Method for forming extended counter electromotive force observer based on first-order low-pass filter

Abstract

The invention discloses a method for forming an extended counter electromotive force observer based on a first-order low-pass filter. The method comprises the following steps: step A, constructing a state equation based on current as a state quantity according to a mathematical model of a built-in permanent magnet synchronous motor; step B, making a difference between the state equation constructed in the step A and a differential equation, and constructing an error-based state equation; and step C, the state equation constructed in the step B is converted to be consistent with the state equation of the first-order low-pass filter, and PI parameters of a regulator included in the extended counter electromotive force observer designed based on the first-order low-pass filter are obtained. According to the method, the estimation design of the PI parameter by the traditional extended back electromotive force observer is converted into the design of the cut-off frequency of the first-order low-pass filter, the implementation is easier, and the adjustment is simpler and more convenient.

Description

Technical Field

[0001] The invention belongs to the field of power electronics, and in particular relates to speed sensorless vector control of a permanent magnet synchronous motor based on an extended back electromotive force observer. Background Art

[0002] Built-in permanent magnet synchronous motors are widely used in various fields due to their advantages such as high power density, high efficiency and simple structure. In vector control, the motor rotor position information is obtained through the position encoder installed on the motor, which is the basis for realizing coordinate transformation and vector control. However, in the field of wind power generation and new energy, motors usually operate in harsh environments, and the use of encoders will reduce the reliability of the system. In order to improve the reliability of the system, position sensorless technology can be mainly divided into two categories: the first category is the high-frequency signal injection method based on the motor salient pole characteristics. This method is suitable for zero and low speed areas. According to the different injection signals, it can be divided into pulse high-frequency injection method, square wave high-frequency injection method and rotating high-frequency injection method. The other category is the model method based on back-EMF. This method is suitable for medium and high speed areas. The algorithms for observing the rotor position based on back-EMF include model reference adaptive method, Kalman filter method, sliding mode observer method, etc.

[0003] Usually, the traditional back-EMF observer can be equivalent to a low-pass filter, and the estimated position and speed are adjusted by adjusting the PI parameters. The PI parameters of this method need to obtain a range of PI parameter values ​​through the transfer function, taking into account various factors such as system stability. Not only is the amount of calculation large, but the final PI parameters are only a range value, and a certain amount of trial and error is required to determine the PI parameters. Summary of the invention

[0004] The purpose of the present invention is to solve the defects existing in the prior art, and a new back-EMF calculation method is proposed according to the transformation of the state equation of the motor, and the transfer function of the estimated back-EMF is consistent with the transfer function of the first-order low-pass filter. Compared with the traditional extended back-EMF observer, the PI parameters need to be adjusted, and factors such as stability need to be considered. The method of designing an extended back-EMF observer based on a first-order low-pass filter converts the adjustment of the PI parameters into a design problem of the cutoff frequency of the first-order low-pass filter, which greatly simplifies the parameter design process and makes debugging easier. The technical solution adopted by the present invention is as follows:

[0005] The method for forming an extended back electromotive force observer based on a first-order low-pass filter comprises the following steps:

[0006] Step A: constructing a state equation based on current as a state quantity according to a mathematical model of an interior permanent magnet synchronous motor;

[0007] Step B: Subtract the state equation constructed in step A from the differential equation to construct an error-based state equation;

[0008] Step C: The state equation constructed in step B is transformed to be consistent with the state equation of the first-order low-pass filter, and the PI parameters of the regulator included in the extended back-EMF observer are obtained based on the first-order low-pass filter.

[0009] The present invention designs an extended back-electromotive force observer based on a first-order low-pass filter, thereby directly obtaining PI parameters; the present invention converts the estimation design of PI parameters by a traditional extended back-electromotive force observer into the design of the cut-off frequency of a first-order low-pass filter, which is easier to implement and simpler to adjust.

[0010] In some embodiments, step A comprises:

[0011] In order to simplify the analysis, the built-in permanent magnet synchronous motor is selected as the analysis object. The voltage equation of the salient pole permanent magnet synchronous motor in the stator two-phase coordinate system is much more complicated than that of the non-salient pole permanent magnet synchronous motor. Many speed observation methods based on calculating the motor back electromotive force applicable to non-salient pole permanent magnet synchronous motors cannot be directly applied to salient pole permanent magnet motors. The extended back electromotive force method is a solution proposed to address the above problems.

[0012] The difference between surface-mount and built-in permanent magnet synchronous motors is whether the internal magnetic circuit is symmetrical. The internal magnetic circuit of the surface-mount type is symmetrical, and its mathematical model in the stationary coordinate system can be expressed as:

[0013]

[0014] The internal magnetic circuit of the built-in type is asymmetric, and its mathematical model in the stationary coordinate system can be expressed as:

[0015]

[0016] In the formula, u α 、u β They represent the alpha and beta axis components of the stator voltage respectively; Rs represents the stator resistance; p represents the differential operator; i α 、i β Respectively represent the alpha and beta axis components of the stator current; L α , L β Respectively represent the inductance of alpha and beta axes, L αβ is the coupling inductance between alpha and beta; ω e represents the synchronous angular frequency; ψ f represents the flux linkage of permanent magnet;

[0017] The above formula is the mathematical model of IPMSM (internal permanent magnet synchronous motor) based on extended back EMF. The extended back EMF mentioned here includes two parts: one is the back EMF in the traditional sense, which is directly related to the speed of the motor rotor and the size of the magnetic flux generated by the permanent magnet embedded in the rotor; the other is the stator inductance saliency, which makes it easy to link the extended back EMF mathematical model of IPMSM with the speed and position of the motor. Trying to obtain the above back EMF is the basis of the estimation algorithm.

[0018] The mathematical model of the interior permanent magnet synchronous motor needs to be adjusted:

[0019]

[0020] In the formula is the estimated stator current of alpha and beta axes; Respectively represent the alpha and beta axis components of the stator voltage; L d , L q Respectively represent the inductance of d and q axes; ω e represents the synchronous angular frequency; They represent the back electromotive force of alpha and beta axes respectively; Rs represents the stator resistance.

[0021] The extended back EMF cannot be measured, so the difference between the measured current and the estimated current can be used as the input of the observer.

[0022] In some embodiments, step B comprises:

[0023] The first-order state equation is:

[0024]

[0025] The mathematical model of the interior permanent magnet synchronous motor is:

[0026]

[0027] Subtracting the above formula, we get:

[0028]

[0029] In the formula, Represents the error of back electromotive force; e α 、e β It is expressed as the actual back EMF value of alpha and beta axes; It is expressed as the estimated back EMF value of the alpha and beta axes; e is the error between the estimated current and the actual current. By linking the current error with the back EMF, the value of the back EMF can be estimated based on the current error.

[0030] In some embodiments, step C comprises:

[0031] A new calculation formula for back electromotive force is proposed:

[0032]

[0033] Transform the above formula:

[0034]

[0035] According to the error formula, we can transform it into:

[0036]

[0037] Multiply the above formula by K to get:

[0038]

[0039] Where k is the cutoff frequency of the first-order low-pass filter; L s represents inductance; s represents the frequency domain operator.

[0040] The above formula is an extended back-EMF observer based on a first-order low-pass filter design. Compared with the traditional extended back-EMF observer, the setting of PI parameters is greatly simplified and directly converted into the design problem of the cutoff frequency of the first-order low-pass filter. The extended back-EMF observer based on the first-order low-pass filter is essentially a PI regulator, but the PI parameters can be directly obtained: K p =kL s ; K i =kR s Compared with the traditional extended back-EMF observer, whose PI parameters can only be determined by trial and error, the extended back-EMF observer based on LPF improvement is easier to implement and debug.

[0041] The present invention has the following characteristics and advantages: Compared with the traditional extended back-EMF observer, the extended back-EMF observer based on the first-order low-pass filter of the present invention has the following characteristics and advantages: (1) simple structure and easy implementation; (2) PI parameters do not need to go through a complex tuning process, but are converted into the design of the cutoff frequency of the first-order low-pass filter, which greatly simplifies the debugging process. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The variation of estimated back EMF using the traditional extended back EMF observer method;

[0043] Figure 2 The estimated back electromotive force change of the extended back electromotive force observer method based on the first-order low-pass filter of the present invention;

[0044] Figure 3 The estimated speed tracking changes of the traditional extended back-EMF observer method;

[0045] Figure 4 It is the estimated speed tracking change of the novel extended back electromotive force observer method based on the first-order low-pass filter of the present invention;

[0046] Figure 5 The change of estimated back EMF under sudden loading of the traditional extended back EMF observer method;

[0047] Figure 6 This is the change of the estimated back electromotive force during sudden loading according to the extended back electromotive force observer method based on the first-order low-pass filter of the present invention. DETAILED DESCRIPTION

[0048] The present invention is described in detail below with reference to the accompanying drawings.

[0049] Example 1

[0050] The method for forming an extended back-electromotive force observer based on a first-order low-pass filter of the present invention comprises the following steps:

[0051] Step A: constructing a state equation based on the current as a state quantity according to the mathematical model of the interior permanent magnet synchronous motor, so that the back electromotive force is an estimated value;

[0052] In order to simplify the analysis, the built-in permanent magnet synchronous motor is selected as the analysis object. The voltage equation of the salient pole permanent magnet synchronous motor in the stator two-phase coordinate system is much more complicated than that of the non-salient pole permanent magnet synchronous motor. Many speed observation methods based on calculating the motor back electromotive force applicable to non-salient pole permanent magnet synchronous motors cannot be directly applied to salient pole permanent magnet motors. The extended back electromotive force method is a solution proposed to address the above problems.

[0053] The difference between surface-mount and built-in permanent magnet synchronous motors is whether the internal magnetic circuit is symmetrical. The internal magnetic circuit of the surface-mount type is symmetrical, and its mathematical model in the stationary coordinate system can be expressed as:

[0054]

[0055] The internal magnetic circuit of the built-in type is asymmetric, and its mathematical model in the stationary coordinate system can be expressed as:

[0056]

[0057] Where, L α =(Ld +L q ) / 2+(L d -L q )·cos(2θ) / 2,L β =(L d +L q ) / 2-(L d -L q )·cos(2θ) / 2,L αβ =(L d -L q )·sin(2θ) / 2.

[0058] The above formula is the mathematical model of IPMSM based on extended back-EMF. The extended back-EMF mentioned here includes two parts: one is the back-EMF in the traditional sense, which is directly related to the speed of the motor rotor and the size of the magnetic flux generated by the permanent magnet embedded in the rotor; the other is the stator inductance saliency, which makes it easy to link the extended back-EMF mathematical model of IPMSM with the speed and position of the motor. Trying to obtain the above back-EMF is the basis of the estimation algorithm.

[0059] The mathematical model of the interior permanent magnet synchronous motor needs to be adjusted:

[0060]

[0061] In the formula, The extended back EMF cannot be measured, so the difference between the measured current and the estimated current can be used as the input of the observer.

[0062] Step B: Subtract the state equation constructed in A from the differential equation to construct the error-based state equation;

[0063] The first-order state equation is:

[0064]

[0065] The mathematical model of the interior permanent magnet synchronous motor is:

[0066]

[0067] Subtracting the above formula, we get:

[0068]

[0069] e is the error between the estimated current and the actual current; by linking the current error with the back EMF, the value of the back EMF can be estimated based on the current error.

[0070] Step C: A new method for estimating back EMF is proposed. After transformation, the state equation is consistent with the state equation of the first-order low-pass filter. By designing the cutoff frequency, the design of PI parameters is omitted. Compared with the traditional extended back EMF observer, it is easier to implement and debug.

[0071] The present invention proposes a new calculation formula for back electromotive force:

[0072]

[0073] Transform the above formula:

[0074]

[0075] According to the error formula, we can transform it into:

[0076]

[0077] Multiply the above formula by K to get:

[0078]

[0079] The above formula is an extended back-EMF observer based on a first-order low-pass filter design. Compared with the traditional extended back-EMF observer, the setting of PI parameters is greatly simplified and directly converted into the design problem of the cutoff frequency of the first-order low-pass filter. The extended back-EMF observer based on the first-order low-pass filter is essentially a PI regulator, but the PI parameters can be directly obtained: K p =kL s ; K i =kR s Compared with the traditional extended back-EMF observer, whose PI parameters can only be determined by trial and error, the extended back-EMF observer based on LPF improvement is easier to implement and debug.

[0080] Example 2

[0081] Simulation test

[0082] Before simulation verification, in order to reflect the effectiveness of the simulation, the motor parameters of the built-in permanent magnet synchronous motor are as follows: DC bus voltage U dc =550V; stator resistance R s =1.12Ω; permanent magnet ψ f =0.263Wb; d-axis inductance L d =12.52mH; q-axis inductance L q =23.37mH; moment of inertia J = 0.005kg.m 2 ; Pole pair number P n =4.

[0083] like Figure 1As shown in Figure 1, the estimated back EMF changes using the traditional extended back EMF observer method. As can be seen from the figure, the estimated back EMF has a high harmonic content, resulting in a large back EMF estimation error.

[0084] like Figure 2 The figure shows the change of the estimated back EMF of the extended back EMF observer method based on the first-order low-pass filter of the present invention. It can be seen from the figure that the estimated back EMF using the new extended back EMF observer based on the first-order low-pass filter has less harmonic content, the waveform tends to be sinusoidal and the estimation error is greatly reduced.

[0085] Figure 3 The figure shows the estimated speed tracking change of the traditional extended back-EMF observer method. As can be seen from the figure, the speed estimated by the traditional extended back-EMF observer has large jitter, large speed estimation error, and the jitter degree is aggravated when loaded, which increases the estimation error.

[0086] Figure 4 The estimated speed tracking change of the novel extended back electromotive force observer method based on the first-order system filter of the present invention is smooth and has a small error, and the estimation accuracy can still be maintained under load.

[0087] Figure 5 The change of estimated back EMF under sudden loading of the traditional extended back EMF observer method; Figure 6 This is the change of the estimated back electromotive force during sudden loading according to the extended back electromotive force observer method based on the first-order low-pass filter of the present invention.

[0088] Those skilled in the art should understand that the above embodiments are merely exemplary embodiments and that various changes, substitutions, and alterations may be made without departing from the spirit and scope of the present application.

Claims

1. A method for forming an extended back electromotive force observer based on a first-order low-pass filter, characterized in that: The following steps are involved: Step A: constructing a state equation based on current as a state quantity according to a mathematical model of an interior permanent magnet synchronous motor; Step B: Subtract the state equation constructed in step A from the differential equation to construct an error-based state equation; Step C: The state equation constructed in step B is transformed to be consistent with the state equation of the first-order low-pass filter, and the PI parameters of the regulator included in the extended back-EMF observer are obtained based on the first-order low-pass filter.

2. The method for forming an extended back electromotive force observer according to claim 1, characterized in that: The mathematical model of the built-in permanent magnet synchronous motor in step A is expressed as follows: In the formula, u α 、u β They represent the alpha and beta axis components of the stator voltage respectively; Rs represents the stator resistance; p represents the differential operator; i α 、i β Respectively represent the alpha and beta axis components of the stator current; L α , L β Respectively represent the inductance of alpha and beta axes, L αβ is the coupling inductance between alpha and beta; ω e represents the synchronous angular frequency; ψ f represents the flux linkage of permanent magnet; The error-based state equation is expressed as follows: In the formula is the estimated stator current of alpha and beta axes; Respectively represent the alpha and beta axis components of the stator voltage; L d , L q Respectively represent the inductance of d and q axes; ω e represents the synchronous angular frequency; They represent the back electromotive force of alpha and beta axes respectively; Rs represents the stator resistance; It is the stator current input of alpha and beta axis.

3. The method for forming an extended back electromotive force observer according to claim 2, characterized in that: The state equation based on the error in step B is expressed as follows: In the formula, Represents the error of back electromotive force; e α 、e β It is expressed as the actual back EMF value of alpha and beta axes; It is expressed as the estimated back EMF value of alpha and beta axes; e represents the error between the estimated current and the actual current.

4. The method for forming an extended back electromotive force observer according to claim 3, characterized in that: The extended back electromotive force observer in step C is obtained by the following method: The calculation formula of back electromotive force is: Where k is the cutoff frequency of the first-order low-pass filter; L s represents inductance; s represents the frequency domain operator; Transform the above formula: According to the error formula, we can transform it into: Multiply the above formula by K to get:

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