CN114598206A - Design Method of Rotor Position Observer in Wide Speed Range of Permanent Magnet Synchronous Motor - Google Patents

Abstract

The invention relates to the field of sensorless control of a permanent magnet synchronous motor, in particular to a design method for a rotor position observer in a wide speed range of a permanent magnet synchronous motor, comprising: transforming a three-phase permanent magnet synchronous motor into a Park-transformed two-phase stationary coordinate system The voltage and estimated back EMF are used as the input variables of the control system to establish the current model of the permanent magnet synchronous motor; the Gaussian error function is used instead of the sign function to establish the sliding mode observer of the permanent magnet synchronous motor. The specific harmonics of the back EMF observed by the observer are filtered, and the estimated rotor speed and estimated rotor position are calculated by the normalized phase-locked loop; the multi-proportional resonance controller is used to effectively suppress the back EMF harmonics; through the continuous Gaussian error function It effectively suppresses the system chattering problem and improves the estimation accuracy of the motor speed and rotor position in the full speed range.

Description

Design Method of Rotor Position Observer in Wide Speed Range of Permanent Magnet Synchronous Motor

technical field

The invention relates to the field of sensorless control of a permanent magnet synchronous motor, in particular to a design method for a rotor position observer in a wide speed range of a permanent magnet synchronous motor.

Background technique

In the control system of the permanent magnet synchronous motor, the position and speed detection of the rotor is indispensable. Generally, the position and speed are measured by installing a mechanical sensor, but the installation of the mechanical sensor will bring great disadvantages. Even in some special environments, the installation of mechanical sensors is not supported. Therefore, by detecting some electrical signals (such as current and voltage) of the permanent magnet synchronous motor and through appropriate signal processing, the information such as the position and speed of the rotor can be estimated. The closed-loop control system technology formed by this method is called permanent magnet synchronous motor. Magnetic synchronous motor without position sensor technology.

Sensorless control techniques can be divided into two categories: (1) methods based on back EMF or flux linkage (2) methods based on saliency. The first category is PMSM-based model methods, such as: Sliding Mode Observer Method (SMO), Model Reference Adaptive Method (MRAS), Kalman Filter (EKF), and so on. The second type of method is to inject high-frequency signals into the stator windings, and obtain the rotor position information (rotor electrical angle and rotor electrical angular velocity) from the output current. This method is suitable for starting the motor when it is stationary and running at low speed. For example, rotating high frequency injection method, pulse vibration high frequency voltage injection method and high frequency square wave injection method.

Due to its simple algorithm, robustness to disturbance and good dynamic performance, the SMO method has been widely used in the sensorless driver of PMSM. Sliding mode observer is a special nonlinear control system. It is an observer that estimates rotor position information based on the back EMF of the reconstructed motor. It has strong robustness and is insensitive to parameter changes and external disturbances. But precisely because of this discontinuous control, the sliding mode observer has a large high frequency jitter, especially in the estimated back EMF, so the suppression of sliding mode chattering is the main problem, and with the development of electric vehicles , Permanent magnet synchronous motor without position sensor control strategy has broad prospects for development.

SUMMARY OF THE INVENTION

The present invention aims to solve the above problems, thereby providing a method for designing a wide-speed-range rotor position observer of a permanent magnet synchronous motor capable of improving system control accuracy and reducing rotor electrical angle and electrical angular velocity calculation errors.

The invention solves the problem, and the technical solution adopted is:

A method for designing a rotor position observer in a wide speed range of a permanent magnet synchronous motor, comprising the following steps:

S1: Taking the three-phase permanent magnet synchronous motor as the control object, the mathematical model of the permanent magnet synchronous motor in the two-phase static coordinate system is,

Among them, u _α and u _β are the stator voltage components in the two-phase stationary coordinate system, e _α and e _β are the back electromotive force in the two-phase stationary coordinate system, respectively, and i _α and i _β are the stator under the two-phase stationary coordinate system. Current component, R is the equivalent resistance on the stator winding, L is the equivalent inductance on the stator winding, ω _e is the rotor electrical angular velocity, θ _e is the rotor electrical angle, ψ is the rotor permanent magnet flux linkage;

The current and voltage components of the three-phase stationary coordinate system a-b-c and the two-phase stationary coordinate system α-β satisfy the following relationship:

The current components of the two-phase stationary coordinate system α-β and the two-phase rotating coordinate system d-q can be transformed into each other through Park transformation and inverse Park transformation. Park transformation,

Inverse Park Transform,

Among them, i _a , i _b i _c , and _{u a} , _ub , and uc represent three-phase current and three-phase voltage values, respectively, and _id and i _q represent current components in a two-phase rotating coordinate system, respectively.

S2: The Gaussian error function used in the sliding mode control function is defined as,

The sliding mode observer is a special nonlinear control system. It is an observer that estimates the rotor position information based on the back electromotive force of the reconstructed motor. The selection of the mode gain, the sliding mode surface model sn _is designed as follows in the present invention,

The sliding mode control function is

和

是两相静止坐标系下的估计定子电流分量；in,

and

is the estimated stator current component in the two-phase stationary coordinate system;

S3: The voltage of the three-phase permanent magnet synchronous motor in the two-phase stationary coordinate system after Park transformation and the estimated back electromotive force are used as the input variables of the control system, and the sliding mode observer (SMO) model of the permanent magnet synchronous motor is established.

where k is the switching gain of the observer, k>{|e _α |,|e _β |}; when the sliding mode reaches the sliding mode surface, z _α and z _β are equivalent to the estimated back EMF of the α-axis and β-axis ;

S4: Since the characteristics of the inverter will show nonlinear changes, in addition, the influence of the permanent magnet material and the permanent magnet synchronous motor topology will also increase the back EMF harmonics; it will lead to the existence of 6K±1 times in the back EMF estimation result. harmonics, which can cause distortion of the stator current, and non-sinusoidal back EMF can cause fluctuation errors in the estimated rotor electrical angle and estimated rotor electrical angular velocity.

The proportional resonance controller can realize the tracking of the AC signal without static error. Since the gain of the proportional resonance controller at the resonance point is infinite, and the gain outside the resonance point is very small, it can achieve the effect of suppressing harmonics. Therefore, in the formula ( 9) on the basis of the PMSM back-EMF multi-proportional resonant filter is established to perform specific harmonic filtering on the estimated back-EMF;

The ideal proportional resonant controller (PR) transfer function is,

Among them: K _P is the proportional gain, K _R is the resonance gain, ω _f is the resonance angular frequency, and the gain of the ideal proportional resonance controller is infinite at the resonance frequency;

Because the bandwidth of the ideal PR controller is narrow and the frequency response gain is infinite, the system will be very sensitive to the change of parameters, so the ideal proportional resonance controller is difficult to realize in practical control;

Therefore, the present invention adopts the quasi-proportional resonant controller to filter the estimated back electromotive force to widen the filtering bandwidth. The transfer function of the multi-proportional resonant filter is:

where ω _c is the system cut-off angular frequency;

Since there are 6K±1 harmonics in the back EMF, the present invention uses multiple quasi-proportional resonant controllers in parallel to filter out specific harmonics for the estimated back EMF. The multi-proportional resonant filter model adopted in the present invention is:

Among them, K _P is the proportional gain, ω _c is the cut-off angular frequency of the system, h is the specific frequency harmonic, K _rh is the resonance gain of the h harmonic, and s represents the complex number, that is, the complex frequency domain;

并反馈到永磁同步电机滑模观测器输入端，形成闭环控制；The estimated back electromotive force z _{α and z β obtained by the permanent magnet synchronous motor sliding mode observer, and the fifth and seventh harmonics of the estimated back electromotive force z α and z β are extracted} through the multi-proportional resonant filter. back EMF of

And feed back to the input end of the permanent magnet synchronous motor sliding mode observer to form a closed-loop control;

S5: When the motor runs at low speed, the signal-to-noise ratio of the back EMF is low, which will increase the speed estimation error, which is not conducive to high-precision control. Therefore, the amplification factor H is introduced into the formula (9), and H is the back EMF filtered by the multi-proportional resonance controller. Since the filtered back EMF is closer to the fundamental wave, the accuracy of the estimated value will be improved, and the introduction of H makes the estimated back EMF expanded. When the motor is running at low speed, the system can still accurately extract the rotor position information. The sliding mode observer (SMO) model of the synchronous motor is,

为经过多比例谐振滤波器滤波后的估计反电动势，H为放大因子；in,

is the estimated back EMF filtered by the multi-proportional resonant filter, and H is the amplification factor;

作为归一化锁相环的输入变量，通过归一化锁相环计算出转子电角度和转子电角速度，同时将估计转子电角速度作为多比例谐振滤波器的谐振频率，从而实现频率自适应控制；则估计转子电角速度和估计转子电角度的计算模型如下：S6: The filtered estimated back EMF

As the input variables of the normalized phase-locked loop, the rotor electrical angle and rotor electrical angular velocity are calculated through the normalized phase-locked loop, and the estimated rotor electrical angular velocity is used as the resonant frequency of the multi-proportional resonant filter, so as to realize the frequency adaptive control ; then the calculation model for estimating the rotor electrical angular velocity and estimating the rotor electrical angle is as follows:

是估计转子电角速度，

是估计转子电角度。Among them, k _i is the integral gain, k _p is the proportional gain,

is the estimated rotor electrical angular velocity,

is the estimated rotor electrical angle.

The present invention that adopts the above-mentioned technical scheme, compared with the prior art, its outstanding feature is:

The invention provides a method for observing a rotor position in a wide speed domain of a permanent magnet synchronous motor, which belongs to the technical field of sensorless control of a permanent magnet synchronous motor; the invention uses a Gaussian error function (erf) instead of a sign function (sign) in the sliding mode control function At the same time, the multi-proportional resonant filter (MPR) is used to filter the specific harmonics in the back EMF observed by the new permanent magnet synchronous motor sliding mode observer (SMO), and remove the traditional The low-pass filter in the sliding mode observer of the permanent magnet synchronous motor; the amplification factor is introduced to expand the filtered back EMF, so that the sliding mode observer can accurately calculate the rotor position even when the motor is running at low speed, and improve the low speed operation of the motor. lower rotor position (rotor electrical angle) and rotor speed (rotor electrical angular velocity) estimation accuracy; using this method improves the rotor speed and rotor position estimation data accuracy of the permanent magnet synchronous motor in the full speed range, and comprehensively improves the motor control accuracy, A method is provided for sensorless control of permanent magnet synchronous motor.

Description of drawings

Figure 1 is an image of the Gaussian error function and the sign function;

Fig. 2 is the overall control block diagram of the permanent magnet synchronous motor control system in the present invention;

3 is a structural block diagram of a permanent magnet synchronous motor sliding mode observer and a multi-proportional resonant filter in an embodiment of the present invention;

4 is a structural block diagram of a normalized phase-locked loop implemented in the present invention;

Figure 5 is a block diagram of a proportional resonance structure;

6 is a structural block diagram of a multi-ratio resonant filter in the implementation of the present invention;

Fig. 7-(a) is the error waveform of the estimated rotor electrical angular velocity and the actual rotor electrical angular velocity under the steady state of the permanent magnet synchronous motor sliding mode observer according to the embodiment of the present invention;

Fig. 7-(b) is the error waveform of the estimated rotor electrical angle and the actual rotor electrical angle under the steady state of the sliding mode observer of the permanent magnet synchronous motor according to the embodiment of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the embodiments, the purpose is only to better understand the content of the present invention, therefore, the examples do not limit the protection scope of the present invention.

As shown in Figures 1 to 7, the parameters of the three-phase permanent magnet synchronous motor in this embodiment are as follows:

进行控制，如图2，本实施例采用的永磁同步电机控制系统主要包括：d轴电流PI调节器、q轴电流PI调节器、转速PI调节器、基于多比例谐振滑模控制器(永磁同步电机滑模观测器和多比例谐振滤波器)、归一化锁相环、Clark变换模块、Park变换模块、反Park变换模块、空间矢量脉宽调制模块，三相逆变器、三相永磁同步电机。In this embodiment, the permanent magnet synchronous motor control strategy adopts the initial value of the d-axis reference current component

For control, as shown in Figure 2, the permanent magnet synchronous motor control system adopted in this embodiment mainly includes: a d-axis current PI regulator, a q-axis current PI regulator, a rotational speed PI regulator, a multi-proportional resonance sliding mode controller (permanent Magnetic synchronous motor sliding mode observer and multi-proportional resonant filter), normalized phase-locked loop, Clark transformation module, Park transformation module, inverse Park transformation module, space vector pulse width modulation module, three-phase inverter, three-phase Permanent magnet synchronous motor.

First, given the reference electrical angular velocity ω _ref , input the difference between the reference electrical angular velocity and the estimated rotor electrical angular velocity value into the rotational speed PI regulator, and output the reference current of the q-axis of the motor

与q轴实际电流i_q的差值输入q轴电流PI调节器，将d轴参考电流

与d轴实际电流i_d的差值输入d轴电流PI调节器，得到两相旋转坐标系下的定子电压分量u_q，u_d；The q-axis reference current

The difference from the actual current i _q of the q-axis is input to the q-axis current PI regulator, and the reference current of the d-axis is

The difference with the actual current id of the _d -axis is input to the d-axis current PI regulator, and the stator voltage components u _q and _ud under the two-phase rotating coordinate system are obtained;

Input u _q and _ud into the inverse Park transform module, and output the stator voltage components u _α and u _β in the two-phase stationary coordinate system;

Input u _α and u _β to the space vector pulse width modulation module, and output six PWM with dead zone;

Input six PWM channels with dead zone into the three-phase inverter to output three-phase voltage;

Input the three-phase voltage into the three-phase permanent magnet synchronous motor, and collect the three-phase currents _ia , _ib and _ic of the three-phase permanent magnet synchronous motor at the same time;

Input i _a , i _b , _ic into the Clark transform module, and output the stator current components i _α , i _β in the two-phase stationary coordinate system;

Input i _α , i _β into the Park transformation module to obtain the actual current i _q of the q-axis and the actual current id of the _d -axis, and a current closed loop is formed at this time;

As shown in Figure 3, input u _α , u _β , i _α , i _β into the proportional resonance sliding mode observer, and the output estimates the back EMF

输入至归一化锁相环，输出估计转子电角速度

和估计转子电角度

Will

Input to normalized phase locked loop, output estimated rotor electrical angular velocity

and estimated rotor electrical angle

再输入至系统中的Park变化模块、反Park变化模块，进行两相静止坐标系、两相旋转坐标系电流分量转化参数；Will

Then input it to the Park change module and the inverse Park change module in the system to convert the parameters of the current component of the two-phase stationary coordinate system and the two-phase rotating coordinate system;

作为输入量输入转速PI调节器，形成转子转速闭环。Will

Input the speed PI regulator as the input quantity, form the rotor speed closed loop.

Further, as shown in Figure 3, the calculation process of estimating the rotor electrical angular velocity and estimating the rotor electrical angle in the multi-proportional resonant sliding mode controller includes:

到电流误差模型，得到两相静止坐标系下的定子电流估计值

Enter the stator voltage components u _α , u _β in the two-phase stationary coordinate system, the estimated back EMF z _α , z _β before filtering and the estimated back EMF after filtering

To the current error model, the estimated value of the stator current in the two-phase static coordinate system is obtained

和采集三相永磁同步电机实际电流得到的i_α、i_β输入滑模控制函数进行高斯处理，得到滤波前的估计反电动势z_α、z_β；Will

Gaussian processing is performed with the input sliding mode control function i _α and i _β obtained by collecting the actual current of the three-phase permanent magnet synchronous motor to obtain the estimated back EMF z _α and z _β before filtering;

代入如图6的多比例谐振滤波器中，输出滤波之后的估计反电动势

带入如图4的归一化锁相环中，得到估计转子电角速度和估计转子位置。The estimated back EMF z _α , z _β before filtering and the estimated rotor electrical angular velocity

Substitute into the multi-proportional resonant filter as shown in Figure 6, and output the estimated back EMF after filtering

Bring it into the normalized phase-locked loop as shown in Figure 4, and obtain the estimated rotor electrical angular velocity and estimated rotor position.

The design process of the sliding mode observer model of the permanent magnet synchronous motor is as follows:

First, define the sliding surface model s _n ,

和

估计定子电流分量。where i _α and i _β are the stator current components in the α-β coordinate system,

and

Estimate the stator current component.

Then, the PMSM model is:

Among them, u _α and u _β are the stator voltage components in the two-phase static coordinate system, e _α and e _β are the back electromotive force in the two-phase static coordinate system, respectively, and i _α and i _β are the stator in the two-phase static coordinate system. The current component, R is the equivalent resistance on the stator winding, L is the equivalent inductance on the stator winding, ω _e is the rotor electrical angular velocity, θ _e is the rotor electrical angle, and ψ is the rotor permanent magnet flux linkage.

The new sliding mode observer model of permanent magnet synchronous motor can be expressed as:

Among them, "^" represents the estimated value, E(s _α ) and E(s _β ) are sliding mode control functions, k is the switching gain of the observer, and H is the amplification factor.

When sliding mode motion occurs, E(s _α ) and E(s _β ) contain useful rotor position information (rotor electrical angle, rotor electrical angular velocity), and the sliding mode control function is expressed as a Gaussian error function:

where the Gaussian error function is defined as:

Equation (12) is subtracted from Equation (1) to obtain the actual current and estimated current error model as shown in Figure 3:

It can be seen from the above formula that the switching function contains back EMF information, so the rotor electrical angular velocity and rotor electrical angle can be calculated, but since the back EMF contains harmonics, the error of the control system will be large.

As shown in Figure 5, the present embodiment uses a quasi-proportional resonant controller to filter the estimated back EMF to widen the filtering bandwidth. The quasi-proportional resonant controller model is:

其中，多比例谐振滤波器模型为：In this embodiment, multiple quasi-proportional resonant controllers are connected in parallel to form a multi-proportional resonant controller, and the estimated back electromotive forces of the α-axis and β-axis are z _α , z _β are filtered by the multi-proportional resonant controller, and the fifth and seventh harmonics are filtered by the multi-proportional resonant controller. Filter out to get the filtered estimated back EMF

Among them, the multi-scale resonant filter model is:

Among them, the value of h can be adjusted according to the actual control requirements;

At the same time, when the system reaches the sliding mode, there are:

Meanwhile, equation (18) is written as:

At this time, the value of output H is twice that of the back EMF. Therefore, using H instead of the traditional back EMF to estimate the rotor electrical angle and rotor electrical angular velocity solves the calculation error caused by the small back EMF and small signal-to-noise ratio when the motor runs at low speed. The problem.

If the sliding mode exists and is stable, the error tends to zero as time tends to infinity. According to the Lyapunov stability principle, choose:

Then the SMO stability condition is:

因此本实施例中基于宽速域滑模控制器是稳定的。Substituting equation (18) into equation (20), we can get

Therefore, the sliding mode controller based on the wide speed domain in this embodiment is stable.

In the normalized phase-locked loop module, the normalized back EMF error can be expressed as:

时，则上式能够被重写为：When the rotor electrical angle estimation error is less than

, the above formula can be rewritten as:

A normalized phase locked loop can track the input signal so that the output signal has the same frequency or phase as the input signal. Therefore, the phase-locked loop with back EMF normalization is not affected by the rotor speed, which can improve the robustness of the system.

The electrical angular velocity of the motor and the electrical angle of the rotor can be expressed as:

According to the control block diagram shown in Figure 2, the control system of the present invention is simulated based on the dspace hardware-in-the-loop simulation experiment platform. Figure 7-(a) is the motor speed waveform diagram and speed when the motor is under rated load and the speed is 1500/min. Error, Figure 7-(b) is the motor rotor position waveform diagram and position error when the motor is under rated load and the speed is 1500/min.

The system uses a multi-proportional resonant sliding mode observer and a normalized phase-locked loop to replace the traditional mechanical sensor to calculate the rotor and rotational speed, forming a speed and current double closed-loop system. Through the multi-proportional resonant controller, the back EMF harmonics can be effectively suppressed; the system chattering can be effectively suppressed by using the continuous Gaussian error function instead of the sign function; the low-speed accuracy of the sliding mode observer is improved by introducing an amplification factor; The method improves the estimation accuracy of the motor speed and rotor position in the full speed range.

The above descriptions are only preferred feasible embodiments of the present invention, and are not intended to limit the scope of rights of the present invention. All equivalent changes made by using the contents of the description of the present invention and the accompanying drawings are included in the scope of rights of the present invention. .

Claims (1)

1. A method for designing a rotor position observer in a wide speed range of a permanent magnet synchronous motor, comprising the steps of: S1: Taking the three-phase permanent magnet synchronous motor as the control object, the mathematical model of the permanent magnet synchronous motor in the two-phase static coordinate system α-β is,

Among them, u _α and u _β are the stator voltage components in the two-phase stationary coordinate system, e _α and e _β are the back electromotive force in the two-phase stationary coordinate system, respectively, and i _α and i _β are the stator under the two-phase stationary coordinate system. Current component, R is the equivalent resistance on the stator winding, L is the equivalent inductance on the stator winding, ω _e is the rotor electrical angular velocity, θ _e is the rotor electrical angle, ψ is the rotor permanent magnet flux linkage; The current and voltage components of the three-phase stationary coordinate system a-b-c and the two-phase stationary coordinate system α-β satisfy the following relationship:

The current component in the two-phase stationary coordinate system α-β and the current component in the two-phase rotating coordinate system d-q can be transformed into each other through Park transformation and inverse Park transformation. Park transformation,

Inverse Park Transform,

Among them, i _a , i _b i _c and u _a , _ub , uc are the three-phase current and three-phase voltage values, respectively, and _id and i _q represent the current components in the two-phase rotating coordinate system, respectively _; It is characterized by: S2: The sliding mode control function is processed by the Gaussian error function, The sliding surface model _sn is constructed as,

The Gaussian error function is defined as,

The sliding mode control function is

in,

and

is the estimated value of the stator current component in the two-phase stationary coordinate system; erf(x) is the Gaussian error function; S3: Using the model equation in the two-phase static coordinate system of the three-phase permanent magnet synchronous motor, in which the voltage and the estimated back electromotive force are used as the input variables of the control system, and the sliding mode observer (SMO) model of the permanent magnet synchronous motor is established.

where k is the switching gain of the observer, k>{|e _α |,|e _β |}; when the sliding mode reaches the sliding mode surface, z _α and z _β are equivalent to the estimated back EMF of the α-axis and β-axis ; S4: Use multiple quasi-proportional resonant controllers in parallel to filter out specific harmonics of the estimated back EMF. The multi-proportional resonant filter model is,

Among them, K _P is the proportional gain, ω _c is the cut-off angular frequency of the system, h is the specific frequency harmonic, K _rh is the resonance gain of the h harmonic, ω _f is the resonance frequency, s represents the complex number, that is, the complex frequency domain; The estimated back electromotive force z _{α and z β obtained by the permanent magnet synchronous motor sliding mode observer, and the fifth and seventh harmonics of the estimated back electromotive force z α and z β are extracted} through the multi-proportional resonant filter. back EMF of

And feed back to the input end of the permanent magnet synchronous motor sliding mode observer to form a closed-loop control; S5: The amplification factor H is introduced into the sliding mode observer (SMO) model of the permanent magnet synchronous motor, then the new sliding mode observer model of the permanent magnet synchronous motor after the introduction of the amplification factor is,

in,

is the estimated back EMF filtered by the multi-proportional resonant filter, and H is the amplification factor; S6: The filtered estimated back EMF

As the input variable of the normalized phase-locked loop, the rotor electrical angle and rotor electrical angular velocity are calculated by the normalized phase-locked loop, and the estimated rotor electrical angular velocity is used as the resonant frequency of the multi-proportional resonant filter, so as to realize the frequency adaptive control ; then the calculation model for estimating the rotor electrical angular velocity and estimating the rotor electrical angle is as follows:

Among them, k _i is the integral gain, k _p is the proportional gain,

is the estimated rotor electrical angular velocity,

is the estimated rotor electrical angle.

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