor in the two-phase stationary coordinate system is obtained, and the first-order differential equation of the rotor speed is as follows:

Among them, R _s is the stator resistance, R _r is the rotor resistance; L _m is the mutual inductance; σ=1-L _m ² /L _s L _r is the flux leakage coefficient; ψ _ra and ψ _rβ are the α and β axes of the rotor flux linkage Component; i _sα , i _sβ are the α and β axis components of the stator current.

Further, the step (2) is specifically:

Taking the current error as the sliding mode surface, the following sliding film observer is designed:

Further, in the step (3), the control rate output by the synovial film observer is brought into the observer model to obtain the rotor flux open-loop estimation expression based on the helical synovial film observer:

In the formula, are the estimated values of the stator current and rotor flux linkage in the α and β components respectively, and i _sα , i _sβ , U _sα , and U _sβ are the known quantities of the system. The designed spiral synovium observer takes i _sα , i _sβ as input, /> is the feedback quantity, z ₁₁ , z ₁₂ , z ₂₁ , z ₂₂ are the control signals output by the observer.

Further, the error model can be obtained by subtracting the observation model from the original model of the motor:

Further, taking the α-axis component of the stator current and rotor flux linkage as an example, the sliding mode surface Choose the Lyapunov function:

in, The first derivative of V(x) with respect to time is: /> in:

if /> Then Ω ₁ >0, Ω ₂ >0, h _i >0, then: 4h ₂ h ₄ >(8h ₂ +9h ₁ ² )h ₃ ² . According to Lyapunov's theorem, the system must be uniformly asymptotically stable only if the above conditions are met.

Further, the pulse width modulation module realizes the inverter by controlling the on-off of the six switching devices in the three-phase full-bridge circuit, specifically: inputting the stator voltage reference value output by the voltage loop to the pulse width modulation module, passing through the space The vector pulse width modulation method controls the on-off of the six switching devices in the three-phase full-bridge circuit to realize the inverter, including:

Judging the sector according to the stator voltage on the d and q axis components;

Calculate the action time of the main vector and sub-vector of each sector;

Calculate the vector switching time for each sector.

Further, the rotor speed estimation module uses a model reference adaptive method to use the voltage model as a reference model, and the formula is as follows:

Further, a controller design module, the controller design module includes a speed loop design and a current loop design, the speed loop adopts a pi controller, and the current loop adopts conventional decoupling control;

Beneficial effect

The invention provides a method for observing the flux linkage of an asynchronous motor rotor based on a Super-twisting algorithm. Has the following advantages:

1. As a special second-order sliding film observer, it maintains the advantages of the traditional sliding film and only needs the information of the sliding surface s. At the same time, it suppresses the chattering of the system, removes the limitation of the relative order, and improves the control precision of the system.

2. It is essentially a nonlinear observer. For the asynchronous motor model with multiple variables, strong coupling, and nonlinear characteristics, the observation performance is better than that of a linear observer. The observer design does not fully depend on the motor model.

3. In view of the fact that the speed sensor increases the cost and complexity of the system and reduces the reliability of the system. For the problem of low recognition efficiency, the model reference adaptive technology is used to estimate the rotor speed, and the speed sensor is not required to reduce the cost.

Description of drawings

Fig. 1 is the system structural representation of a kind of asynchronous motor rotor flux observation method based on Super-twisting algorithm described in the present invention;

Fig. 2 is a block diagram of rotor flux open-loop estimation in a method for observing the rotor flux of an asynchronous motor based on the Super-twisting algorithm according to the present invention;

Fig. 3 is a block diagram of closed-loop estimation of rotor flux in a method for observing rotor flux of asynchronous motor based on Super-twisting algorithm according to the present invention

Fig. 4 is a response curve between the estimated value of the stator current α axis and the actual value in the asynchronous motor rotor flux observation method based on the Super-twisting algorithm according to the present invention;

Fig. 5 is a response curve between the estimated value of the stator current β-axis and the actual value in the asynchronous motor rotor flux observation method based on the Super-twisting algorithm according to the present invention;

Fig. 6 is a response curve between the estimated value of the rotor flux α axis and the actual value in a method for observing the rotor flux of an asynchronous motor based on the Super-twisting algorithm according to the present invention;

Fig. 7 is a response curve between the rotor flux β-axis estimated value and the actual value in the asynchronous motor rotor flux observation method based on the Super-twisting algorithm according to the present invention;

Fig. 8 is an error response curve between the estimated value of the rotor flux α axis and the actual value in a method for observing the rotor flux of an asynchronous motor based on the Super-twisting algorithm according to the present invention;

Fig. 9 is an error response curve between the estimated value of the rotor flux β axis and the actual value in a method for observing the rotor flux of an asynchronous motor based on the Super-twisting algorithm according to the present invention;

Detailed ways

The present invention will be described in further detail below according to the drawings and embodiments. The described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

As shown in Figure 1, a method for observing the rotor flux linkage of an asynchronous motor based on the Super-twisting algorithm mainly includes a controller design module, a pulse width modulation module, a rotor speed estimation module, and a rotor flux linkage identification module, among which:

The controller design module includes a speed loop design and a current loop design, the speed loop adopts a pi controller, and the current loop adopts decoupling control;

The pulse width modulation module realizes the inverter by controlling the on-off of six switching devices in the three-phase full-bridge circuit;

The rotor speed estimation module adopts a model reference adaptive method, takes the voltage model as a reference model, and uses the current model as an adjustable model, and uses the error of the output of the reference model and the adjustable model to form an adaptive law to realize the speed Track reference models;

The rotor flux identification module adopts the Super-twisting sliding film algorithm, constructs a sliding surface through the known stator voltage and current information, and inputs the designed control rate into the observer model to obtain the observed value of the rotor flux.

Among them, the asynchronous motor parameters are shown in Table 1:

Table 1 Asynchronous Motor Parameters

A method for observing the rotor flux of an asynchronous motor based on the Super-twisting algorithm described in this embodiment adopts a second-order synovial film observer design, including:

Step (1) Obtain the fourth-order nonlinear differential equation of the squirrel-cage asynchronous motor under the two-phase stationary coordinate system according to the motor model;

Step (2) according to the fourth-order differential equation described in the step (1) with the current error as the sliding mode surface, design the sliding film observer;

In step (3), the designed synovial film control rate is brought into the observer model to obtain the rotor flux open-loop estimation expression based on the helical synovial film observer.

Described step (1) is specifically:

Assumption 1: Spatial harmonics are ignored. Assuming that the three-phase windings are symmetrical, and the electrical angle is 120° in space, the generated magnetomotive force is distributed according to the sinusoidal law along the circumference of the air gap;

Assumption 2: Neglecting the saturation of the magnetic circuit, it is considered that the self-inductance and mutual inductance of each winding are constant;

Assumption 3: Neglect core loss;

According to the motor model, the fourth-order nonlinear differential equation of the squirrel-cage asynchronous motor in the two-phase stationary coordinate system is obtained, and the first-order differential equation of the rotor speed is as follows:

Among them, R _s is the stator resistance, R _r is the rotor resistance; L _m is the mutual inductance; σ=1-L _m ² /L _s L _r is the flux leakage coefficient; ψ _ra and ψ _rβ are the α and β axes of the rotor flux linkage Component; i _sα , i _sβ are the α and β axis components of the stator current.

Described step (2) is specifically:

Taking the current error as the sliding mode surface, the following sliding film observer is designed:

In the step (3), the control rate output by the synovial film observer is brought into the observer model to obtain the rotor flux open-loop estimation expression based on the helical synovial film observer:

In the formula, are the estimated values of the stator current and rotor flux linkage in the α and β components respectively, and i _sα , i _sβ , U _sα , and U _sβ are the known quantities of the system. The designed spiral synovium observer takes i _sα , i _sβ as input, /> is the feedback quantity, z ₁₁ , z ₁₂ , z ₂₁ , z ₂₂ are the control signals output by the observer.

Further, the error model can be obtained by subtracting the observation model from the original model of the motor:

Further, taking the α-axis component of the stator current and rotor flux linkage as an example, the sliding mode surface Choose the Lyapunov function:

in, The first derivative of V(x) with respect to time is: /> in:

if /> Then Ω ₁ >0, Ω ₂ >0, h _i >0, then: 4h ₂ h ₄ >(8h ₂ +9h ₁ ² )h ₃ ² . According to Lyapunov's theorem, the system must be uniformly asymptotically stable only if the above conditions are met.

The above-mentioned flux linkage observation model has strong robustness, but it is an open-loop structure in essence, and the solution to the rotor flux linkage includes a pure integral link, and there are integral drift and initial value error. In addition, the sliding film control rate contains an estimate of the rotor flux linkage, which increases the uncertainty range of the model and increases the observation burden of the observer. A large control gain is often required to ensure rapid convergence and meet the control accuracy.

Aiming at the insufficiency of the open-loop estimation of rotor flux linkage based on the helical synovium observer, a model-compensated helical synovial observer is proposed. By bringing the rotor flux value observed by the spiral synovial film observer into the first-order differential equation of the estimated value of the stator current as the feedback value, the scope of the observed value is reduced, the observation accuracy and convergence speed are improved, and the original open-loop structure is also changed. For magnetic chain closure. Then the structure of the observer under the flux linkage closed loop becomes:

Therefore, the closed-loop estimation expression of rotor flux linkage based on the helical synovium observer can be obtained:

The pulse width modulation module described in this embodiment implements the inverter by controlling the on-off of the six switching devices in the three-phase full-bridge circuit, specifically: the stator voltage reference value output by the voltage loop is input to the pulse width modulation module, through The space vector pulse width modulation method controls the on-off of the six switching devices in the three-phase full-bridge circuit to realize the inverter, including:

Judging the sector according to the stator voltage on the d and q axis components;

Calculate the action time of the main vector and sub-vector of each sector;

Calculate the vector switching time for each sector.

The rotor speed estimation module described in this embodiment adopts the model reference adaptive method and uses the voltage model as a reference model, and the formula is as follows:

The current model is used as an adjustable model, and the two models have the same output rotor flux linkage. Using the output error of the two models, an appropriate adaptive law is formed to adjust the parameters of the adjustable model in real time, so as to achieve the output tracking reference of the control object purpose of the model.

In order to verify the effectiveness of the controller, in MATLAB (MATLAB is a commercial mathematical software produced by MathWorks in the United States, it is used for data analysis, wireless communication, deep learning, image processing and computer vision, signal processing, quantitative finance and risk management, robots, Control system and other fields.) Establish the simulation model of asynchronous motor vector control.

It is found through experiments that under the same data conditions:

Figures 8-9 show that the rotor flux linkage observed by the proposed rotor flux linkage algorithm is within 0.15wb of the true value.

It can be seen that the present invention can improve the control precision of the asynchronous motor under vector control, and realize accurate orientation of the rotor magnetic field.

The above description is only to illustrate the implementation of the present invention, and is not intended to limit the present invention. For those skilled in the art, any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.

Claims (10)

1. The method for observing the flux linkage of the rotor of the asynchronous motor based on the Super-rotating algorithm is characterized by comprising the following steps of:

the controller design module comprises a rotating speed ring design and a current ring design, wherein the rotating speed ring adopts a pi controller, and the current ring adopts decoupling control;

the pulse width modulation module is used for realizing inversion by controlling the on-off of six switching devices in the three-phase full-bridge circuit;

the rotor rotating speed estimation module adopts a model reference self-adaption method to take a voltage model as a reference model, takes a current model as an adjustable model, and forms a self-adaption law by utilizing errors of output quantities of the reference model and the adjustable model so as to realize a rotating speed tracking reference model;

and the rotor flux linkage identification module adopts a Super-rotating sliding film algorithm, a sliding die surface is constructed through known stator voltage and current information, and a design control rate is input into an observer model to obtain a rotor flux linkage observation value.

2. The method for observing the flux linkage of the rotor of the asynchronous motor based on the Super-rotating algorithm as claimed in claim 1, wherein the method for observing the flux linkage of the rotor of the asynchronous motor adopts a second-order synovial membrane observer design and comprises the following steps:

step (1) obtaining a fourth-order nonlinear differential equation of the squirrel-cage asynchronous motor under a two-phase static coordinate system according to a motor model;

step (2), designing a synovial membrane observer by taking the current error as a sliding mode surface according to the fourth-order differential equation in the step (1);

and (3) bringing the designed synovial membrane control rate into an observer model to obtain a rotor flux open-loop estimation expression based on the spiral synovial membrane observer.

3. The method for observing the flux linkage of the rotor of the asynchronous motor based on the Super-rotating algorithm according to claim 2, wherein the step (1) is specifically as follows:

and obtaining a fourth-order nonlinear differential equation rotor rotating speed first-order differential equation of the squirrel-cage asynchronous motor under a two-phase static coordinate system according to a motor model, wherein the first-order differential equation comprises the following formula:

wherein R is _s Represents the stator resistance, R _r Is rotor resistance; l (L) _m Is mutual inductance; sigma=1-L _m ² /L _s L _r Is a magnetic leakage systemA number; psi phi type _ra 、ψ _rβ Is the alpha, beta axis component of the rotor flux linkage; i.e _sα ,i _sβ Is the alpha, beta axis component of the stator current.

4. The method for observing the flux linkage of the rotor of the asynchronous motor based on the Super-rotating algorithm according to claim 3, wherein the step (2) is specifically as follows:

taking the current error as a sliding mode surface, designing the following sliding film observer:

5. the Super-rotating algorithm-based asynchronous motor rotor flux linkage observation method according to claim 4, wherein the control rate output by the synovial observer is brought into an observer model to obtain a rotor flux linkage open-loop estimation expression based on the spiral synovial observer:

in the method, in the process of the invention,estimated values of stator current and rotor flux linkage in alpha and beta components, i _sα ,i _sβ ,U _sα ,U _sβ Is a known quantity for the system. Spiral synovial observer is designed to be i _sα ,i _sβ For input quantity, < >>As feedback quantity, z ₁₁ ,z ₁₂ ,z ₂₁ ,z ₂₂ Is a control signal output by the observer.

6. The method for observing the flux linkage of the rotor of the asynchronous motor based on the Super-rotating algorithm according to any one of claims 4 and 5, wherein an error model can be obtained by subtracting an observation model from an original model of the motor:

7. the method for observing rotor flux linkage of asynchronous motor based on Super-rotating algorithm as defined in claim 6, wherein the slip form surface is formed by taking the component of stator current and rotor flux linkage in alpha axis as an example Selecting Lyapunov function:

wherein,,

the first derivative of V (x) with respect to time is:wherein:

if->Omega. Then ₁ ＞0,Ω ₂ ＞0,h _i > 0, then there is: 4h ₂ h ₄ ＞(8h ₂ +9h ₁ ² )h ₃ ² . According to Lyapunov theorem, only systems meeting the above conditions need to be consistently progressive stable.

8. The method for observing the flux linkage of the rotor of the asynchronous motor based on the Super-rotating algorithm according to claim 1, wherein the pulse width modulation module realizes inversion by controlling the on-off of six switching devices in a three-phase full-bridge circuit, specifically comprises the following steps: the stator voltage reference value output by the voltage loop is input to a pulse width modulation module, and the on-off of six switching devices in a three-phase full-bridge circuit is controlled to realize inversion by a space vector pulse width modulation method, and the method comprises the following steps:

judging the sector according to the components of the stator voltage on d and q axes;

calculating the action time of the main vector and the auxiliary vector of each sector;

each sector vector switching time is calculated.

9. The method for observing the flux linkage of the asynchronous motor rotor based on the Super-rotating algorithm according to claim 1, wherein the rotor rotating speed estimation module adopts a model reference adaptive method to take a voltage model as a reference model, and the formula is as follows:

10. the method for observing the flux linkage of the rotor of the asynchronous motor based on the Super-rotating algorithm according to claim 1, wherein the controller design module comprises a rotating speed ring design and a current ring design, the rotating speed ring adopts a pi controller, and the current ring adopts conventional decoupling control.