KR20100068866A - Sensorless control method of permanent magnet synchronous motor - Google Patents

Abstract

PURPOSE: A method for sensorless control of the permanent magnet type synchronous motor is provided to use the sensorless algorithm applying the repetition adaptation sliding mode observation plane. The rotor electrical angle and electrical angle speed of the permanent magnet type synchronous motor are decided. CONSTITUTION: The input voltage from the inverter(11) is applied and the stator current actually obtains. The estimated current value calculates in the repetition adaptation sliding mode observation plane(21) on the fixed state equation. Error when estimated current value is compared with actual current value obtains. The rotator angle pitches by using the control input value of the observation plane of the final obtaining through the observation plane.

Description

Sensorless control method of permanent magnet synchronous motor

The present invention relates to a sensorless control method of a permanent magnet synchronous motor, and more particularly, to determine rotor electric angle and electric angular velocity of a permanent magnet synchronous motor using a sensorless algorithm using a repetitive adaptive sliding mode observer. It is about a method.

Recently, various applications using high-speed motors with operating ranges of tens of thousands of rpm or more have been developed or commercialized. Typical examples include a micro turbine generator using a permanent magnet synchronous motor, a turbo blower, an air compressor for a fuel cell, and an electric motor for a high speed processing machine.

Permanent Magnet Synchronous Motor (PMSM), which is widely used for driving high-speed motors, needs to know the rotor position accurately for accurate torque control.

To this end, an encoder or resolver is attached to the rotor to measure the rotation angle and speed in real time, and then the torque and speed control is performed by reflecting it in a vector control algorithm.

However, when the sensor is attached to measure the rotation angle of the rotor, there is a problem that the installation of the sensor is difficult or cause a malfunction depending on the use environment.

In particular, in the case of a high speed motor of tens of thousands of rpm, there is a disadvantage that there is no suitable sensor or an expensive sensor is attached.

In order to solve this problem, various sensorless algorithms capable of calculating the position and speed of the rotor in real time without sensors for measuring the speed and position have been proposed, and many studies have been conducted.

The sensorless algorithm for the rotation angle estimation of a permanent magnet synchronous motor (PMSM) has been studied to estimate the rotor electromotive force by using the circuit equation of the synchronous motor to find the position of the rotor.

In addition, algorithms using state estimators and algorithms using Kalman filters have been proposed, but it is difficult to obtain accurate motor parameters with the proposed method. There is this difficult problem.

Accordingly, the present invention has been made in view of the above problems, and an object thereof is to provide a sensorless algorithm capable of accurately calculating rotor position and speed in real time without a separate measuring sensor.

In order to achieve the above object, the present invention,

A process for determining the electric angle and angular velocity of a rotor for sensorless control of a permanent magnet synchronous motor.

를 산출하여 구하는 단계와; c) 추정 전류값

를 실제 전류값 i_s와 비교하여 오차를 구하고, 하기 식(E1)에 의해 관측기의 제어 입력인 z_s를 구하는 단계와; d) 상기 b) ~ c) 단계를 반복하여 상기 관측기에서 추정된 전류가 일정 오차 범위 내에서 수렴하면 상기 관측기를 통해 구해진 최종의 z_s를 이용해 회전자 각도

를 결정하고, 구해진 회전자 각도를 미분하여 회전자의 전기각속도

를 결정하는 단계;를 포함하는 영구자석형 동기 전동기의 센서리스 제어방법을 제 공한다.a) applying an input voltage v _s from the inverter to obtain an actual stator current i _s ; b) Estimated current values based on the state equations set in the iterative adaptive sliding mode observer.

Calculating and obtaining; c) estimated current value

Calculating an error by comparing the current to the actual current value i _s, and obtaining z _s , which is a control input of the observer, by the following equation (E1); d) If the current estimated by the observer converges within a certain error range by repeating steps b) to c), the rotor angle is obtained by using the final z _s obtained through the observer.

And the electric angular velocity of the rotor by differentiating the obtained rotor angle

It provides a sensorless control method of a permanent magnet synchronous motor comprising a.

Formula (E1):

는 하기 식(E2)로 정의되고, K는 상기 관측기의 피드백 게인 값임. 하기 식(E2)에서 E_lim은 오차 설정치임.here,

Is defined by the following equation (E2), and K is the feedback gain value of the observer. In the following equation (E2), E _lim is the error setting value.

Formula (E2):

At this time, when the state equation for the current of the permanent magnet synchronous motor is the following equation (E3) is characterized in that the state equation for the current estimation of the observer is defined by the following equation (E4).

Formula (E3):

here,

이고,

ego,

e _s is the counter electromotive force, K _e is the counter electromotive force constant, and ω _r is the electric angular velocity of the rotor.

Formula (E4):

Also in step d),

The rotor angle is calculated by obtaining the arc tangent of the two counter electromotive force components in the following equation (E5) using the voltage information of z _s obtained through the observer.

Formula (E5):

는

, 즉 저역통과필터(Low Pass Filter)를 통과하여 노이즈를 저감시키면서 발생하는 위상지연의 보상값임. here,

Is

That is, it is the compensation value of the phase delay that occurs while reducing the noise passing through the low pass filter.

로 설정되어 z_s로부터 추정된 회전자 전기각속도

의 절대값에 비례하는 값을 가지며, 상기 식의 k, k₀는 양의 값으로 설정되는 것을 특징으로 한다.In addition, the feedback gain K is

Rotor electric angular velocity estimated from z _s

It has a value proportional to the absolute value of, wherein k, k ₀ of the formula is characterized in that it is set to a positive value.

Accordingly, according to the present invention, in the process for determining the rotor position and speed of the permanent magnet type synchronous motor, the current is estimated through an iterative adaptive sliding mode observer, and the error is obtained by comparing the estimated current with the actual current. When the current estimated by the observer converges within a certain error range, the rotor angle and electric angular velocity are determined using z _s obtained through the observer, so that the rotor position and speed can be accurately calculated in real time without a separate measuring sensor. It is possible to implement a sensorless algorithm.

Hereinafter, the present invention will be described in more detail with reference to the accompanying drawings.

In the present invention, a sensorless algorithm applying a sliding mode observer for sensorless control of a permanent magnet synchronous motor (PMSM) is proposed, and the operation state at the initial start and rated speed is compared and examined.

Although the sliding mode observer has a strong characteristic against parameter fluctuations and disturbances, the sliding mode observer causes an error in estimating the rotation angle by chattering, which is difficult to apply. For this purpose, the boundary layer is set and the linear function is placed in the boundary layer to reduce the ripple.

In addition, to improve the tracking speed of the counter electromotive force, the sliding mode observer is repeatedly executed to minimize the error of the counter electromotive force estimated during the PWM cycle, thereby minimizing the measurement error by improving the problem of chattering as the error accumulates in the next cycle operation. .

Until now, in order to drive high speed permanent magnet synchronous motor of more than tens of thousands of rpm, it is possible to find out the speed by using low-cost Hall sensor and obtain the position information of the rotor, or start up by running v / f up to several thousand rpm. Sensorless operation is implemented.

However, in this case, a large current can be applied at the time of initial start-up, and there is a fear of start-up failure depending on the rotor and load conditions at start-up. In order to solve this problem, we describe a driving sensorless algorithm that runs from the initial start to the rated speed without the speed and position sensors.

) 및 전기각속도(

)를 결정하기 위한 과정으로서, a) 인버터로부터의 입력 전압 v_s가 인가되어 실제 고정자 전류 i_s가 구해지는 단계와; b) 반복 적응 슬라이딩 모드 관측기에 설정된 상태 방정식을 토대로 추정 전류값

를 산출하여 구하는 단계와; c) 추정 전류값

를 실제 전류값 i_s와 비교하여 오차를 구하고, 하기 수학식 7에 의해 관측기의 제어 입력인 z_s를 구하는 단계와; d) 상기 b) ~ c) 단계를 반복하여 상기 관측기에서 추정된 전류가 일정 오차 범위 내에서 수렴하면 상기 관측기를 통해 구해진 최종의 z_s를 이용해 회전자 각도를 결정하고, 구해진 회전자 각도를 미분하여 회전자의 전기각속도를 결정하는 단계;가 진행된다.In the present invention, the electric angle of the rotor for the sensorless control of the permanent magnet synchronous motor (

) And electric angular velocity (

A process for determining an actual stator current i _s by applying an input voltage v _s from the inverter; b) Estimated current values based on the state equations set in the iterative adaptive sliding mode observer.

Calculating and obtaining; c) estimated current value

Calculating an error by comparing the current with the actual current value i _s, and obtaining z _s which is a control input of the observer by Equation 7 below; d) If the current estimated by the observer converges within a certain error range by repeating steps b) to c), the rotor angle is determined using the final z _s obtained through the observer, and the obtained rotor angle is differentiated. Determining the electric angular velocity of the rotor.

Hereinafter, with reference to the accompanying drawings for the present invention in more detail, Figure 1 is a view showing the coordinate system of the permanent magnet synchronous motor, Figure 2 is a block showing a repeat adaptive sliding mode observer according to the present invention 3 is a block diagram showing the overall configuration of a motor control system including a repeat adaptive sliding mode observer according to the present invention.

First, the voltage equation in the two-phase synchronous coordinate system of the permanent magnet synchronous motor is as follows. Equations 1 and 2 are voltage equations of a stator reference sync coordinate system.

는 고정자 자기 인덕턴스를, ω_r은 회전자의 각속도(전기각속도)를, i_qs는 q축 전류를 각각 나타낸다. Equation 1 is a voltage equation of the d-axis, v _ds represents the d-axis voltage, R _s = R _a represents the stator winding resistance, i _ds represents the d-axis current,

Is the stator magnetic inductance, ω _r is the angular velocity (electric angular velocity) of the rotor, and i _qs is the q-axis current.

는 역기전력 상수를 나타낸다. 수학식 2에서 ω_rK_e는 역기전력이 된다.Equation 2 is a voltage equation of the q-axis, v _ds , v _qs is the voltage of the synchronous coordinate system, v _qs represents the q-axis voltage, i _ds , i _qs is the current of the synchronous coordinate system, i _qs is the q-axis current Indicates.

Represents the back EMF constant. In Equation 2 ω _r K _e is the counter electromotive force.

In addition, since the counter electromotive force and the magnetic flux are estimated using the voltage and current of the stationary coordinate system to estimate the rotor position of the high speed permanent magnet synchronous motor 12, the voltage equation in the two-phase stationary coordinate system of the synchronous motor for this purpose is as follows. .

A voltage equation of the equation (3) and Equation (4) is the stator based on rotating coordinates, v _αs, v _βs is the voltage in the still coordinate system, v _αs is the α-axis voltage of the still coordinate system, v _βs are β-axis voltage of the still coordinate system, Indicates. i _{αs, βs} i is a current of the rotating coordinates, i _αs is the α-axis current of the rotating coordinates, i _βs represents the β-axis current of the rotating coordinates (the stator β-axis current). θ _r represents the electrical angle of the rotor, respectively.

When the equations 3 and 4 are developed as the state equations for the current, the equations (5) are as follows.

here,

And A ₁₁ , A ₂₂ = -R _s / L _s <0, B ₁₁ , B ₂₂ = 1 / L _s > 0, and the current i _s in Equation 5 is obtained by sensing with a current sensor to be.

On the other hand, many studies have been conducted to control the position and speed of the rotor of the permanent magnet synchronous motor 12, but various algorithms have been proposed. have.

In particular, it is important to select a driving technique that can implement a sensorless algorithm within a limited computational capacity because it must be accompanied by a large ripple current by the PWM output due to a small motor constant and a high current control period due to the high fundamental frequency. .

Therefore, in the present invention, a sensorless algorithm using a sliding adaptive mode observer 21, which is a more advanced algorithm, is constructed by applying a sliding mode observer for which gain selection and design of the observer are easy.

The state equation of the observer 21 is as follows, and its block diagram is as shown in FIG.

가 추정하는 상태 변수이며, v_s는 인버터(11)의 출력 전압이 된다. ^ 표시는 실제 측정이 아니고 계산에 의한 추정값(관측 기(observer)를 이용한 추정값), 즉 시스템 모델링을 통한 수학적인 연산에 의해 계산된 예측치이다. z_s는 인버터(11)로부터의 입력 전압인 v_s와 상태 변수인 전류 i_s를 만족시키기 위한 관측기(21)의 제어 입력인데, 이는 수학식 5를 보면 역기전력 성분 e_s와 같다. 즉, e_s를 알면 그로부터 전기각을 구할 수 있다. Equation 6 is a state equation of the observer for estimating state variables i _{α s} and i _{β s} of Equation 5. In Equation 6,

Is the state variable to be estimated, and v _s is the output voltage of the inverter 11. ^ Is not an actual measurement, but an estimate by calculation (an estimate using an observer), that is, a prediction calculated by mathematical operations through system modeling. z _s is a control input of the observer 21 for satisfying the input voltage v _s from the inverter 11 and the state variable current i _s , which is equal to the counter electromotive force component e _s . In other words, if we know e _s, we can find the electric angle from it.

를 실제 i_s와 비교하여 오차를 구하고, 그로부터 하기 수학식 7에 의해 z_s를 구한다. 이때, z_s를 구하는 방법으로 슬라이딩 모드 제어 이론을 도입하여 함수를 정의하는데, 종의 1, 0, -1의 함수가 아니고 경계면을 두어 E_lim의 좁은 경계를 두어서 오차가 작은, 즉 수렴한 구간에서는 선형적으로 값이 변하게 수정된 함수를 정의하였다. 이렇게 하면 채터링이 큰 슬라이딩 모드 제어기의 단점을 해결할 수 있고, 동시에 우수한 응답 결과를 얻을 수 있다. To accurately estimate i _s , input the actual input voltage v _s

Is compared with actual i _s to find an error, and z _s is obtained from Equation 7 below. In this case, the function of sliding mode control theory is defined by the method of obtaining z _s , and the function is not a function of 1, 0, -1 of the species, but the boundary is placed on the narrow boundary of E _lim so that the error is small. In the interval, the modified function is changed so that the value changes linearly. This solves the shortcomings of sliding mode controllers with large chattering and at the same time provides good response results.

At this time, the error feedback of the observer 21 is as follows. The sign function applied to the conventional sliding mode controller has a fast switching response, but in some cases it causes adverse effects by causing chattering. Thus, by applying the slide function of Equation 8, which improves the advantage, if the estimated current of the observer 21 converges within a certain error range, it improves the response of the observer 21 by obtaining a linear section proportional to the error. do.

)과 슬라이딩 모드의 스위칭 함수의 노이즈(

)(시스템 노이즈와 PWM 슬라이딩 모드 관측기의 채터링 노이즈 등임)가 함께 있다는 의미이다.Equation 9 is based on z _s

) And the noise of the switching function in sliding mode (

) (Such as system noise and chattering noise from a PWM sliding mode observer).

의 노이즈를 제거하면 역기전력 성분만 남는다.Equation 10 means that the noise component is removed from z _s through a low pass filter and only the fundamental wave component is input. z _s through a lowpass filter

If you remove the noise, only the back EMF component remains.

Then, as in Equation 11, the magnetic flux is obtained by integrating the counter electromotive force component from which the noise is removed.

는 전류 오차에서 구한 슬라이딩 모드 관측기(21)의 스위칭값이 된다. 이 값에는 수학식 5의 역기전력 e_s와 슬라이딩 모드 관측기의 채터링에 의해 고주파 성분

가 포함되어 있으므로, 이를 제거하기 위해 저역통과필터가 필요로 하며, 이로 인한 위상 지연을 보상하는 기능이 필요하게 된다.Of equation (7)

Is the switching value of the sliding mode observer 21 obtained from the current error. This value includes high frequency components by the counter electromotive force e _s of Equation 5 and chattering of the sliding mode observer.

Since a low pass filter is needed to eliminate this, a function of compensating for the phase delay is needed.

The position of the rotor can be obtained by using the voltage information of z _s obtained through the observer 21, which is shown in Equation 12.

By calculating arc tangents of two counter electromotive force components in Equation 12, the rotor angle, which is the position of the rotor, can be known.

는

, 즉 저역통과필터(Low Pass Filter)를 통과하여 노이즈를 저감시키면서 발생하는 위상지연의 보상값이다. Ksilde 함수를 적용하여 반복하여 추정함으로써 실제 구한 z_αs, z_βs는 이미 고주파가 많이 제거된 상태의 역기전력 추정값을 얻지만, 보다 기본파 성분을 얻기 위하여 저역통과필터를 통과하여 노이즈 없는 추정값을 얻게 된다. here,

Is

That is, it is a compensation value of the phase delay that occurs while reducing the noise passing through the low pass filter. By applying the Ksilde function repeatedly, z _{α s} and z _{β s} actually obtained are back electromotive force estimates with high frequencies removed, but pass through a low pass filter to obtain more fundamental wave components. .

를 구한다. 0<k_ω≤1 이며, k_ω=1이면 45도 보상, k_ω=0.1이면 90도 보상을 한다. 실험을 통하여 적절한 k_ω를 설정한다. Kslide함수와 반복을 통하여 기본파 성분에 가까운 신호를 얻기에 기존 알고리즘에 비해서 1에 가까운 값을 설정하여 위상 지연을 최소화 할수있다.At this time, cutoff frequency

. 0 <k _ω ≤ 1, and if k _ω = 1, 45 degree compensation, if k _ω = 0.1, 90 degree compensation. Experiment to set the appropriate k _ω . It is possible to minimize the phase delay by setting a value close to 1 compared to the existing algorithm because the signal close to fundamental wave component is obtained through Kslide function and repetition.

By differentiating the angle in Equation 13, the angular velocity of the rotor can be obtained.

The conditions for setting the feedback gain K of the sliding mode observer 21 are as follows.

The condition for satisfying the sliding mode condition of the observer 21 is

When the condition satisfying the expression (16) is solved by the equations (14) and (15), it is as follows.

이고,

는 가우시안 분포를 가진다면 수학식 16을 만족하기 위해서는

를 충족하여야 한다. K를 선정할 때 큰 값을 설정하면 응답은 빠르지만 슬라이딩 모드의 단점인 채터링이 발생하고, 작은 값을 설정하면 응답의 지연으로 관측기(21)가 수렴하지 못하고 위상 지연이 발생하는 문제가 있다. Where, always

ego,

If is a Gaussian distribution,

Must meet. When selecting K, a large value is set, but the response is fast but chattering, which is a disadvantage of the sliding mode, occurs, and when a small value is set, the observer 21 cannot converge and a phase delay occurs due to a delay of the response. .

Therefore, since K is a function of the counter electromotive force, the adaptive observer 21 is configured by setting it to a value proportional to the speed.

을 유추할 수 있다.Here, in e _{α s} , K _e ω _r

Can be inferred.

In constructing the observer 21 for position and velocity estimation, current and voltage have a frequency and magnitude because they use signals from a static coordinate system. However, the calculation of the observer 21 is synchronized with the current controller, and the rotation speed and the magnitude of the voltage of the electric motor are proportional to each other, so that the phase delay occurs in the high speed mode, causing difficulty in estimation.

To solve this problem, the entire system operates the observer 21 in tracking mode and repeats the observer several times for every sample to operate the observer in regulation mode to minimize the error every cycle.

At this time, in order to prevent chattering at the portion where the current error becomes zero, a modified function of the slide function of Equation 8 is applied to stabilize the convergence.

1 is a view showing a coordinate system of a permanent magnet synchronous motor,

2 is a block diagram illustrating an iterative adaptive sliding mode observer according to the present invention;

Figure 3 is a block diagram showing the overall configuration of a motor control system including a repeat adaptive sliding mode observer according to the present invention.

<Explanation of symbols for the main parts of the drawings>

11 Inverter 12 Permanent Magnet Synchronous Motor (PMSM)

21: Iterative Adaptive Sliding Mode Observer

Claims (4)

A process for determining the electric angle and angular velocity of a rotor for sensorless control of a permanent magnet synchronous motor. a) applying an input voltage v _s from the inverter to obtain an actual stator current i _s ; b) Estimated current values based on the state equations set in the iterative adaptive sliding mode observer.

Calculating and obtaining; c) estimated current value

Calculating an error by comparing the current to the actual current value i _s, and obtaining z _s , which is a control input of the observer, by the following equation (E1); d) If the current estimated by the observer converges within a certain error range by repeating steps b) to c), the rotor angle is obtained by using the final z _s obtained through the observer.

And the electric angular velocity of the rotor by differentiating the obtained rotor angle

The sensorless control method of the permanent magnet synchronous motor comprising a. Formula (E1):

here,

Is defined by the following equation (E2), and K is the feedback gain value of the observer. In the following equation (E2), E _lim is the error setting value. Formula (E2):

The method according to claim 1, When the state equation for the current of the permanent magnet synchronous motor is the following equation (E3), the state equation for estimating the current of the observer is defined by the following equation (E4) sensorless of the permanent magnet synchronous motor Control method. Formula (E3):

here,

ego, e _s is the counter electromotive force, K _e is the counter electromotive force constant, and ω _r is the electric angular velocity of the rotor. Formula (E4):

The method according to claim 1, In step d), The rotor angle is a sensorless control method of a permanent magnet synchronous motor, characterized in that calculated by calculating the arc tangent of the two back EMF components in the following equation (E5) using the voltage information of z _s obtained through the observer. Formula (E5):

here,

Is

That is, it is the compensation value of the phase delay that occurs while reducing the noise passing through the low pass filter. The method according to claim 1, The feedback gain K is

Rotor electric angular velocity estimated from z _s

The sensorless control method of a permanent magnet synchronous motor having a value proportional to the absolute value of, wherein k, k ₀ of the equation is set to a positive value.

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