A modeling method for switched reluctance motor based on polynomial Fourier series

Abstract

This invention relates to a switched reluctance motor (SRM) modeling method based on a polynomial Fourier series. This method obtains the SRM's torque, current, flux, and rotor position characteristics through offline measurements and constructs a data table. The data table is then fitted using a derived polynomial Fourier series formula and the data fitting tool cftool. This method replaces the traditional complex and cumbersome data table with a small number of coefficients, modeling the SRM using a polynomial Fourier series equation. Simulations have demonstrated that this method not only effectively reduces storage space usage but also achieves high accuracy, facilitating the practical application of SRMs.

Description

Technical Field

[0001] The present invention belongs to the field of motor control and relates to a switched reluctance motor modeling method based on polynomial Fourier series. Background Art

[0002] With the advancement of technology, many aircraft systems driven by hydraulic, mechanical, and pneumatic devices have been converted to electric drives. While simplifying aircraft powertrains, this also places stringent demands on the stability and robustness of the drive motors. The switched reluctance motor, with its simple structure, excellent stability, and high-temperature resistance, has made it a strong contender in the aviation motor market.

[0003] High-performance, robust control of switched reluctance motors (SRMs) requires precise modeling of their torque and current characteristics. However, the nonlinearity caused by magnetic circuit saturation, eddy currents, and hysteresis effects in SRMs makes mathematical simulation of their magnetic torque and current characteristics difficult. Traditionally, these characteristics have been described using data tables. During experiments with SRM speed control, the applicant discovered that the data tables used for SRM modeling took up a significant amount of storage space, increasing the motor's control costs and posing challenges to large-scale practical application. Summary of the Invention

[0004] Technical problems to be solved

[0005] To overcome the shortcomings of existing technologies, this paper proposes a switched reluctance motor (SRM) modeling method based on a polynomial Fourier series. The method first measures the SRM's flux linkage, rotor position, current, and torque characteristics, constructing a traditional data table. This data table is then described using a polynomial Fourier series model. This replaces the traditional complex and cumbersome data table with a small number of coefficients, allowing the SRM to be modeled using a polynomial Fourier series equation. This method not only effectively reduces storage space usage but also achieves high accuracy, thus promoting the practical application of SRMs.

[0006] Technical Solution

[0007] A switched reluctance motor modeling method based on polynomial Fourier series, characterized by comprising the following steps:

[0008] Step 1: Measure the torque characteristics, current characteristics, flux characteristics and rotor position characteristics of the switched reluctance motor and construct a data table i ph (θ ph ,ψ ph ), T ph (θ ph ,ψ ph );where θ ph is the rotor position, iph is the phase current value, ψ ph is the phase flux linkage value, T ph is the motor output torque;

[0009] Step 2: Provide a torque model in the form of a polynomial Fourier series:

[0010]

[0011] The coefficients a kj , where k = 1, 2, 3, 4, j = 1, 2, 3, 4 are obtained by using the fitting tool cftool to fit the data table T ph (θ ph , ψ ph );

[0012] where: M, N are the orders of the Fourier series equation, θ ph is the rotor position, ψ ph is the phase flux linkage value, T ph is the motor output torque;

[0013] Step 3: Provide a current model in the form of a polynomial Fourier series:

[0014]

[0015] The coefficients b kj , where k = 1, 2, 3, 4, j = 1, 2, 3, 4 are obtained by using the fitting tool cftool to fit the data table i ph (θ ph , ψ ph );

[0016] where M, N are the orders of the Fourier series equation, θ ph is the rotor position, i ph is the phase current value, ψ ph is the phase flux linkage value.

[0017] In the said Step 2 M = 4, N = 4.

[0018] In the said Step 3 M = 4, N = 4.

[0019] Beneficial effects

[0020] This paper proposes a polynomial Fourier series-based switched reluctance motor modeling method. This method obtains the switched reluctance motor's torque, current, flux, and rotor position characteristics through offline measurements and constructs a data table. This data table is then described using a polynomial Fourier series model. This method uses a polynomial Fourier series formula to model the switched reluctance motor, simplifying the model and reducing the model's memory requirements. Simulations have verified the effectiveness of this method, demonstrating its simplicity, ease of implementation, and high modeling accuracy. This method effectively reduces the application cost of switched reluctance motors and promotes their practical application. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 The motor torque simulation diagram output by the traditional data table model and the polynomial Fourier series model proposed by the present invention;

[0022] Figure 2 The motor phase current simulation diagrams are output by the traditional data table model and the polynomial Fourier series model proposed by the present invention;

[0023] Figure 3 The motor torque error and phase current error diagrams are output by the traditional data table model and the polynomial Fourier series model proposed in this invention. DETAILED DESCRIPTION

[0024] The present invention will now be further described with reference to the embodiments and accompanying drawings:

[0025] The motor used in this example is a 1kW three-phase 12 / 8-pole switched reluctance motor.

[0026] Step 1: Measure the torque characteristics, current characteristics, flux characteristics and rotor position characteristics of the switched reluctance motor and construct a data table ψ ph (θ ph ,i ph ),i ph (θ ph ,ψ ph ), T(θ ph ,ψ ph );where θ ph is the rotor position, i ph is the phase current value, ψ ph is the phase flux value, T ph Output torque for the motor;

[0027] Step 2: The torque characteristic of the switched reluctance motor is assumed to be in the form of a sinusoidal Fourier series. By simplifying the original Fourier series formula

[0028]

[0029] Available

[0030]

[0031] Further a(θ ph ) is simplified to a fourth-order polynomial about the rotor position, and finally the torque modeling formula based on the polynomial Fourier series given by the present invention can be obtained:

[0032]

[0033] Use the fitting tool cftool to fit the data table T(θ obtained in step 1 ph ,ψ ph ), and obtain the coefficient a of the torque modeling formula kj Numeric value;

[0034] in M=4, N=4 is the order of the Fourier series, θ ph is the rotor position, i ph is the phase current value, ψ ph is the phase flux value, T ph is the motor output torque, a(θ ph ) is the rotor position θ ph function;

[0035] Step 3: Similar to the torque characteristic formula based on the polynomial Fourier series derived in step 2, the current modeling formula is given

[0036]

[0037] Use the fitting tool cftool to fit the data table i obtained in step 1 ph (θ ph ,ψ ph ), the coefficient b of the current characteristic modeling formula can be obtained kj ;

[0038] in is the coefficient of the Fourier series obtained by fitting, M=4, N=4 is the order of the Fourier series, θ ph is the rotor position, i ph is the phase current value, ψ ph is the phase flux linkage value.

[0039] Take the motor running at 1000rpm as an example. Figure 1 The figure shows a comparison of the motor torque output by the traditional data table and the motor torque value output by the polynomial Fourier series model proposed in the present invention. Figure 2 The figure is a comparison chart of the motor current output by the traditional data table and the motor current value output by the polynomial Fourier series model proposed in the present invention. Figure 3The figure shows the difference between the motor current and torque values output by the traditional data table and the polynomial Fourier series model proposed in the present invention. As can be seen from the figure, the output value of the polynomial Fourier series model proposed in the present invention is very close to the output value of the traditional data table model. The maximum current difference in one cycle is 1.7A, and the maximum torque difference is 0.5N / m. It can be seen that the method proposed in the present invention maintains a high accuracy while greatly reducing the storage requirements.

[0040] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A switched reluctance motor modeling method based on polynomial Fourier series, characterized by: The following steps are involved: Step 1: Measure the torque characteristics, current characteristics, flux characteristics and rotor position characteristics of the switched reluctance motor and construct a data table i ph (θ ph ,ψ ph ), T ph (θ ph ,ψ ph );where θ ph is the rotor position, i ph is the phase current value, ψ ph is the phase flux value, T ph Output torque for the motor; Step 2: Give the torque model in the form of a polynomial Fourier series: The coefficient a in the torque model kj ,k=1,2,3,4,j=1,2,3,4 is obtained by: using the fitting tool cftool to fit the data table T ph (θ ph ,ψ ph ); Where: M, N are the orders of the Fourier series equation, θ ph is the rotor position, ψ ph is the phase flux value, T ph Output torque for the motor; Step 3: Give the current model in the form of a polynomial Fourier series: The coefficient b in the current model kj , for k = 1, 2, 3, 4, j = 1, 2, 3, 4, the calculation is as follows: Use the fitting tool cftool to fit the data table i ph (θ ph , ψ ph ); Where M and N are the orders of the Fourier series equation, θ ph is the rotor position, i ph is the phase current value, ψ ph is the phase flux linkage value.

2. The switched reluctance motor modeling method based on polynomial Fourier series according to claim 1, characterized in that: In step 2 M=4,N=4.

3. The method for representing switched reluctance motor characteristics based on polynomial Fourier series according to claim 1, characterized in that: In step 3 M=4,N=4.

Images