阅读说明：本技术 基于滑模观测器的永磁同步电机控制方法 (Permanent magnet synchronous motor control method based on sliding-mode observer ) 是由 宗剑 闫永辉 郭永馨 姜豪 李富雄 董建功 于 2021-01-27 设计创作，主要内容包括：本发明提供了一种基于滑模观测器的永磁同步电机控制方法,该方法包括：构建同步旋转坐标系下永磁同步电机的数学模型和滑模观测器；采用滑模观测器对电流进行估计,并定义滑模面函数,当系统进入滑动模态后,通过低通滤波器滤除反电动势中的高频信号,得到等价控制量；建立电动机三相定子绕组端电压方程,并根据同步旋转坐标变换原理,得到变换矩阵；将变换矩阵带入到三相定子电压方程中,得到包含有转子信息的反电动势方程；通过反电动势方程构建闭环PI调节器,并根据闭环PI调节器确定永磁同步电机的转子位置信息。从而避免了因反正切函数中存在抖阵,造成角度估计有较大误差的问题,可以减小滑模控制的抖阵,提高转子位置和转速的估算精度。(The invention provides a sliding-mode observer-based permanent magnet synchronous motor control method, which comprises the following steps: constructing a mathematical model and a sliding mode observer of the permanent magnet synchronous motor under a synchronous rotating coordinate system; estimating the current by adopting a sliding mode observer, defining a sliding mode surface function, and filtering a high-frequency signal in back electromotive force by a low-pass filter after a system enters a sliding mode to obtain equivalent control quantity; establishing a terminal voltage equation of a three-phase stator winding of the motor, and obtaining a transformation matrix according to a synchronous rotation coordinate transformation principle; the transformation matrix is brought into a three-phase stator voltage equation to obtain a back electromotive force equation containing rotor information; and constructing a closed-loop PI regulator through a back electromotive force equation, and determining the rotor position information of the permanent magnet synchronous motor according to the closed-loop PI regulator. Therefore, the problem that the angle estimation has larger error due to the existence of the dither matrix in the arc tangent function is solved, the dither matrix controlled by the sliding mode can be reduced, and the estimation precision of the position and the rotating speed of the rotor is improved.)

1. A permanent magnet synchronous motor control method based on a sliding-mode observer is characterized by comprising the following steps:

step 1: constructing a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system;

step 2: rewriting a dynamic system equation of the stator current according to a mathematical model of the permanent magnet synchronous motor under a d-q rotating coordinate system;

and step 3: determining a current error state equation according to the dynamic equation of the stator current, expressing the current error state equation by a vector form, and constructing a sliding mode observer;

and 4, step 4: estimating the current by adopting the sliding mode observer, defining a sliding mode surface function, and filtering a high-frequency signal in back electromotive force by a low-pass filter after the system enters a sliding mode to obtain equivalent control quantity;

and 5: replacing a sign function in an ideal sliding mode by a hyperbolic tangent function with smooth continuous characteristics;

step 6: estimating the position of a rotor through a phase-locked loop, establishing a voltage equation of a winding end of a three-phase stator of the motor, and obtaining a transformation matrix for transforming three-phase voltage to a d-q rotating coordinate system according to a synchronous rotating coordinate transformation principle;

and 7: the transformation matrix is brought into a three-phase stator voltage equation to obtain a back electromotive force equation containing rotor information;

and 8: and constructing a closed-loop PI regulator through a back electromotive force equation, and determining the rotor position information of the permanent magnet synchronous motor according to the closed-loop PI regulator.

2. The sliding-mode observer-based permanent magnet synchronous motor control method according to claim 1, wherein the mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system in the step 1 is as follows:

wherein: u. of_d、u_qThe direct-axis component and the quadrature-axis component of the stator voltage under a two-phase rotating coordinate system are respectively represented, R is the stator resistance, and L is the stator resistance_dIs a direct axis inductor, L_qIs a quadrature axis inductance, omega_eIs the electrical angular velocity, #_fIs a permanent magnet flux linkage i_dAnd i_qRespectively the direct and quadrature components of the stator current.

3. The sliding-mode observer-based permanent magnet synchronous motor control method according to claim 1, wherein the dynamic system equation of the stator current in the step 2 is as follows:

wherein: i.e. i_dAnd i_qRespectively the direct and quadrature components of the stator current, E_dAnd E_qDirect and quadrature components of back electromotive force, respectively, wherein E_d＝0，E_q＝ω_eψ_f，L_dIs a direct axis inductor, L_qIs a quadrature axis inductance, omega_eIs the electrical angular velocity, #_fIs a permanent magnet flux linkage u_d、u_qThe direct-axis component and the quadrature-axis component of the stator voltage under the two-phase rotating coordinate system are respectively, and R is the stator resistance.

4. The sliding-mode observer-based permanent magnet synchronous motor control method according to claim 1, wherein the sliding-mode observer equation in the step 3 is as follows:

wherein the content of the first and second substances,a current observation for the d-axis component of the stator current,is the observed value of the q-axis current component of the stator current, k is the sliding mode gain, V_d、V_qRespectively, induced electromotive force u in d-q rotating coordinate system_d、u_qThe direct-axis component and the quadrature-axis component of the stator voltage under a two-phase rotating coordinate system are respectively represented, R is the stator resistance, and L is the stator resistance_dIs a direct axis inductor, L_qIs a crossShaft inductance, ω_eAs electrical angular velocity, i_dAnd i_qRespectively the direct and quadrature components of the stator current.

5. The sliding-mode observer-based permanent magnet synchronous motor control method according to claim 4, wherein the current error state equation in the step 3 is as follows:

wherein current observation error For the current observation error of the d-axis component of the stator current,a current observation error for a stator current q-axis component;

the current error state equation is expressed in vector form as follows:

wherein the content of the first and second substances,as a function of the slip film surface,for current observation errors, current observation error vectorsInduced electromotive force vector V ═ V_d V_q]^TThe back electromotive force vector E ═ E_d E_q]^T；

The state matrix A, B is:

6. the sliding-mode observer-based permanent magnet synchronous motor control method according to claim 5, wherein the sliding-mode surface function in the step 4 is as follows:

wherein when it is satisfiedWhen the sliding mode observer enters a sliding mode, when the sliding mode gain is larger than a preset value,

when the system enters the sliding mode, the back electromotive force equation is as follows:

wherein the content of the first and second substances,d-axis current observed value and q-axis current observed value, i_d、i_qD-axis component and q-axis component of the stator current, respectively;

after the counter electromotive force is subjected to low-pass filtering, the obtained equivalent control quantity is as follows:

wherein, when the sliding mode can be reachedThen, an expression of the sliding mode gain k is calculated as follows:

wherein n is a normal number, and when n is 2, the synovial membrane reaching condition is satisfied

7. The sliding-mode observer-based permanent magnet synchronous motor control method according to claim 6, wherein the step 6 comprises:

when the phase-locked loop method is adopted to estimate the position of the rotor, the constructed three-phase stator voltage equation is as follows:

wherein u is the maximum amplitude of the stator terminal voltage of the motor, and u is_a、u_b、u_cThe stator voltages are respectively the components of the three-phase stationary coordinate system.

Transformation matrix for transforming three-phase stator voltage to d-q rotating coordinate system

Wherein the content of the first and second substances,using an estimated phase angle of the output of the phase-locked loop ofAnd is Is the rotor speed, whereinWherein V_qFor quadrature axis voltage,. psi_fIs a permanent magnet flux linkage.

8. The sliding-mode observer-based permanent magnet synchronous motor control method according to claim 7, wherein the step 7 comprises:

substituting the transformation matrix into the constructed three-phase stator voltage equation to obtain a back electromotive force equation containing the rotor position information, wherein the back electromotive force equation comprises the following steps:

wherein the condition V is satisfied_dref＝V_d＝0，To estimate the phase angle, θ_eIs the actual phase angle.

Technical Field

The invention relates to the technical field of motor control, in particular to a permanent magnet synchronous motor control method based on a sliding-mode observer.

Background

With the application of rare earth cobalt, neodymium iron boron and the like in the manufacture of permanent magnet materials, the permanent magnet synchronous motor obtains huge development space, and the permanent magnet synchronous motor is widely applied to the industrial fields of electric automobiles, aerospace, rail transit and the like due to the advantages of simple structure, high power density and the like.

In the vector control of the permanent magnet synchronous motor, a photoelectric encoder and other traditional mechanical sensors are often adopted for identifying the rotating speed. The installation of the mechanical sensor not only increases the volume of the motor, but also increases the manufacturing cost of the motor. Moreover, the mechanical sensor is easily affected by ambient temperature and vibration, is damaged, is not easy to maintain, and has poor reliability. Therefore, the speed-sensorless control method is adopted to replace the traditional mechanical sensor to realize the identification and estimation of the position and the rotating speed of the rotor, thereby not only improving the stability of the motor, but also reducing the manufacturing cost of the motor.

Currently, there are many speed sensorless control methods, which can be roughly classified into methods suitable for high speed and low speed, wherein the high frequency voltage injection method is suitable for the situation where the motor operates at low speed, and the position information of the rotor is estimated mainly by detecting the saliency of the motor.

However, the above method has limitations, and requires a motor having a certain saliency effect. When the motor runs at a high speed, a speed-sensor-free control method such as model reference self-adaption, Kalman filtering, a sliding-mode observer and the like can be adopted. The model reference self-adaptive control method is very dependent on motor parameters, and the robustness is poor. The Karl filtering method adopts minimum variance estimation, has large calculated amount and is not easy to realize.

Disclosure of Invention

Aiming at the defects in the prior art, the invention aims to provide a permanent magnet synchronous motor control method based on a sliding-mode observer.

According to the permanent magnet synchronous motor control method based on the sliding-mode observer, the technical scheme is as follows:

step 1: constructing a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system;

step 2: rewriting a dynamic system equation of the stator current according to a mathematical model of the permanent magnet synchronous motor under a d-q rotating coordinate system;

and step 3: determining a current error state equation according to the dynamic equation of the stator current, expressing the current error state equation by a vector form, and constructing a sliding mode observer;

and 4, step 4: estimating the current by adopting the sliding mode observer, defining a sliding mode surface function, and filtering a high-frequency signal in back electromotive force by a low-pass filter after the system enters a sliding mode to obtain equivalent control quantity;

and 5: replacing a sign function in an ideal sliding mode by a hyperbolic tangent function with smooth continuous characteristics;

step 6: estimating the position of a rotor through a phase-locked loop, establishing a voltage equation of a winding end of a three-phase stator of the motor, and obtaining a transformation matrix for transforming three-phase voltage to a d-q rotating coordinate system according to a synchronous rotating coordinate transformation principle;

and 7: the transformation matrix is brought into a three-phase stator voltage equation to obtain a back electromotive force equation containing rotor information;

and 8: and constructing a closed-loop PI regulator through a back electromotive force equation, and determining the rotor position information of the permanent magnet synchronous motor according to the closed-loop PI regulator.

Optionally, the mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system is as follows:

wherein: u. of_d、u_qAre respectively fixedThe direct-axis component and quadrature-axis component of the sub-voltage in a two-phase rotating coordinate system, R is stator resistance, and L is_dIs a direct axis inductor, L_qIs a quadrature axis inductance, omega_eIs the electrical angular velocity, #_fIs a permanent magnet flux linkage i_dAnd i_qRespectively the direct and quadrature components of the stator current.

Optionally, the dynamic system equation of the stator current is as follows:

wherein: i.e. i_dAnd i_qRespectively the direct and quadrature components of the stator current, E_dAnd E_qDirect and quadrature components of back electromotive force, respectively, wherein E_d＝0，E_q＝ω_eψ_f，L_dIs a direct axis inductor, L_qIs a quadrature axis inductance, omega_eIs the electrical angular velocity, #_fIs a permanent magnet flux linkage u_d、u_qThe direct-axis component and the quadrature-axis component of the stator voltage under the two-phase rotating coordinate system are respectively, and R is the stator resistance.

Optionally, the sliding-mode observer equation is as follows:

wherein the content of the first and second substances,a current observation for the d-axis component of the stator current,is the observed value of the q-axis current component of the stator current, k is the sliding mode gain, V_d、V_qRespectively, induced electromotive force u in d-q rotating coordinate system_d、u_qThe direct-axis component and the quadrature-axis component of the stator voltage under a two-phase rotating coordinate system are respectively represented, R is the stator resistance, and L is the stator resistance_dIs a direct axis inductor, L_qIs a quadrature axis inductance, omega_eAs electrical angular velocity, i_dAnd i_qRespectively the direct and quadrature components of the stator current.

Optionally, the current error state equation is as follows:

wherein current observation errorFor the current observation error of the d-axis component of the stator current,a current observation error for a stator current q-axis component;

wherein the current error state equation is expressed in a vector form as follows:

wherein the content of the first and second substances,as a function of the slip film surface,for current observation errors, current observation error vectorsInduced electromotive force vector V ═ V_d V_q]^TThe back electromotive force vector E ═ E_d E_q]^T；

Wherein the state matrix A, B is:

optionally, the sliding mode surface function is as follows:

wherein when it is satisfiedWhen the sliding mode observer enters a sliding mode, when the sliding mode gain is larger than a preset value,

when the system enters the sliding mode, the back electromotive force equation is as follows:

wherein the content of the first and second substances,d-axis current observed value and q-axis current observed value, i_d、i_qD-axis component and q-axis component of the stator current, respectively;

after the counter electromotive force is subjected to low-pass filtering, the obtained equivalent control quantity is as follows:

wherein, when the sliding mode can be reachedThen, an expression of the sliding mode gain k is calculated as follows:

wherein n is a normal number, and when n is 2, the synovial membrane reaching condition can be satisfied

Optionally, when the phase-locked loop method is used to estimate the rotor position, the three-phase stator voltage equation is constructed as follows:

wherein u is the maximum amplitude of the stator terminal voltage of the motor, and u is_a、u_b、u_cThe stator voltages are respectively the components of the three-phase stationary coordinate system.

Transformation matrix for transforming three-phase stator voltage to d-q rotating coordinate system

Wherein the estimated phase angle using the output of the phase locked loop isAnd isIs the rotor speed, whereinWherein V_qFor quadrature axis voltage,. psi_fIs a permanent magnet flux linkage.

Optionally, the transformation matrix is substituted into the constructed three-phase stator voltage equation, and the back electromotive force equation containing the rotor position information is obtained as follows:

wherein the condition V is satisfied_dref＝V_d＝0，To estimate the phase angle, θ_eIs the actual phase angle.

Compared with the prior art, the invention has the following beneficial effects:

the sliding-mode observer-based permanent magnet synchronous motor control method provided by the invention avoids the problem that the angle estimation has larger error due to the existence of a jitter matrix in an arc tangent function, can reduce the jitter matrix of sliding-mode control, and improves the estimation precision of the position and the rotating speed of a rotor.

Drawings

Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:

fig. 1 is a schematic diagram of a control principle of a sliding-mode observer-based permanent magnet synchronous motor according to an embodiment of the present invention;

fig. 2 is a control block diagram of a closed-loop PI regulator constructed by the phase-locked loop technology according to an embodiment of the present invention;

FIG. 3 is a schematic diagram illustrating a variation curve of an estimated value and an actual value of a rotation speed according to an embodiment of the present invention;

FIG. 4 is a schematic diagram illustrating a variation curve of an estimated value of a rotor position and an actual value according to an embodiment of the present invention;

fig. 5 is a schematic diagram of a variation curve of the induced electromotive force according to the embodiment of the present invention.

Detailed Description

The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.

Fig. 1 is a schematic diagram of a control principle of a sliding-mode observer-based permanent magnet synchronous motor according to an embodiment of the present invention, and as shown in fig. 1, i is adopted_dControl scheme 0, direct axis current i_dThe feedback value is subjected to PI regulation to obtain a given value of the direct-axis voltageThe deviation between the given rotating speed and the estimated rotating speed is regulated by PI to obtain the given value of the quadrature axis currentQuadrature axis current i with feedback_qThe deviation of the direct axis voltage is regulated by PI to obtain the given value of the direct axis voltageThe voltage under the two-phase static coordinate system is obtained by carrying out inverse Park conversion on the given value of the direct-axis voltage and the given value of the quadrature-axis voltageAndvoltage of alpha axisAnd beta axis voltageThe voltage space vector modulation SVPWM is input to the motor, and the motor is controlled by an inverter. Meanwhile, the three-phase stator current measured at the motor end is subjected to Clack transformation to obtain a current component i of an alpha-beta axis of a static coordinate system_αAnd i_βThen, obtaining a direct-axis current feedback value i through Park conversion_dAnd quadrature axis current feedback value i_qCurrent closed loop control is formed, and the three-phase stator voltage is measured from the motor end,obtaining a stator voltage component u under a rotating d-q coordinate through Clark transformation_dAnd u_qWhile feeding back the current to the value i_dAnd i_qAs input of the synovial membrane observer, a counter electromotive force observed value E is output_dAnd E_qInputting the estimated value into a phase-locked loop to obtain an estimated value of the rotor speedAnd rotor position estimate

The method comprises the following specific implementation steps:

firstly, a mathematical model of the permanent magnet synchronous motor under a synchronous rotation coordinate system needs to be constructed, and the mathematical model comprises the following steps:

in the formula u_d、u_qThe d-axis component and the q-axis component of the stator voltage under a two-phase rotating coordinate system are shown, R is the stator resistance, L is the voltage of the stator_dIs d-axis inductance, L_qIs a q-axis inductance, i_dIs a direct axis current, i_qIs quadrature axis current, omega_eIs the electrical angular velocity, #_fIs a permanent magnet flux linkage.

According to a mathematical model of the three-phase permanent magnet synchronous motor under a synchronous rotating coordinate system, a rewritten stator current equation is as follows:

wherein, d-axis counter electromotive force E_dQ-axis counter electromotive force E equal to 0_q＝ω_eψ_f。

In order to obtain the value of the induced electromotive force in the stator current equation, the sliding mode observer is designed as follows:

wherein the content of the first and second substances,as an observed value of the d-axis current,as observed for q-axis current, V_dInduced electromotive force, V, for d-axis_qAnd k is the sliding mode gain, and sgn is a sign function.

Subtracting the expression (2) from the expression (3) to obtain a state equation of the current error system as follows:

wherein the content of the first and second substances,for the d-axis current observation error,for q-axis current observation error, satisfyE_d、E_qRespectively corresponding to the back electromotive force under the d-q coordinate system.

The current error state equation is expressed in vector form:

wherein the current error observed valueInduced electromotive force V ═ V_d V_q]^TCounter electromotive force E ═ E_d E_q]^T。

The state matrices a and B are respectively:

estimating the current by using a slip form observer, and defining a slip form surface function as follows:

wherein when it is satisfiedWhen this happens, the system enters the sliding mode.

When the synovial gain is sufficiently large, the condition is satisfied:

substituting equation (6) into equation (8) yields a back electromotive force expression:

the counter electromotive force E comprises discontinuous high-frequency signals, and equivalent control quantity is obtained after low-pass filtering:

wherein, the sliding mode gain k can be determined by the reachable conditionAnd (6) obtaining. Namely:

fig. 2 is a control block diagram of a closed-loop PI regulator constructed by the phase-locked loop technology according to the embodiment of the present invention, and the specific design process includes:

firstly, a three-phase stator voltage equation needs to be constructed:

where u is the three-phase stator terminal voltage amplitude, let us say_e＝ω_et, electrical angular velocity ω_e＝πp_nn/30, wherein p_nThe number of the magnetic pole pairs of the motor is n, and the mechanical rotating speed of the motor is n.

And transforming the three-phase stator voltage to a transformation matrix under a synchronous rotating coordinate system as follows:

wherein the estimated phase angle output by the phase-locked loop technique isAnd estimating the phase angle

The phase angle error estimated by the phase locked loop is defined as:

current phase angle estimation errorThe estimated value of the rotor position will converge to the actual position of the rotor。

By substituting equation (13) into equation (12), an induced electromotive force equation can be obtained:

wherein, V_dInduced electromotive force of d-axis, V_qFor the induced electromotive force of the q axis, when the rotor position estimated by the phase-locked loop tracks the actual rotor position, that is, the phase angle error is zero, a closed-loop PI regulator can be constructed by the formula (15), so that the rotor position information is obtained.

Fig. 3 is a schematic diagram of a variation curve of the estimated value and the actual value of the rotating speed in the embodiment of the invention, as shown in fig. 3, it can be seen that the actual rotating speed and the estimated rotating speed of the motor are basically coincident, and the validity of the sliding mode observer is verified. The initial given rotating speed is 1200r/min, after the transient oscillation, the actual rotating speed of the motor reaches the given rotating speed, the good dynamic performance of the sliding mode observer is reflected, and the accuracy of the system is verified.

Fig. 4 is a schematic diagram of a variation curve of an estimated value of a rotor position and an actual value according to an embodiment of the present invention, as shown in fig. 4, it can be seen that the estimated rotor position substantially coincides with the actual rotor position, and the accuracy of the sliding mode observer is further verified.

FIG. 5 is a schematic diagram of a variation curve of the induced electromotive force according to the embodiment of the present invention, as shown in FIG. 5, it can be seen that V_dAnd V_qThe method can track the actual value of the induced electromotive force in real time, explains the position-sensor-free control method of the sliding mode observer under the synchronous rotating coordinate system, and can meet the actual control requirement of the motor.

The invention also provides a sliding-mode observer-based permanent magnet synchronous motor control system which is used for executing the sliding-mode observer-based permanent magnet synchronous motor control method.

It should be noted that, the steps in the sliding-mode observer-based permanent magnet synchronous motor control method provided by the present invention can be implemented by using corresponding modules, devices, units, etc. in the sliding-mode observer-based permanent magnet synchronous motor control system, and those skilled in the art can implement the step flow of the method with reference to the technical scheme of the system, that is, the embodiment in the system can be understood as a preferred example for implementing the method, and details are not described here.

Those skilled in the art will appreciate that, in addition to implementing the system and its various devices provided by the present invention in purely computer readable program code means, the method steps can be fully programmed to implement the same functions by implementing the system and its various devices in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system and various devices thereof provided by the present invention can be regarded as a hardware component, and the devices included in the system and various devices thereof for realizing various functions can also be regarded as structures in the hardware component; means for performing the functions may also be regarded as structures within both software modules and hardware components for performing the methods.

The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.