Linear reluctance motor single-frequency hysteresis nonlinear modeling method based on phase shift rational basis

Abstract

The invention discloses a linear reluctance motor single-frequency hysteresis nonlinear modeling method based on a phase shift rational basis, and relates to the technical field of ultra-precision motion control. Firstly, mechanism analysis is performed on a hysteresis loop between input current and output magnetic flux of the linear reluctance motor, modeling is performed based on a phase shift rational basis, then a hysteresis phenomenon between the input current and the output magnetic flux of the linear reluctance motor is decomposed and divided into an ascending part and a descending part, and the descending part is divided into a descending part and a descending part. And finally, performing parameter estimation by using a least square algorithm. The complexity of the hysteresis model can be simplified, the to-be-identified parameters of the hysteresis model can be reduced, the identification difficulty of the hysteresis model can be reduced, the hysteresis phenomenon at the turning point can be modeled more accurately, and the precision of the hysteresis model of the linear reluctance motor can be improved.

Description

Technical Field

[0001] The invention relates to the technical field of ultra-precision motion control, and in particular to a single-frequency hysteresis nonlinear modeling method for a linear reluctance motor based on a phase-shift rational basis. Background Art

[0002] In compliance with Moore's Law in the semiconductor industry, in order to meet the stringent requirements of future high-precision, short-stroke industrial motion systems in terms of production volume and accuracy, it is necessary to develop actuators that can effectively provide high output density. The currently proposed actuator based on magnetic resistance, namely the linear reluctance motor, can provide higher output density and lower energy dissipation, but its output has complex nonlinearity, and its complex nonlinearity problem must be solved before it can be effectively applied to nano-precision positioning scenarios.

[0003] From a control perspective, the main force nonlinearities include the inherent quadratic nonlinearity between current and force, the position dependence of the force, and the rate-dependent hysteresis nonlinearity of the ferromagnetic core. Therefore, a comprehensive study of control methods must be conducted to achieve consistent and accurate nanopositioning forces, and addressing the hysteresis phenomenon in soft ferromagnetic materials becomes critical as it becomes more prominent. An effective method for compensating for magnetization hysteresis is to use the inverse model of the hysteresis model, so it is critical to accurately model the hysteresis phenomenon.

[0004] Domestic and foreign scholars have studied the hysteresis nonlinearity of reluctance motors. For this type of complex hysteresis nonlinearity, a variety of models have been developed and studied. According to different modeling principles, it is mainly divided into two categories: physical hysteresis model and phenomenological hysteresis model. The physical hysteresis model is a model established using physical laws. It describes hysteresis based on the physical properties and structure of the material itself. The Jiles-Atherton model and the Maxwell model are both typical physical hysteresis models. However, since the models established based on physical laws are relatively complex, the calculation is difficult, and the modeling accuracy is limited, they are generally difficult to apply to actual control systems. The phenomenological hysteresis model is a model established to describe the hysteresis phenomenon of the material. According to the input and output data obtained from the experiment, various intelligent algorithms are used to identify the parameters in the model, so that various actual hysteresis systems can be simulated, but it will ignore the physical properties and structure of the material itself, such as the Duhem model, the Bouc-Wen model, the Preisach model, etc. At present, these existing models generally have the disadvantages of complex models, many parameters to be identified, and the hysteresis model is not accurate enough when the current is reversed, that is, at the turning point.

[0005] An invention patent application with publication number CN117130276A, publication date November 28, 2023, and name “A piezoelectric ceramic hysteresis compensation method based on Duhem hysteresis model” provides a piezoelectric ceramic hysteresis compensation method. This method uses the inverse model of the Duhem model for feedforward control to achieve compensation for the hysteresis characteristics of piezoelectric ceramics. However, the Duhem model in this patent has many parameters to be identified, and the identification is difficult.

[0006] An invention patent application with publication number CN115857311A, publication date March 28, 2023, and name “A hysteresis compensation control method for a micro-vibration suppression platform” provides a hysteresis compensation control method for a micro-vibration suppression platform. The method introduces a frequency factor, improves the Bouc-Wen model, and uses it as a feedforward control, which can improve the dynamic performance and steady-state accuracy of the micro-vibration suppression platform. This patent is more accurate than the Bouc-Wen model, but it is not a model established for the hysteresis phenomenon of linear reluctance motors. The model establishment at the turning point is not accurate enough and is not suitable for hysteresis compensation of linear reluctance motors. Summary of the invention

[0007] In order to solve the problems that the physical hysteresis model has a complex structure and many parameters to be identified, and the phenomenological hysteresis model ignores the mechanism, resulting in inaccurate model establishment, the present invention provides a single-frequency hysteresis nonlinear modeling method for a linear reluctance motor based on a phase-shift rational basis, which can simplify the complexity of the hysteresis model, reduce the parameters to be identified in the hysteresis model, reduce the difficulty of identifying the hysteresis model, and can more accurately model the hysteresis phenomenon at the turning point, thereby improving the accuracy of the hysteresis model of the linear reluctance motor.

[0008] To achieve the above object, the present invention adopts the following technical solution: a linear reluctance motor single-frequency hysteresis nonlinear modeling method based on phase shift rational basis, comprising the following steps:

[0009] Step 1: Analyze the mechanism of the hysteresis loop between the input current and output flux of the linear reluctance motor and model it based on the phase shift rational basis;

[0010] The expression of the output flux signal B is expanded as follows:

[0011]

[0012] In the formula, A 1 represents the amplitude of the output magnetic flux, w represents the angular frequency, t represents the time, represents the phase difference between the input current and the output magnetic flux, Δ represents the error interference term of the output magnetic flux, and I represents the input current signal;

[0013] Among them Taylor expansion of the term:

[0014]

[0015] Then the expression of the output flux signal B is written as:

[0016]

[0017] Rewrite it as:

[0018] B=aI 4 +bI 2 +cI+d (5)

[0019] in,

[0020] Step 2: Decompose the hysteresis phenomenon between the input current and the output magnetic flux of the linear reluctance motor into a rising part and a falling part;

[0021] The rising and falling parts of the hysteresis loop are symmetrical about the origin. Assuming formula (5) is the output flux expression of the rising part, the output flux expression of the falling part is:

[0022]

[0023] Order I d = -I, B d = -B, then we get a d =-a, b d =-b,c d =c,d d =d;

[0024] Step 3: Use the least squares algorithm to estimate parameters;

[0025] First, the input and output data of the linear reluctance motor are collected, and then decomposed into the rising part and the falling part. Assume that there are n sampling points and the input current is recorded as I = [I 1 ,I 2 ,...,I n ] T , the output flux is recorded as B = [B 1 ,B 2 ,...B n ] T , then formula (5) is written in matrix form as follows:

[0026]

[0027] The input matrix [I 0 I 1 I 2 I 4] is recorded as X, the coefficient matrix [abcd] T Denoted as A, formula (8) is written as:

[0028] XA=B (11)

[0029] The least squares method is used to estimate the parameters of the rising part of the hysteresis loop, and the estimated value of the coefficient matrix is ​​obtained. as follows:

[0030]

[0031] Replace the input matrix X and output matrix B of the ascending part with the input matrix X of the descending part respectively d And the output matrix B d , get the estimated value of the coefficient matrix of the descending part The single-frequency hysteresis nonlinear model of the linear reluctance motor based on the phase-shift rational basis can be obtained.

[0032] Furthermore, the input current signal and the output magnetic flux signal have the same angular frequency, different amplitudes and a phase difference.

[0033] Furthermore, the input current signal I=A 0 sin(wt), where A 0 Indicates the amplitude of the input current.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention first models the hysteresis characteristics with a phase-shift rational basis according to the mechanism of the hysteresis loop, and then divides the hysteresis loop into a rising part and a falling part according to the hysteresis loop phenomenon, and models the two parts respectively, and utilizes mechanism analysis and phenomenon decomposition to accurately model the hysteresis nonlinearity of the linear reluctance motor, and estimates the model parameters using the least squares method, which can simplify the complexity of the hysteresis model, reduce the parameters to be identified in the hysteresis model, and reduce the difficulty of identifying the hysteresis model. At the same time, by modeling the mechanism and phenomenon of the linear reluctance motor, the hysteresis phenomenon at the turning point can be more accurately modeled, thereby improving the accuracy of the hysteresis model of the linear reluctance motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flowchart of the present invention;

[0036] Figure 2 is a physical picture of the linear reluctance motor motion platform established in the embodiment;

[0037] Figure 3 It is an implementation effect diagram obtained in the embodiment. DETAILED DESCRIPTION

[0038] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0039] like Figure 1 As shown, the single-frequency hysteresis nonlinear modeling method of the linear reluctance motor based on the phase-shift rational basis includes the following steps:

[0040] Step 1: Analyze the mechanism of the hysteresis loop between the input current and output flux of the linear reluctance motor and model it based on the phase shift rational basis. Specifically:

[0041] Input current signal I = A 0 sin(wt), output flux signal The input current signal and the output flux signal have the same angular frequency, different amplitude and phase difference, where A 0 Indicates the amplitude of the input current, A 1 represents the amplitude of the output magnetic flux, w represents the angular frequency, t represents the time, It represents the phase difference between input current and output magnetic flux, and Δ represents the error interference term of output magnetic flux.

[0042] The expression of the output flux signal B is expanded as follows:

[0043]

[0044] Among them Taylor expansion of the term:

[0045]

[0046] Among them, o(I 6 ) indicates I 6 Ignoring the higher-order infinitesimals of , we can get:

[0047]

[0048] Then the expression of the output flux signal B is written as:

[0049]

[0050] Then, let Then the expression of the output flux signal B can be rewritten as:

[0051] B=aI 4 +bI 2 +cI+d (5)

[0052] That is, the output flux signal B can be approximately regarded as a quadratic polynomial about the input current signal I.

[0053] Step 2: Decompose the hysteresis phenomenon between the input current and the output magnetic flux of the linear reluctance motor into the rising part and the falling part. Specifically:

[0054] Ideally, the hysteresis loop is centrally symmetrical, so the rising part and the falling part are centrally symmetrical about the origin. If formula (5) is used as the output flux expression of the rising part, the output flux expression of the falling part can be set as:

[0055]

[0056] Since the ascending part and the descending part are symmetrical about the origin, let I d = -I, B d = -B, then we can get a d =-a, b d =-b,c d =c,d d =d.

[0057] Step 3: Use the least squares algorithm to estimate parameters, specifically:

[0058] First, the input and output data of the linear reluctance motor are collected, and then the data is processed and decomposed into the rising part and the falling part. The least squares method is used to estimate the parameters of the rising part of the hysteresis loop. Assuming that there are n sampling points in the rising part, the sampled data is written in matrix form, and the input current is recorded as I = [I 1 ,I 2 ,...,I n ] T , the output flux is recorded as B = [B 1 ,B 2 ,...B n ] T , then formula (5) can be written in matrix form as follows:

[0059]

[0060] Right now:

[0061]

[0062] The input matrix [I 0 I 1 I 2 I 4 ] is recorded as X, that is:

[0063] X=[I 0I 1 I 2 I 4 ] (9)

[0064] The coefficient matrix [abcd] T Denoted as A, that is:

[0065]

[0066] Then formula (8) can be written as:

[0067] XA=B (11)

[0068] According to the least squares method, we can get the estimated value of the coefficient matrix as follows:

[0069]

[0070] Similarly, replace the input matrix X and output matrix B of the ascending part with the input matrix X of the descending part respectively. d And the output matrix B d , get the estimated value of the coefficient matrix of the descending part The single-frequency hysteresis nonlinear model of the linear reluctance motor based on the phase-shift rational basis can be obtained through the above process.

[0071] Example

[0072] In this embodiment, a linear reluctance motor motion platform is established. Figure 2 As shown, the motion platform is composed of a voice coil motor, a grating ruler, an air floating guide rail, a reluctance motor and its supporting device. Among them, the linear reluctance motor is the modeling object of the method of the present invention, which is composed of an I-type mover and an E-type stator. The voice coil motor is responsible for positioning the I-type mover of the linear reluctance motor, the optical ruler is used for position signal measurement, the E-type stator is connected and fixed to the supporting device, and the I-type mover is connected to the guide rail and moves with the guide rail.

[0073] according to Figure 1 The process shown in the figure first establishes a polynomial hysteresis model with four parameters to be identified. Then, the motion platform is positioned using a voice coil motor. The input current frequency data of 10 Hz is collected and decomposed into the rising part and the falling part. The least squares algorithm is used for parameter identification. The implementation effect is combined with Figure 3 As shown in the figure, it can be seen that the identified model can fit the measured data well, and the fitting effect at the turning point is also ideal, which verifies that the modeling method of the present invention has the advantages of fewer model parameters and high model accuracy.

[0074] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0075] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A single-frequency hysteresis nonlinear modeling method for a linear reluctance motor based on a phase-shift rational basis, characterized by: The following steps are involved: Step 1: Analyze the mechanism of the hysteresis loop between the input current and output flux of the linear reluctance motor and model it based on the phase shift rational basis; The expression of the output flux signal B is expanded as follows: In the formula, A1 represents the amplitude of the output magnetic flux, w represents the angular frequency, and t represents the time. represents the phase difference between the input current and the output magnetic flux, Δ represents the error interference term of the output magnetic flux, and I represents the input current signal; Among them Taylor expansion of the term: Then the expression of the output flux signal B is written as: Rewrite it as: B=aI 4 +bI 2 +cI+d (5) in, Step 2: Decompose the hysteresis phenomenon between the input current and the output magnetic flux of the linear reluctance motor into a rising part and a falling part; The rising and falling parts of the hysteresis loop are symmetrical about the origin. Assuming formula (5) is the output flux expression of the rising part, the output flux expression of the falling part is: Order I d = -I, B d = -B, then we get a d =-a, b d =-b,c d =c,d d =d; Step 3: Use the least squares algorithm to estimate parameters; First, the input and output data of the linear reluctance motor are collected, and then decomposed into the rising part and the falling part. Assume that there are n sampling points and the input current is recorded as I = [I1, I2, ..., I n ] T , the output flux is recorded as B = [B1, B2, ... B n ] T , then formula (5) is written in matrix form as follows: The input matrix [I 0 I 1 I 2 I 4 ] is recorded as X, the coefficient matrix [abcd] T Denoted as A, formula (8) is written as: XA=B (11) The least squares method is used to estimate the parameters of the rising part of the hysteresis loop, and the estimated value of the coefficient matrix is ​​obtained. as follows: Replace the input matrix X and output matrix B of the ascending part with the input matrix X of the descending part respectively d And the output matrix B d , get the estimated value of the coefficient matrix of the descending part The single-frequency hysteresis nonlinear model of the linear reluctance motor based on the phase-shift rational basis can be obtained.

2. The single-frequency hysteresis nonlinear modeling method of a linear reluctance motor based on a phase-shift rational basis according to claim 1 is characterized in that: The input current signal and the output magnetic flux signal have the same angular frequency, different amplitudes and a phase difference.

3. The single-frequency hysteresis nonlinear modeling method of a linear reluctance motor based on a phase-shift rational basis according to claim 2 is characterized in that: The input current signal I=A0sin(wt), wherein A0 represents the amplitude of the input current.

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