CN107425781A - A SRM Position Prediction Method Based on Linear Flux Model and Linear Regression Analysis - Google Patents

Abstract

The invention discloses an SRM position estimation method based on a linear flux linkage model and linear regression analysis. This method only needs the flux linkage characteristic data at any two rotor positions in the linear region, so as to obtain the flux linkage values at the two ends of the linear region and use it as a reference. Detect the conduction phase voltage and current value, and calculate the flux linkage value. If the value is between two reference flux linkage values, indicating that the rotor position is in the linear region, the linear flux linkage model is used for position estimation. Otherwise, it indicates that the rotor position is in the nonlinear region. On the premise that the motor speed is constant in a short period of time, linear regression analysis is performed on the position data and sampling numbers in the linear region, and then used to estimate the rotor position in the nonlinear region. To further reduce the cumulative error in single-phase estimation, multi-phase flux linkage characteristics can be used instead of single-phase flux linkage characteristics for position estimation. The method has the advantages of high precision, easy realization and good applicability, and can avoid or reduce the influence of mutual inductance between phases and saturation of magnetic circuit.

Description

A SRM Position Prediction Method Based on Linear Flux Model and Linear Regression Analysis

technical field

The invention relates to an accurate position estimation method of a switched reluctance motor (SRM) based on a linear flux model and linear regression analysis, and belongs to the field of motor position sensorless control.

Background technique

Position information is fundamental to the operation of switched reluctance motors. Usually, position information is obtained by mechanical position sensors, such as resolvers, Hall sensors, photoelectric encoders, etc. However, these mechanical position sensors not only increase the cost and complexity of the drive system, but also their accuracy and reliability are easily affected by environmental factors such as temperature, dust and vibration. Therefore, it is very necessary to study a position sensorless control method with low cost, high precision and high reliability.

In order to realize position sensorless control, researchers have proposed a large number of position estimation methods. These methods are mainly divided into two categories: one is the position estimation method of the non-conducting phase, and the other is the position estimation method of the conducting phase.

The first type of method mainly determines the inductance value of the unsaturated region by injecting high-frequency voltage pulses into the non-excitation phase and detecting the amplitude or rise time of the current, and then obtains the rotor position value or the region where it is located. The disadvantages of this type of method are: when there is current in other phases, the pulse current injected into the phase may be affected by other interactions; the pulse current injected into the non-conductive phase may generate negative torque; in addition, at high speed, the excitation current waveform occupies The main part of the entire phase cycle, limiting the time of pulse injection. Therefore, this type of method is only suitable for starting and low-speed conditions.

The second type of method mainly estimates the rotor position through look-up tables, mathematical models, observers or intelligent algorithms based on the measured excitation phase voltage and current values. The advantage of this type of method is that neither additional power loss is generated nor additional hardware is required. However, most of the existing conduction phase position estimation methods require the flux linkage characteristic data at all or many rotor positions, which increases the difficulty and workload of data acquisition and processing, and often requires a large storage space. In addition, the prediction accuracy of this type of method is easily affected by the mutual inductance between phases and magnetic field saturation.

Contents of the invention

The invention divides the relationship curve between the phase flux linkage and the rotor position of the switched reluctance motor into two regions, and uses a linear flux model and a linear regression analysis for different regions to estimate the rotor position. The technical solution is as follows:

Step 1: In the relationship curve between the phase flux linkage and the rotor position of the switched reluctance motor, define the interval [θ ₁ ,θ _hr ] as the linear region, and the remaining intervals as the nonlinear region. θ ₁ and θ _hr can be obtained by formulas (1) and (2).

θ ₁ ＝θ _a -(β _s +β _r )/2 (1)

θ _hr = θ _a -β _r /2 (2)

where θ _a , β _s and β _r are the alignment position, stator pole arc and rotor pole arc of the motor, respectively.

Obtain the flux linkage characteristic data ψ _x and ψ _y at any two rotor positions θ _x and θ _y in the linear region, and obtain the flux linkage characteristics at the two end points of the linear region by formula (3), where ψ is the phase flux linkage , θ is the rotor position, and the analytical expressions of phase flux linkage and phase current at the endpoints are obtained by fitting.

Step 2: Detect the conduction phase voltage and current value, use the analytical expressions of flux linkage and phase current obtained in the previous step to obtain the flux linkage values ψ ₁ and ψ _hr at the end points of the linear region at this time, and set them as the reference magnetic flux chain.

Use formula (4) to calculate the phase flux linkage value at this time.

Among them, ψ(0) is the initial flux linkage, u, i and r are the phase voltage, phase current and phase resistance of the switched reluctance motor, respectively.

Step 3: If ψ ₁ ≤ψ≤ψ _hr , it means that the rotor position is in the linear region, then the rotor position angle can be obtained through the linear flux linkage model, as shown in formula (5).

Step 4: If ψ ₁ ≤ψ≤ψ _hr is not satisfied, it indicates that the rotor position is in the nonlinear region. At this time, under the assumption that the motor speed is constant in a short period of time, perform linear regression analysis on the position data and sampling numbers in the linear region to determine The coefficients of the unary linear regression function shown in formula (6) are used to estimate the rotor position in the nonlinear region.

in, is the estimated value of the rotor position at the kth sampling point, and k is the number of the sampling point. is a coefficient, which can be calculated by formula (7) based on the data in the linear region.

Among them, θ _k is the rotor position value at the kth sampling point in the linear region.

Step 5: If it is necessary to further reduce the cumulative error introduced when estimating the rotor position in the nonlinear region, multi-phase flux linkage characteristics can be used instead of single-phase flux linkage characteristics for estimation. The principle of phase selection is: use the linear region of each phase to shorten the nonlinear region in single-phase estimation.

Beneficial effects of the present invention: ①The method is simple and easy to realize. Using a simple linear model, only two flux linkage characteristic data at two rotor positions are required, and only a small amount of physical memory is required; ② High precision and strong robustness. The flux linkage characteristics in the linear region have high resolution, low sensitivity to flux linkage errors, and can effectively avoid phase-to-phase mutual inductance and reduce the influence of magnetic circuit saturation on the estimated results. In addition, the cumulative error is reduced through the multi-phase estimation method; ③ the applicability is good. Angular position control, current chopping control and voltage PWM control all have good accuracy and are also suitable for different switched reluctance motor topologies.

Description of drawings

Figure 1 is a curve diagram of the relationship between the single-phase flux linkage and the rotor position of the switched reluctance motor under a certain current.

Fig. 2 is a graph showing the relationship between three-phase flux linkage and rotor position of a three-phase switched reluctance motor under a certain current.

Fig. 3 is a flow chart of the SRM position estimation method based on the linear flux linkage model and linear regression analysis.

detailed description

The technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and specific examples. The motor used in the example is a 1kW three-phase 12/8-pole switched reluctance motor.

Step 1: In the relationship curve between the single-phase flux linkage and the rotor position of the switched reluctance motor under a certain current shown in Figure 1, the linear region [θ ₁ ,θ _hr ] is defined as the linear region, and the remaining interval is the nonlinear region. For the example given switched reluctance motor, β _s , β _r and θ _a are 15°, 17° and 22.5°, respectively. From formulas (1) and (2), it can be concluded that θ ₁ and θ _hr are 6.5° and 14°, respectively.

The flux linkage characteristic data of the switched reluctance motor at 7.5° and 15° can be easily obtained by using the torque balance test method. Since 15° is close to 14°, [6.5°, 15°] is selected as the linear region, and the rest is a non-linear region. The flux linkage at 6.5° can be obtained by formula (8):

The analytical expressions ψ _6.5° (i) and ψ _15° (i) of flux linkage ψ _6.5° and ψ _15° and phase current i are obtained by fitting.

Step 2: Detect the conduction phase voltage and current value, and use the analytical expressions ψ _6.5° (i) and ψ _15° (i) obtained by fitting in the previous step to obtain the flux linkage value ψ _6.5° at the end of the linear region at this time (i ^* ) and ψ _15° (i ^* ), and set as the reference flux linkage, where i ^* is the phase current value at this time. At the same time, the phase flux linkage value ψ(i ^* ) at this time is calculated by using formula (4).

Step 3: If ψ _6.5° (i ^* )≤ψ(i ^* )≤ψ _15° (i ^* ), it indicates that the rotor position is in the linear region, and the rotor position angle can be obtained through the linear flux linkage model, as shown in formula (9) shown.

Step 4: If ψ _6.5° (i ^* )≤ψ(i ^* )≤ψ _15° (i ^* ) is not satisfied, it indicates that the rotor position is in the nonlinear region. The serial number of the sampling point, the coefficient can be obtained from formula (7) with Then substitute into the unary linear regression function shown in formula (6), and use this formula to predict the rotor position at different sampling points in the nonlinear region.

Step 5: In order to further reduce the cumulative error introduced when estimating the position of the nonlinear region, the three-phase flux linkage characteristic is used instead of the single-phase flux linkage characteristic for estimation. According to the selection principle, formulate a phase selection strategy, as shown in Table 1.

In Table 1, ψ _ref is a given reference flux linkage, and ψ _ref =ψ _6.5° is selected in this example. In addition, when the three-phase flux linkage values are greater than _ψref , the selected phase remains unchanged. In the relationship curve between the three-phase flux linkage and the rotor position of the three-phase switched reluctance motor under a certain current shown in Figure 2, the thick solid line represents the part of each phase involved in position estimation determined according to Table 1.

Table 1. A phase selection strategy

In Table 1, ψ _ref is a given reference flux linkage, and ψ _ref =ψ _6.5° is selected in this example. In addition, when the three-phase flux linkage values are greater than _ψref , the selected phase remains unchanged. In the relationship curve between the three-phase flux linkage and the rotor position of the three-phase switched reluctance motor under a certain current shown in Figure 2, the thick solid line represents the part of each phase involved in position estimation determined according to Table 1.

The flowchart of the SRM position estimation method based on the linear flux linkage model and linear regression analysis is shown in FIG. 3 .

Claims (6)

1. A SRM position estimation method based on linear flux linkage model and linear regression analysis, characterized in that: the relationship curve of switched reluctance motor (SRM) phase flux linkage and rotor position is divided into two regions, and for different The region adopts the linear flux linkage model and linear regression analysis to estimate the rotor position respectively. The implementation steps of the position estimation method are as follows: Step 1: In the relationship curve between the phase flux linkage and the rotor position of the switched reluctance motor, define the interval [θ ₁ ,θ _hr ] as the linear region, and the remaining intervals as the nonlinear region, and obtain the two endpoints of the linear region θ ₁ and θ The flux linkage characteristics at _hr , and the analytical expressions of the phase flux linkage and phase current at the endpoints are obtained by fitting; Step 2: Detect the conduction phase voltage and current value, use the analytical expressions of flux linkage and phase current obtained in the previous step to obtain the flux linkage values ψ ₁ and ψ _hr at the end points of the linear region at this time, and set them as the reference magnetic flux chain, and calculate the phase flux linkage value ψ at this time; Step 3: If ψ ₁ ≤ψ≤ψ _hr , indicating that the rotor position is in the linear region, the linear flux model can be used to estimate the rotor position; Step 4: If ψ ₁ ≤ψ≤ψ _hr is not satisfied, it indicates that the rotor position is in the nonlinear region. At this time, under the assumption that the motor speed is constant in a short period of time, perform linear regression analysis on the position data and sampling numbers in the linear region to determine The coefficient of the unary linear regression function is used to estimate the rotor position in the nonlinear region; Step 5: If it is necessary to further reduce the cumulative error introduced in the estimation of the rotor position in the nonlinear region, the multi-phase flux linkage characteristics can be used instead of the single-phase flux linkage characteristics for estimation. The principle of phase selection is: use the linear region of each phase, Shorten the non-linear region during single-phase estimation. 2. a kind of SRM position estimation method based on linear flux linkage model and linear regression analysis according to claim 1, it is characterized in that: two endpoints θ ₁ and θ _hr of linear region described in step 1 can be respectively by formula θ ₁ = θ _a -(β _s + β _r )/2 and θ _hr = θ _a - β _r /2 are calculated, where θ _a , β _s and β _r are the alignment position of the motor, the stator pole arc and the rotor polar arc. 3. a kind of SRM position estimation method based on linear flux linkage model and linear regression analysis according to claim 1, is characterized in that: the flux linkage characteristic at two endpoints θ ₁ and θ _hr of the linear region described in step 1 is through the formula Calculated, where ψ is the phase flux linkage, θ is the rotor position, ψ _x and ψ _y are the flux linkage characteristic data at any two rotor positions θ _x and θ _y in the linear region. 4. a kind of SRM position estimation method based on linear flux linkage model and linear regression analysis according to claim 1, is characterized in that: the phase flux linkage characteristic described in step 2 is by formula Calculated, where ψ(0) is the initial flux linkage, u, i and r are the phase voltage, phase current and phase resistance of the switched reluctance motor, respectively. 5. a kind of SRM position estimation method based on linear flux linkage model and linear regression analysis according to claim 1, it is characterized in that: the rotor position estimation based on linear flux linkage model described in step 3 can be expressed as formula 6. a kind of SRM position estimation method based on linear flux linkage model and linear regression analysis according to claim 1, is characterized in that: the linear regression function described in step 4 can be expressed as in, is the estimated value of the rotor position at the kth sampling point, k is the serial number of the sampling point, As a coefficient, it can be based on the data in the linear zone, by the formula Calculated, where, θ _k is the rotor position value at the kth sampling point in the linear region.