KR100551572B1 - PMSM controller using an adaptive integral binary observer and cotrol method the same - Google Patents

Abstract

The present invention discloses a permanent magnet synchronous motor (PMSM) control apparatus using an adaptive integral binary observer and a control method thereof.

The permanent magnet synchronous motor control apparatus of the present invention includes a speed controller for outputting a current command value to follow the command speed output from the speed commander, and a current controller for outputting a current error between the current command value and the actual current flowing to the brushless DC motor. Determine a switching pattern for the current error, estimate a speed and position of the rotor of the DC motor, a power converter for supplying the voltage to the DC motor, a current detector for sensing the current flowing through the DC motor, The binary observer has an integral switching plane for integrating the current error to estimate the speed and position of the rotor of the DC motor. In this way, by integrating the error between the actual current and the estimated current to increase the dimension of the observer area, it is possible to estimate the speed and position of the motor very stably under steady state as well as in the transiently changing speed, and to operate steadily against the cupping change. Do it.

Adaptive Integral Binary Observer

Description

Permanent magnet synchronous motor controller using adaptive integral binary observer and its control method {PMSM controller using an adaptive integral binary observer and cotrol method the same}

1 is a block diagram showing the configuration of a conventional binar observer.

FIG. 2 is an explanatory diagram showing an error trajectory of the binary observer of FIG. 1; FIG.

3 is a block diagram showing a configuration of a control device according to the present invention.

4 is a block diagram showing a configuration of an adaptive integral binary observer according to the present invention.

5 illustrates a phase plane trajectory of an adaptive integral binary observer according to the present invention.

Fig. 6 is a waveform diagram showing actual speed, estimated speed, and speed estimation error at 1500 [rpm] at no load when the adaptive sliding observer is used.

7 is a waveform diagram showing an actual speed, an estimated speed, and a speed estimation error at 1500 [rpm] at no load when using the adaptive integral binary observer according to the present invention;

Explanation of symbols on the main parts of the drawings

10: speed commander 20: speed controller

30: current controller 40: power converter

50: current detector 60: binary observer

61, 63: adder 62: integrator

64: auxiliary loop adjuster 65: main loop adjuster

66: gain regulator

BLDCM: Brushless DC Motor

The present invention relates to a sensorless control device for a permanent magnet synchronous motor (PMSM) using a binary observer and a control method thereof, and more particularly, to an adaptive integral observer applying a form similar to an adaptive sliding observer. A cylindrical permanent magnet synchronous motor control apparatus using a binary observer and a control method thereof.

Cylindrical permanent magnet synchronous motors are widely used in industrial applications because they have higher torque ratio and efficiency than other motors.

However, since the cylindrical permanent magnet synchronous motor receives magnetic flux from the permanent magnet attached to the rotor, it is necessary to always know the exact position information of the rotor for vector control.

In order to obtain accurate position information of the motor rotor, an electronic position detector using a magnetic sensor such as a resolver, an absolute encoder, or a hall element is used.

Such position detectors are generally expensive and have the disadvantage that separate complex hardware must be configured in the controller. In addition, since it is greatly affected by the surrounding environment such as vibration and humidity, it is restricted in the use environment.

Therefore, the research on sensorless control to indirectly obtain the position of the rotor, which is a big problem in the control of cylindrical permanent magnet synchronous motor, without using the sensor is being actively conducted, and using the control theory among the sensorless control methods A lot of studies have been conducted on the application of an observer for estimating the speed of a motor and the position of a rotor.

When the general linear observer is applied to the sensorless control of a cylindrical permanent magnet synchronous motor, it is difficult to obtain an appropriate observer gain because the entire system is nonlinear. In order to overcome this disadvantage, the sliding mode observer using the sliding mode theory can be applied as a nonlinear observer. However, the conventional sliding mode observer has a drawback of vibration because of the control characteristics of the observer.

There are various methods for solving the disadvantages of the sliding mode observer. Among them, a binary observer using binary theory that has the same advantages as a sliding mode observer and can eliminate vibrations has been proposed.

1 is a block diagram showing the configuration of a conventional binary observer.

The binary observer includes an adder (1) for obtaining an estimated error (σ) between the actual current flowing through the brushless DC motor and the estimated current obtained from the state equation, and the allowable range of the estimated error (σ) obtained from the adder (1). An auxiliary loop adjuster 2 which sets a limit area and sets the gain of the main loop adjuster so as to remain without leaving this area when the estimated error enters the set limit area; and an output and an adder of the auxiliary loop adjuster 2; The main loop regulator 3 outputs a continuous switching function by inputting the estimated error? Of 1), and the gain of the continuous switching function output from the main loop regulator 3 is adjusted to enter the limit region. A gain adjuster 4 is provided to allow the error trajectory to converge stably to the origin.

The binary observer of FIG. 1 has a hyperplane similar to the sliding mode plane of the sliding mode observer, and sets an area around the hyperplane. At this time, by setting the gain of the observer so as not to leave the region of the observer, it has the same robustness as the sliding mode observer. In addition, the binary observer is composed of a main loop and a secondary loop, and the secondary loop has a feature of reducing vibration by generating continuous control inputs by flexibly adjusting the observer gain of the main loop in real time.

However, the set area of the binary observer is set to be parallel to the hyperplane on the state plane, so that the estimated value stays in the area but cannot converge to zero.

)에서 원통형 영구자석 동기전동기의 전압방정식은 수학식 1과 같다.In the conventional binary observer type, only the voltage equation of the motor is used, and the stator coordinate system (

In Equation 1), the voltage equation of the cylindrical permanent magnet synchronous motor is shown in Equation 1.

From here,

In addition to the voltage and current in Equation 1, there is a back EMF component that is expressed as a product of a trigonometric function and a speed term for a position, which makes the entire system nonlinear. Therefore, in order to linearize this, a binary observer for observing a measurable current can be constructed as shown in Equation 2 under the assumption that the velocity is constant within a control period.

From here,

When vector control is performed by speed sensorless, the current and voltage of the motor are measurable variables, and the speed and position are variables to be estimated. Therefore, the hyperplane of the binary observer is defined as an estimation error of current as shown in Equation (3).

In addition, in the case of the binary observer, the defined boundary layer G _δ is set as in Equation 4.

δ: constant (0≤δ <1)

Here, δ is any design parameter representing the width of the G _δ area. If δ is very small in Equation 4, the area becomes the same as the sliding surface, and thus has the same characteristics as the sliding observer.

In the binary observer of Equation 2, the switching function of the observer is determined as shown in Equations 5 and 6 by binary control having Continuous Inertial Auxiliary Loop Coordinate Operator Feedback.

Secondary loop regulator

Where α is a constant

Main loop regulator

The state trace of the binary observer of FIG. 1 described above is shown in FIG. 2. Where t ₀ , t ₁ , t ₂ are the times to reach | σ | = 0, δ / 2 and δ, respectively. The state trace of the binary observer cannot represent the state plane in the two-dimensional plane of the state variable because the state variable is the error of the current for each axis. Accordingly, as shown in FIG. 1, the state trajectory is represented based on the time axis for each state variable.

Gain k ⁰ and α is the binary observer is determined from invariant _δ G (G _δ invariant condition). Herein, the G _δ constant condition refers to a condition in which the estimated error σ (t) once stays in the area G _δ without leaving the G _δ area thereafter. This relationship has a concept similar to the sliding condition in the existing sliding mode control.

By designing the gains K ⁰ and α of the observer to satisfy the G _δ invariant, the binary observer has the same robustness as the sliding observer, but with a continuous estimate without the vibration occurring in the sliding mode.

However, the binary observer cannot guarantee that the estimated value also converges to zero since the width of the region cannot converge to zero in the steady state when the region is set as shown in Equation 4. If the width of the region is narrowed by decreasing the value of δ to ensure zero convergence, it becomes the same as the sliding mode observer and thus does not obtain the continuous estimation gain, which is an advantage of the binary observer.

Accordingly, an object of the present invention to solve the above problem is to improve the performance of a permanent magnet synchronous motor using an adaptive integral binary observer in which a form similar to an adaptive sliding observer is applied to an integral binary observer.

Cylindrical permanent magnet synchronous motor control apparatus using the adaptive integral binary observer of the present invention for achieving the above object, a speed controller for outputting a current command value to follow the command speed output from the speed commander, current command value and brushless A current controller that outputs the current error between the actual current flowing through the direct current motor, a power converter that determines the switching pattern for the current error, and supplies a voltage according to the determined pattern to the DC motor, and detects the current flowing in the DC motor In the control device of a permanent magnet synchronous motor comprising a current detector and a binary observer for estimating the speed and position of a rotor of a DC motor, the binary observer integrates the current error to estimate the speed and position of the rotor of the DC motor. It is characterized by having an integral switching plane.

Cylindrical permanent magnet synchronous motor control method using the adaptive integral binary observer of the present invention, the first step of detecting the actual current flowing to the brushless DC motor; A second step of calculating the estimated current from the state equation of the brushless DC motor; A third step of obtaining an estimation error that is a difference between the actual current and the estimated current; A fourth step of integrating the estimated error and adding the estimated error, and determining a continuous switching function having an integrated switching plane using the addition value; A fifth step of setting a limit area which is an allowable range of the addition value; A sixth step of setting a gain of the auxiliary loop adjuster so that the estimated error does not leave the limit region; A seventh step of determining a switching function by inputting the output of the auxiliary loop regulator whose gain is set in the sixth step; An eighth step of adjusting a gain of the switching function so that the trajectory of the estimated error entered in the limit region set in the fifth step may converge to the origin; And a ninth step of following the speed and position of the brushless DC motor from the switching function whose gain is adjusted in the eighth step.

Hereinafter, with reference to the accompanying drawings will be described in detail a preferred embodiment of the present invention.

3 is a block diagram showing the configuration of a cylindrical permanent magnet synchronous motor control apparatus using an adaptive integral binary observer according to the present invention.

The permanent magnet synchronous motor controller of FIG. 3 includes a speed commander 10 for outputting a command speed set separately, and a speed controller 20 for outputting a current command value to follow the command speed output from the speed commander 10. ), A current controller 30 that outputs a voltage to follow the current command value output from the speed controller 20, and a brushless DC motor (BLDCM) by converting the voltage output from the current controller 30 into a three-phase AC power source. The speed and position of the motor rotor using the power converter 40 to be supplied to the power supply, the current detector 50 for detecting the current flowing through the brushless DC motor, and the current detected by the current detector 50. By estimating the estimated speed is provided to the speed controller 20, the estimated position is provided with a binary observer 60 which is an estimator provided to the current controller 30.

4 is a block diagram illustrating the configuration of the binary observer 60 of FIG. 3 in more detail.

)간의 추정오차(E₁)를 구하는 제 1 가산기(61)와, 제 1 가산기(61)의 출력(E₁)을 적분하는 적분기(62)와, 적분기(62)의 출력과 제 1 가산기(61)의 출력을 가산하는 제 2 가산기(63)와, 제 2 가산기(63)의 출력(

)에 대한 허용범위의 한계영역을 설정하고, 제 1 가산기(61) 의 출력(E₁)이 설정된 한계영역에 들어오면 이 영역을 벗어나지 않고 계속 그 영역내에 머물러 있도록 주루프 조정기의 이득(k₁)을 설정하는 보조루프 조정기(64)와, 보조루프 조정기(64)의 출력과 제 1 가산기(61)의 출력(E₁)을 입력으로하여 연속의 스위칭함수를 출력하는 주루프 조정기(65)와, 주루프 조정기(65)에서 출력되는 연속의 스위칭함수의 이득을 조정하여 한계영역내에 들어온 오차궤적이 원점으로 안정적으로 수렴할 수 있도록 하는 이득 조정기(66)를 구비한다.The binary observer 60 of FIG. 4 is an estimated current obtained from the actual current i flowing through the brushless DC motor and the state equation (

) Output of the first adder from the first adder 61 to obtain the estimation error (E ₁₎ between the first adder (61) output (E ₁₎ integrator 62, the integrator (62 for integrating a) ( The second adder 63 which adds the output of 61; and the output of the second adder 63

Set the limit area of the allowable range, and if the output E ₁ of the first adder 61 enters the set limit area, the gain (k ₁₎ of the main loop adjuster will remain within the area without leaving this area. Main loop adjuster 65 outputting a continuous switching function by inputting the sub loop adjuster 64 for setting?), The output of the sub loop adjuster 64, and the output E ₁ of the first adder 61; And a gain adjuster 66 that adjusts the gain of the continuous switching function output from the main loop adjuster 65 so that the error trajectory entering the limit region can converge stably to the origin.

The operation and effects of the cylindrical permanent magnet synchronous motor control device and binary observer of the present invention having the above-described configuration will be described in detail as follows.

The conventional binary observer described above cannot guarantee to converge the plane of the set observer to the origin. This can reduce the trembling of the estimated value in the steady state, but has the disadvantage of leaving a steady state error. In order to solve the disadvantage of the binary observer, the present invention uses a binary observer having an integral switching plane.

* Binary observer with integral switching plane

First, an integral term is added to the hyperplane in order to improve the steady state performance of the binary observer. The hyperplane of the binary observer of the present invention is defined using the actual value and the estimated value of the current as in the binary observer described above.

는 수학식 7과 같이 정의된다.In the binary observer with the integral switching plane of the present invention, the integral switching plane

Is defined as in Equation 7.

here,

Unlike the hyperplane of Equation 3, Equation 7 integrates the error e of the current obtained by the adder 61 to increase the dimension of the hyperplane. Therefore, unlike the conventional binary observer described above using only the equation of motion, the binary observer 60 of the present invention may exhibit a state trace in a two-dimensional plane as shown in FIG.

The region G _δ defined in the binary observer 60 is defined as in Equation 8.

As can be seen from Equations 7 and 8, it can be seen that the dimension of the region of the binary observer 60 is increased, and the region of the observer 60 can be converged to the origin using this.

The auxiliary loop adjuster 64 and the main loop adjuster 65, which determine the switching function of the binary observer 60 of the present invention having an integral switching plane, are continuous inertia (COFB) and are represented by Equations 9 to 10, respectively. .

Secondary loop regulator:

Main loop regulator:

From here,

Since the binary observer 60 having the integral switching plane of the present invention is also represented by Equation 2, the error equation is represented by Equation 11, and the state trace of the observer 60 is shown in FIG.

From here,

The error from FIG. 5 once reaches the interface of the binary observer 60 and converges along the horizontal axis until e _s = 0.

The gain of the binary observer 60 with the integral switching plane of the present invention can be obtained from the G _δ invariance for the region. For the G _δ constant condition, Equation 12 must be satisfied at the interface of the region G _δ .

가 영역을 벗어나지 않고 계속 영역내에서 머물러 있을 조건은 이득 k₁을 적절하게 선택함으로써 확보되어질 수 있다.In the region G _δ of Equation 8

Can be ensured by appropriately selecting the gain k ₁ .

인 경우를 고려한다.first,

Consider the case.

이라 가정하고, 수학식 12를 만족하도록 이득 k₁을 선택하는 경우, 수학식 13으로부터 이득 k₁은 수학식 14와 같다.

As if the home and selecting the gain k ₁ so as to satisfy the equation (12), the gain k ₁ from the equation (13) is equal to the equation (14).

인 경우에는 수학식 15와 같은 결과를 얻게 된다.On the other hand,

In the case of Equation 15, the result is obtained.

From Equations 14 and 15, Equation 16 can be obtained.

에 대하여 수학식 17이 얻어진다.In the same way,

(17) is obtained.

From equations (16) and (17), an area of k ₁ can be calculated as shown in equation (18).

를 이용하여 구한다. 먼저 시스템의 상태가

을 통과하는 시간을 t₁,

에서 영역의 경계에 도달하는 시간을 t₂라 놓고 수학식 9를 시간에 대해 정리하면,The gain α of the secondary loop adjuster 64 is a function of the gain such that μ (t) satisfies the magnitude | μ | ≥ 1-h at the boundary of the region.

Obtain using First, the state of the system

Time to pass t ₁ ,

If the time to reach the boundary of the domain is t ₂ and Equation 9 is plotted against time,

From here,

의 경우에 대해, μ≤ -(1-h)가 되도록 하는 α는 다음과 같이 구할 수 있다. 여기에서, 반증을 위해 μ(t₂) > -(1-h)라고 가정하고, t₁에서부터 t₂ 까지 λ(t)를 조사하면,

For the case of α, α to be μ ≦ − (1-h) can be obtained as follows. Here, suppose that μ (t ₂ )>-(1-h) for falsification, and investigating λ (t) from t ₁ to t ₂ ,

From here,

Assume that the gain α of the auxiliary loop adjuster 64 of the observer 60 satisfies the inequality such as (19).

By using Equation 19, Equation 20 is arranged, and Substituting Equation 21 here results in Equation 22.

의 경우에 대해서도, 수학식 21과 같은 결과를 얻을 수 있다.The magnitude of λ must be defined as defined above, which means that λ (t ₂ ) = 1 at the boundary of the region, that is, t ₂ , and λ (t ₂ ) <1 becomes a contradiction. λ (t ₂ ) | The relationship ≥ 1-h is always established.

Also in the case of, the same result as in (21) can be obtained.

Since the adaptive integral binary observer 60 does not use the equation of motion, in order to obtain the speed and position information of the motor rotor, an equation for speed and position is required. In the present invention, the Lyapunov function is used to estimate the speed of the motor.

Set the Lyapunov function as shown in Equation 23,

Assuming that the speed of the electric motor is constant within one estimation period, the derivative of Equation 23 can be obtained.

Substituting Equation 11 into Equation 24, the derivative of the Lyapunov function can be written as Equation 25.

From here,

< 0 을 만족해야 한다. 따라서,

< 0 을 만족하도록 하기 위하여 수학식 25로부터 수학식 26 및 27과 같이 두 개의 식으로 분리된다.In order for the system of observer 60 to stabilize, when V > 0 from the Liafnov stability theory,

<0 must be satisfied. therefore,

In order to satisfy <0, two equations (25) and (27) are separated.

If the equation 27 is set to '0' and the inequality of equation 26 is satisfied, the Lyapunov function of equation 23 becomes stable.

The range of k ₁ from the inequality of Equation 26 is the same as Equation 28, and k ₁ must satisfy the condition of Equation 29 because k ₁ must be set to satisfy all of Equation 28.

Equation 27 can be written as follows, and it can be seen that the speed of the motor is related to the information of back EMF and current.

라 근사하여 정리하면, 수학식 31과 같이 전개된다.Θ _r 수학 in equation (30)

If the equation is approximated and summarized, it develops as in Equation (31).

It can be seen that the speed of the rotor can be estimated using Equation 31, and in order to converge the estimated speed quickly and reliably to the actual speed, Equation 31 is proportionally integrated to determine the estimated speed and integrate the estimated position. Calculate

Application to the speed sensorless control operation of the brushless DC motor using the binary observer having the characteristics as described above is designed as shown in Figure 3, as follows.

When the command speed set separately from the speed commander 10 is provided to the speed controller 20, the speed controller 20 transmits a current command value to follow the command speed to the current controller 30.

Then, the current controller 30 obtains an error between the current command value transmitted from the speed controller 20 and the actual current of the brushless DC motor BLDCM detected through the current detector 50 and outputs the error to the power converter 40.

Accordingly, the power converter 40 determines a switching pattern for the current error obtained by the current controller 30, and outputs the voltage adjusted by the determined switching pattern to the brushless DC motor BLDCM.

At this time, the difference (E ₁ ) between the real current detected by the current detector 50 in the adder 61 of the binary observer 60 and the estimated current calculated from the state equation of the brushless DC motor is calculated to be the integrator 62 and the main unit. Supply to loop adjuster 65.

)을 보조루프 조정기(64)로 출력한다.The integrator 62 then integrates the current error E ₁ to increase the dimension of the hyperplane so that the state trace appears in the two-dimensional plane as shown in FIG. 5. The adder 63 adds the output of the integrator 62 and the output of the adder 61 to increase the output value (D) as shown in equation (7).

) Is output to the auxiliary loop adjuster 64.

)을 이용하여 그 출력값(

)이 존재해도 되는 한계영역(G_δ)을 설정하고, 이 설정한 영역(G_δ)으로 들어가면 그 후로 계속 정의되는 영역(G_δ)을 벗어나지 않고 영역(G_δ)내에 머물러 있도록 하는 주루프 조정기(65)의 이득을 조정하여 주루프 조정기(65)를 출력한다.The secondary loop regulator 64 outputs the output of the adder 63

With the output value (

Main loop adjuster which sets the limit region G _δ where) may exist, and stays within the region G _δ without leaving the defined region G _δ after entering the set region G _δ . The gain of 65 is adjusted to output the main loop adjuster 65.

)를 생성하여 이득 조정기(66)로 제공한다.Accordingly, the main loop regulator 65 has a switching function in which the gain α output from the sub loop regulator 64 is adjusted.

) And provide it to the gain adjuster 66.

)의 이득(K)을 조정하여 출력한다.Therefore, the gain adjuster 66 outputs the switching function output from the main loop adjuster 65 so that the error trajectory in the defined area G _δ can converge stably to the origin.

Adjust the gain (K) and output it.

)의 출력으로부터 회전자의 속도 및 위치를 얻는다.This gain-adjusted switching function (

From the output of) we get the speed and position of the rotor.

6 and 7 show the actual velocity (upper), estimated velocity (medium) and velocity estimation error at 1500 [rpm] at no load when the adaptive sliding observer and the adaptive integral binary observer 60 of the present invention are used, respectively. It is a waveform diagram which shows (below), and the unit of a vertical axis with respect to speed is 1000 [rpm / div].

It can be seen that the waveforms of FIGS. 6 and 7 show good estimation performance.

However, in the case of using the adaptive sliding observer, as shown in the waveform of the speed estimation error, it can be seen that the speed error is large. However, when the adaptive integral binary observer 60 of the present invention is used, it can be seen that the estimated speed converges rapidly to the actual speed, and that the speed is accurately estimated before the speed reaches a steady state.

It converges to the current detected at every sample period due to the G _δ constant condition. The error and estimated position generated at this time are substituted into Equation 31 and proportionally integrated to obtain an estimated speed. Equation 31 satisfies the condition that the Liafnov function of Equation 23 is stable, and thus, the velocity estimation error of FIG. 7 converges to zero.

As such, when controlling the electric motor using the adaptive integral binary observer 60 of the present invention, it is possible to solve the vibration phenomenon, which is a reduction of the speed estimation error and a problem of the sliding observer in the steady state.

As described above, the present invention increases the dimension of the observer area by integrating the error between the actual current and the estimated current, thereby stably estimating the speed and position of the motor in a steady state as well as in a transient state in which the speed changes rapidly, and load It also works reliably against changes.

Claims (3)

A speed controller for outputting a current command value to follow the command speed output from the speed commander, a current controller for outputting a current error between the current command value and the actual current flowing through the brushless DC motor, and a switching pattern for the current error. A power converter for determining and supplying the voltage according to the determined pattern to the DC motor, a current detector for sensing a current flowing in the DC motor, and a binary observer for estimating the speed and position of the rotor of the DC motor. In the motor controller: The binary observer has an integral switching plane for integrating the current error to estimate the speed and position of the DC motor rotor, The binary observer, A first adder for calculating an estimated error between an actual current flowing through the DC motor and an estimated current obtained from a state equation; An integrator that integrates the estimated error of the first adder; A second adder for adding an output of the integrator and an estimated error of the first adder; An auxiliary range for setting a limit region of the allowable range for the output of the second adder, and setting a gain of the main loop adjuster so that the estimated error of the first adder stays within the region without leaving this area when the estimated error of the first adder enters the limit region; Loop regulator; A main loop adjuster for outputting a continuous switching function using the output of the auxiliary loop adjuster and the estimated error of the first adder; And a gain adjuster which adjusts the gain of the continuous switching function output from the main loop adjuster so that the error trajectory within the limit region can converge stably to the origin. Permanent magnet synchronous motor controller. delete Detecting a real current flowing through the brushless DC motor; A second step of calculating an estimated current from the state equation of the brushless DC motor; Obtaining an estimated error that is a difference between the actual current and the estimated current; A fourth step of integrating the estimated error and adding the estimated error, and determining a continuous switching function having an integrated switching plane using the addition value; A fifth step of setting a limit region which is an allowable range of the addition value; A sixth step of setting a gain of an auxiliary loop adjuster so that the estimated error does not leave the limit area; A seventh step of determining the switching function by inputting the output of the auxiliary loop regulator whose gain is set in the sixth step; An eighth step of adjusting a gain of the switching function so that the trajectory of the estimated error entering the limit region set in the fifth step may converge to the origin; And And a ninth step of following the speed and position of the brushless DC motor from the switching function whose gain is adjusted in the eighth step.

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