A control method for magnetic bearings of pressure-differential generator based on multi-mode switching

Abstract

The present application proposes a pressure difference generator magnetic levitation bearing control method based on multi-modal switching, which belongs to the field of bearing control technology, including: establishing integer-order transfer function models and fractional-order transfer function models respectively; obtaining the first modal frequency and the first modal vibration shape of each order according to finite element modal analysis; obtaining the second modal frequency and the second modal vibration shape of each order according to hammer modal experiments; optimizing the fractional-order transfer function model according to the modal frequency error and the modal vibration shape error of each order; performing multi-modal switching PID control with the integer-order transfer function model and the optimal fractional-order transfer function model as objects, so as to realize the control of the magnetic levitation bearing. The present application solves the problem that the current magnetic bearing model has large errors and the control object model is single and cannot accurately express the rotor dynamic characteristics in the full speed range, and realizes a precise control model in the full speed range.

Description

Technical Field

[0001] The present invention belongs to the technical field of bearing control, and in particular relates to a pressure difference generator magnetic suspension bearing control method based on multi-mode switching. Background Art

[0002] During natural gas transportation, high-pressure natural gas must pass through pressure regulating stations to reduce its pressure for consumption. Traditional methods rely on throttling and pressure reduction with pressure regulating valves, resulting in significant loss of pressure energy (differential pressure energy) as heat, resulting in extremely low energy utilization. To recover this differential pressure energy, natural gas differential pressure power generation technology has emerged. Traditional differential pressure generators rely on mechanical bearings, which present significant friction losses, high maintenance costs, and limited speeds. The application of magnetic levitation technology can address these bottlenecks.

[0003] The magnetically levitated pressure-difference generator uses active magnetic bearings to support the motor rotor, achieving frictionless rotor suspension. This generator offers advantages such as high speed, high efficiency, and active controllability, and has broad application prospects in a wide range of fields.

[0004] Due to factors such as machining errors and external interference, all rotating machinery exhibits unbalanced vibration. Furthermore, when the natural gas pressure differential is excessive, causing the generator speed to increase to the critical bending speed, the rotor will exhibit various bending modal characteristics. In severe cases, this can damage the protective bearings and limit the increase in speed. As the frequency increases, the eddy current effect in the bearings cannot be ignored, increasing the error in traditional magnetic bearing models. Furthermore, most traditional magnetic bearing control methods use PID control, which does not require high model accuracy, lacking robustness and precision. Furthermore, PID control parameters are often set using trial and error methods and prior knowledge, resulting in low efficiency.

[0005] Since the dynamic characteristics of the rotor in the rigid modal range and the flexible modal range are significantly different, most of the current magnetic bearing control methods use a rigid rotor model for controller design. However, as the rotor speed increases and transitions from the rigid mode to the flexible mode, a single control model cannot accurately describe the dynamic characteristics of the flexible rotor in the high speed range.

[0006] At present, most model parameter tuning methods for magnetic levitation bearings only consider the modal frequency as the optimization target, but the influence of the modal vibration mode on the accuracy of the model and the control effect cannot be ignored. Since there will be an error between the actual displacement sensor collection point and the point where the magnetic levitation bearing actually acts on the rotor shaft, when the motor speed increases to the bending frequency, the rotor begins to exhibit bending modal characteristics. At this time, the direct error between the sensor measurement point and the actual action point of the magnetic levitation bearing will be amplified, which may cause a large offset in the bearing control and cause the rotor to collide with the protective bearing. Summary of the Invention

[0007] In view of the shortcomings of the existing technology, the present application proposes a pressure difference generator magnetic suspension bearing control method based on multi-mode switching.

[0008] In a first aspect, the present application proposes a method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching, comprising:

[0009] The integer-order transfer function model and fractional-order transfer function model of the magnetic bearing of the pressure-differential generator are established respectively;

[0010] Based on the three-dimensional solid model of the pressure difference generator, the finite element modal analysis of the rotor of the pressure difference generator is performed to obtain the first modal frequency and the first modal vibration shape of each order;

[0011] The hammer modal experiment is carried out on the pressure difference generator to obtain the second mode frequency and the second mode vibration shape of each order;

[0012] According to the difference between the first modal frequency of each order and the second modal frequency of each order, the modal frequency error of each order is obtained;

[0013] According to the difference between the first mode vibration shape of each order and the second mode vibration shape of each order, the mode vibration shape error of each order is obtained;

[0014] Optimizing the fractional-order transfer function model according to the modal frequency errors and modal vibration shape errors of each order to obtain an optimal fractional-order transfer function model;

[0015] Taking the integer-order transfer function model and the optimal fractional-order transfer function model as the objects respectively, multi-mode switching PID control is performed to realize the control of the magnetic levitation bearing.

[0016] The steps of respectively establishing an integer-order transfer function model and a fractional-order transfer function model of the magnetic bearing of the pressure-differential generator include:

[0017] The electromagnetic force exerted by two single-degree-of-freedom magnetic bearings on the rotor is calculated by magnetic circuit analysis.

[0018] The electromagnetic forces of the two magnetic bearings on the rotor are linearized, and the single-degree-of-freedom integer-order transfer function model of the magnetic bearings of the pressure-differential generator is derived based on the dynamic equations of the rotor.

[0019] According to the integer-order transfer function model and considering the influence of eddy current effect on magnetic levitation bearings, a fractional-order transfer function model is established.

[0020] According to the integer-order transfer function model and considering the influence of eddy current effect on the magnetic suspension bearing, a fractional-order transfer function model is established, including:

[0021] According to the angular frequency of the rotor, the expression of the magnetic flux changing with the angular frequency of the rotor is obtained;

[0022] Based on the expression of magnetic flux changing with the angular frequency of the rotor, the expression of effective magnetic resistance in time-varying magnetic field is derived;

[0023] According to the effective magnetic resistance expression in the time-varying magnetic field, the relationship between electromagnetic force, rotor displacement and control current is modified;

[0024] The Laplace transform is performed on the relationship between the corrected electromagnetic force, rotor displacement and control current, and the control current is used as input and the rotor displacement as output to obtain a fractional-order transfer function model.

[0025] The method of performing finite element modal analysis on the rotor of the pressure difference generator based on the three-dimensional solid model of the pressure difference generator to obtain the first modal frequency and the first modal vibration shape of each order includes:

[0026] Based on the three-dimensional solid model of the pressure difference generator, the finite element modal analysis is performed on the rotor of the pressure difference generator to obtain the motion equation in the finite element analysis;

[0027] Simplifying the motion equation, setting the damping matrix and the dynamic excitation force to zero, and obtaining a simplified motion equation;

[0028] The simplified motion equation is solved using differential equations to obtain the relationship between the rotor displacement and the amplitude vector and natural frequency of the pressure difference generator.

[0029] Substituting the relationship between the rotor displacement, the amplitude vector matrix of the pressure differential generator, and the natural frequency of the pressure differential generator into the simplified motion equation, it is found that the only condition for the simplified motion equation to have a non-zero solution is that the coefficient is zero;

[0030] When the coefficient is zero, the simplified motion equation is solved to obtain the amplitude vector and eigenvalue of each order of the pressure difference generator. The amplitude vector of each order of the pressure difference generator is used as the first modal vibration shape of each order, and the eigenvalue is used as the first modal frequency of each order.

[0031] The method of optimizing the fractional-order transfer function model according to the modal frequency errors and modal vibration shape errors of each order to obtain the optimal fractional-order transfer function model includes:

[0032] Step S6.1: setting the initialization temperature of the simulated annealing algorithm, and randomly generating an initial solution of the simulated annealing algorithm, using the initial solution as the current solution, and using the initialization temperature as the current temperature;

[0033] Step S6.2: Perform random perturbations on the current solution to generate a new solution;

[0034] Step S6.3: setting the objective function based on the modal frequency error of each order and the modal shape error of each order;

[0035] Step S6.4: Calculate the objective function value of the current solution and the objective function value of the new solution;

[0036] Step S6.5: Calculate the increment of the evaluation function based on the objective function value of the current solution and the objective function value of the new solution;

[0037] Step S6.6: Calculate the acceptance probability based on the objective function value of the current solution, the objective function value of the new solution, and the current temperature;

[0038] Step S6.7: If the increment of the evaluation function is less than zero, the new solution is accepted and used as the current solution for the next iteration;

[0039] Step S6.8: When the increment of the evaluation function is greater than or equal to zero, determine whether the acceptance probability is greater than a preset probability threshold;

[0040] Step S6.9: If the acceptance probability is greater than a preset probability threshold, the new solution is accepted and used as the current solution for the next iteration. The preset probability threshold is a random number between 0 and 1.

[0041] Step S6.10: If the acceptance probability is less than or equal to the preset probability threshold, the new solution is not accepted and the current solution is retained;

[0042] Step S6.11: Lower the current temperature according to the preset cooling strategy;

[0043] Step S6.12: When the current temperature drops to a preset temperature threshold and the current number of iterations is greater than a preset maximum number of iterations, stop the iteration and output the optimal fractional-order transfer function model;

[0044] Step S6.13: If the current temperature has not dropped to the preset temperature threshold or the current number of iterations is not greater than the preset maximum number of iterations, the lowered temperature is used as the current temperature, and the process returns to step S6.2 to continue iteration.

[0045] The method of performing multi-mode switching PID control on an integer-order transfer function model and an optimal fractional-order transfer function model to realize control of a magnetic bearing includes:

[0046] Obtaining the rotational speed of the rotor of the pressure difference generator;

[0047] When the speed of the rotor is greater than a preset speed threshold, a fractional-order PID controller is used to control the rotor based on an optimal fractional-order transfer function model, and parameters of the fractional-order PID controller are tuned using a genetic algorithm;

[0048] When the rotation speed of the rotor is less than or equal to a preset rotation speed threshold, a traditional PID controller is used to perform control with an integer-order transfer function model as the object.

[0049] The parameters of the fractional-order PID device are tuned using a genetic algorithm, including:

[0050] Step S7.2.1: Setting a value range for the parameters of the fractional-order PID controller, using a set of parameters of the fractional-order PID controller as an individual in the genetic algorithm, wherein the set of parameters of the fractional-order PID controller includes: an integral order parameter, a differential order parameter, a proportional control coefficient, an integral control coefficient, and a differential control coefficient;

[0051] Step S7.2.2: Initialize all individuals in the genetic algorithm, randomly generate different values ​​within the parameter range, encode each individual, and obtain the initial population, which is used as the current population;

[0052] Step S7.2.3: Initialize the parameters of the population in the genetic algorithm, which include: the number of individuals in the population, the number of iterations, the probability of crossover, and the probability of mutation;

[0053] Step S7.2.4: Determine a fitness function using the error, adjustment time, overshoot, and control variable of the fractional-order PID controller. The fitness function determines the probability of each individual surviving during the iteration process.

[0054] Step S7.2.5: Iteratively evolve the current population, including: calculating the fitness value of the current population using the fitness function, calculating the crossover probability of each individual, randomly selecting two individuals for crossover, performing numerical perturbations on the randomly selected individuals based on the mutation probability, and evolving to a new generation, wherein the crossover between two individuals involves exchanging a parameter from one set of encoded parameters with a parameter from another set of encoded parameters;

[0055] Step S7.2.6: When the number of iterations reaches the initial set value or the value of the fitness function is less than the preset fitness threshold, stop the iteration and output the optimal fractional-order PID parameters;

[0056] Step S7.2.7: When the number of iterations reaches the initial set value or the value of the fitness function is greater than or equal to the preset fitness threshold, return to step S7.2.5 and continue iterating with the new generation as the current population.

[0057] In the second aspect, the present application proposes an electronic device comprising: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the method for controlling a pressure difference generator magnetic bearing based on multi-mode switching.

[0058] In a third aspect, the present application proposes a computer-readable storage medium storing executable instructions, which, when executed, enable a processor to execute the method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching.

[0059] In a fourth aspect, the present application proposes a computer program product, comprising a computer program or instructions, which, when executed by a processor, implements the aforementioned method for controlling a pressure difference generator magnetic bearing based on multi-mode switching.

[0060] Beneficial effects:

[0061] This application proposes a pressure difference generator magnetic levitation bearing control method based on multi-mode switching, which solves the problem that the current magnetic bearing model has large errors and the control object model is single and cannot accurately express the rotor dynamic characteristics within the full speed range. This application uses two indicators, modal vibration shape and modal frequency, to optimize the parameters of the magnetic bearing model, which can provide the controller with an accurate control model within the full speed range to achieve the purpose of stably crossing the modal resonance point. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A flow chart of a method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching according to an embodiment of the present application;

[0063] Figure 2 A flowchart of a method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching according to an embodiment of the present application;

[0064] Figure 3 Schematic diagram of an equivalent model of a pressure difference generator according to an embodiment of the present application;

[0065] Figure 4 A schematic diagram of the finite element analysis process of an embodiment of the present application;

[0066] Figure 5 Schematic diagram of the process of optimizing the fractional-order transfer function model using the simulated annealing algorithm according to an embodiment of the present application;

[0067] Figure 6 Schematic diagram of the multi-mode switching control process of an embodiment of the present application;

[0068] Figure 7 A diagram of a differential control structure of the rotor and magnetic bearing of a magnetic levitation motor according to an embodiment of the present application;

[0069] Figure 8 Schematic diagram of the genetic algorithm flow in the embodiment of the present application;

[0070] Figure 9 Structural block diagram of the fractional-order PID controller according to an embodiment of the present application;

[0071] Figure 10 Control block diagram of the fractional-order PID controller according to an embodiment of the present application;

[0072] Among them, 1-rotor, 2-spring unit. DETAILED DESCRIPTION

[0073] The specific implementation methods of the present application are further described in detail below with reference to the accompanying drawings and examples.

[0074] In response to the problem that a single control model in the existing technology cannot accurately describe the dynamic characteristics of the flexible rotor in the high speed range, and the problem that most current model parameter tuning methods of magnetic levitation bearings only consider the modal frequency as the optimization target, this application proposes a pressure difference generator magnetic levitation bearing control method based on multi-mode switching. This application uses ANSYS software to perform physical modeling of the motor, and performs finite element modal analysis on it to obtain its modal parameters of each order, and uses the modal vibration shape and modal frequency as two indicators to optimize the parameters of the magnetic bearing model; in the process of the motor speed gradually increasing from zero, whenever it encounters 70% of the critical speed of the next stage, the program for switching model parameters will be triggered to switch the control model to realize multi-mode switching control; in the five parameter tuning methods of fractional-order PID, a genetic algorithm is used, with the various performance indicators of the controller as the objective function, to perform rapid global optimization.

[0075] Example 1:

[0076] This embodiment provides a method for controlling a magnetic bearing of a pressure difference generator based on multi-mode switching. Figure 1 、 Figure 2 Shown, including:

[0077] Step S1: establishing an integer-order transfer function model and a fractional-order transfer function model of the magnetic bearing of the pressure differential generator respectively;

[0078] This embodiment takes a single-degree-of-freedom magnetic levitation motor system as an example, temporarily ignoring the coupling relationship between the degrees of freedom and assuming that the models of the radial degrees of freedom are consistent. This embodiment first requires magnetic bearing modeling, which includes three aspects:

[0079] (1) Calculate the electromagnetic force expression of the magnetic bearing on the rotor through magnetic circuit analysis;

[0080] Specifically, step S1.1: calculate the electromagnetic force of the two single-degree-of-freedom magnetic bearings on the rotor using the magnetic circuit analysis method. The calculation formula is as follows:

[0081] ;

[0082] ;

[0083] in, is the electromagnetic force exerted on the rotor of the magnetic levitation motor in a single degree of freedom by the first pair of coils in the two pairs of coils perpendicular to each other, It is divided into the electromagnetic force exerted by the second pair of coils in the two pairs of coils perpendicular to each other on the rotor of the magnetic levitation motor in a single degree of freedom. k is the product of the vacuum magnetic permeability of the magnetic levitation motor, the number of coil turns and the cross-sectional area of ​​the iron core. is the control current of the magnetic levitation motor, is the bias current of the magnetic levitation motor, is the rotor displacement center point of the magnetic levitation motor, x is the rotor displacement of the magnetic levitation motor, and the rotor displacement is measured by the eddy current sensor. is the magnetic pole angle of the magnetic levitation motor.

[0084] (2) Derivation of a single-degree-of-freedom integer-order model of a magnetic bearing based on the rotor dynamics equations;

[0085] Specifically, step S1.2: linearize the electromagnetic forces of the two magnetic bearings on the rotor, and derive a single-degree-of-freedom integer-order transfer function model of the magnetic bearing of the pressure differential generator based on the dynamic equation of the rotor. The calculation formula is as follows:

[0086] ;

[0087] in, is the integer-order transfer function model of the magnetic bearing in a single degree of freedom, is the output of the integer-order transfer function model, is the input of the integer-order transfer function model, s is a complex variable, is the current-force stiffness of the differential pressure generator, is the displacement force stiffness of the pressure difference generator, and m is the mass of the magnetic bearing.

[0088] (3) Considering the influence of eddy current effect on magnetic bearings, a fractional-order magnetic bearing model is established;

[0089] The eddy current effect is caused by the induced current generated by the conductor in a changing magnetic field. These currents will generate their own magnetic field, which interacts with the original magnetic field, thereby affecting the magnitude of the magnetic resistance. In order to accurately analyze such systems, it is necessary to introduce the concept of effective magnetic resistance.

[0090] Specifically, step S1.3: based on the integer-order transfer function model and taking into account the influence of eddy current effect on the magnetic suspension bearing, a fractional-order transfer function model is established, including:

[0091] Step S1.3.1: Based on the rotor angular frequency, obtain an expression for how the magnetic flux changes with the rotor angular frequency;

[0092] Specifically, the concept of effective magnetic resistance is introduced to derive the expression of the change of magnetic flux with frequency, which is calculated as follows:

[0093] ;

[0094] in, is the magnetic flux of the differential pressure generator, is the angular frequency of the differential pressure generator, The length of the ferromagnetic material of the differential pressure generator, is the magnetic permeability of air, is the relative magnetic permeability of the ferromagnetic material of the magnetic levitation motor, is the current in the coil of the pressure difference generator; is the first intermediate parameter, ,in is the electrical conductivity of the ferromagnetic material of the magnetic levitation motor, is the cross-sectional area of ​​the magnetic pole, is the number of turns of the electromagnetic coil, is the height of the magnetic pole.

[0095] Step S1.3.2: Based on the expression of the magnetic flux changing with the angular frequency of the rotor, derive the expression of the effective magnetic resistance in the time-varying magnetic field, which is calculated as follows:

[0096] ;

[0097] For the convenience of expression, the constant term in the above formula is represented by an intermediate parameter c, that is, Therefore, the effective magnetic resistance when the rotor is in the equilibrium position is calculated as follows:

[0098] ;

[0099] in, is the effective magnetic reluctance of the static magnetic field, which is calculated as follows:

[0100] ;

[0101] in, is the air gap distance between the stator and the rotor when the rotor is in equilibrium position.

[0102] Step S1.3.3: Modify the relationship between electromagnetic force, rotor displacement, and control current based on the effective magnetic resistance expression in the time-varying magnetic field;

[0103] Specifically, the parameters in the integer-order model are corrected based on the effective magnetic resistance derived in step S1.3.2. First, the relationship between the electromagnetic force, rotor displacement, and control current is corrected. The calculation formula is as follows:

[0104] ;

[0105] in, is the acceleration of the rotor, and x is the distance the rotor deviates from the center position.

[0106] Step S1.3.4: Perform a Laplace transform on the relationship between the corrected electromagnetic force, rotor displacement, and control current, using the control current as input and the rotor displacement as output to obtain a fractional-order transfer function model. The calculation formula is as follows:

[0107] ;

[0108] The highest order of its characteristic polynomial is 2.5, and c is the second intermediate parameter.

[0109] Step S2: performing finite element modal analysis on the rotor of the pressure differential generator based on the three-dimensional solid model of the pressure differential generator to obtain the first modal frequency and the first modal vibration shape of each order;

[0110] This embodiment also requires multimodal analysis, which specifically includes four aspects:

[0111] (1) Build a 3D solid model of the motor in SolidWorks;

[0112] (2) Perform finite element modal analysis on the motor rotor in ANSYS software to solve the modal parameters;

[0113] (3) Conduct hammer modal test to measure the modal frequency and modal vibration shape of the rotor pair;

[0114] (4) Based on the error between theoretical and experimental results, the simulated annealing algorithm is used to optimize the parameters of the magnetic bearing model for multiple modes.

[0115] The detailed description is as follows:

[0116] (1) Build a 3D solid model of the motor in SolidWorks;

[0117] Specifically, a three-dimensional solid model of the magnetic levitation motor rotor shaft is constructed in SolidWorks software, including steps S2.1 to S2.3;

[0118] Step S2.1: Design the magnetic levitation motor in a 1:1 scale according to the actual size of the motor body;

[0119] Step S2.2: Model the bearing seat of the magnetic levitation motor (i.e., the pressure difference generator), and replace the upper and lower radial and axial magnetic bearings of the rotor 1 with four spring units 2 in the upper, lower, left, and right directions respectively. The equivalent model of the pressure difference generator is as follows: Figure 3 As shown, the flexible support effect of the magnetic bearing is simulated as realistically as possible and the model is simplified;

[0120] Step S2.3: Setting the stiffness value of spring unit 2 to the ratio of the levitation force exerted by the magnetic bearing on the rotor to the air gap when the rotor is suspended, thereby obtaining a three-dimensional solid model of the pressure difference generator;

[0121] (2) Perform finite element modal analysis on the motor rotor in ANSYS software to solve the modal parameters;

[0122] Import the three-dimensional solid model built in steps S2.1 to S2.3 into ANSYS software for finite element modal analysis, as shown in the following example: Figure 4 As shown, the modal vibration shapes and natural frequencies of each order are solved according to the finite element analysis process;

[0123] Step S2.4: The three-dimensional solid model file of the pressure difference generator built in steps S2.1 to S2.3 (i.e., the rotor finite element model, such as Figure 4 (as shown in the figure), save it as a .U format file, open ANSYS software, select and load the target file to realize the linear structure import of the model;

[0124] Step S2.5: Perform ANSYS pre-processing (including defining element types, setting motor material properties, and setting real constants), then mesh the model, select SOLID187 type elements, and simulate the magnetic bearing module using spring element 2;

[0125] Step S2.6: Setting boundary conditions, including: ignoring the influence of axial vibration on radial vibration mode, and applying two symmetrical fixed constraints to the axial position of the rotor;

[0126] Step S2.7: Import the modal analysis module, load and solve, expand the mode and perform finite element modal analysis.

[0127] Among them, the finite element modal analysis is performed on the rotor of the pressure difference generator to obtain the first modal frequency and the first modal vibration shape of each order, including:

[0128] Step S2.7.1: Based on the three-dimensional solid model of the pressure differential generator, perform finite element modal analysis on the rotor of the pressure differential generator to obtain the motion equation in the finite element analysis. The calculation formula is as follows:

[0129] ;

[0130] in, is the mass matrix of the differential pressure generator, is the damping matrix of the pressure difference generator, is the rotor stiffness of the pressure difference generator, is the acceleration of the rotor of the pressure difference generator, is the speed of the rotor of the pressure difference generator, is divided into the displacement of the rotor of the pressure difference generator, is the dynamic excitation of the rotor load of the pressure difference generator.

[0131] Step S2.7.2: Simplify the equation of motion by setting the damping matrix and dynamic excitation force to zero to obtain the simplified equation of motion. The calculation formula is as follows:

[0132] ;

[0133] Step S2.7.3: Use the differential equation to solve the simplified equation of motion to obtain the relationship between the rotor displacement and the amplitude vector and natural frequency of the pressure difference generator.

[0134] ;

[0135] in, is the natural frequency of the system, is the amplitude vector matrix of the system, t is the running time, is the initial phase;

[0136] Step S2.7.4: Substitute the relationship between the rotor displacement, the amplitude vector matrix of the pressure differential generator, and the natural frequency of the pressure differential generator into the simplified motion equation. The only condition for the simplified motion equation to have a non-zero solution is that the coefficient is zero.

[0137] Specifically, according to Cramer's method, it can be determined that when the rotor structure is in free vibration, the amplitudes at each node of the rotor are not all zero. Therefore, after substituting the rotor displacement calculation formula obtained in step S2.7.3 into the calculation formula in step S2.7.2, the only condition for the obtained calculation formula to have a non-zero solution is that the coefficient is zero, resulting in the following calculation formula:

[0138] ;

[0139] Step S2.7.5: When the coefficient is zero, solve the simplified motion equation to obtain the amplitude vector and eigenvalue of each order of the pressure difference generator, and use the amplitude vector of each order of the pressure difference generator as the first modal vibration shape of each order, and use the eigenvalue as the first modal frequency of each order.

[0140] Solve for the eigenvector and eigenvalues , which represent the modal vibration shape and modal frequency respectively. After solving the modal frequency and modal vibration shape, the modal vibration shape diagram and Campbell diagram of each order calculation result are generated in ANSYS software.

[0141] After long-term and rigorous analysis of the magnetic bearings used in pressure-differential generators, it was discovered that numerous uncertainties and simplifications can lead to modeling errors during the finite element modeling of magnetic bearings. For example, the magnetic bearing action and sensor acquisition points differ. This issue can be ignored in low-speed rigid modes, but at high speeds, the rotor shaft exhibits flexibility and complex bending modes, which further amplifies the impact of the difference between the magnetic bearing action and sensor acquisition points. Therefore, the modal vibration shape parameter must be considered in the modeling process. The error between the theoretically calculated modal vibration shape values ​​and the experimentally measured values ​​is used to optimize and adjust the model parameters, achieve accurate modeling, and lay a solid foundation for subsequent controller design.

[0142] (3) Conduct hammer modal test to measure the modal frequency and modal vibration shape of the rotor pair;

[0143] Step S3: performing a hammer modal test on the pressure difference generator to obtain the second modal frequency and the second modal vibration shape of each order;

[0144] In this embodiment, a hammer modal test is performed on the rotor shaft of the pressure differential generator. The voltage signal is collected using an acceleration sensor and then input into a computer for analysis to solve the second modal frequency and the second modal vibration shape of each order of the rotor shaft.

[0145] A multi-point excitation and single-point response test method is adopted. According to the results of grid division, ten equally divided points are selected as excitation positions and hammered in sequence. The rotor is vertically suspended on the bracket, and an accelerometer is installed at a randomly selected hammering point. The boundary condition is set to a free-free state. A data acquisition instrument is used to transmit the voltage signals of the force hammer and the accelerometer to the computer, and then N-MODEL modal analysis software is used for data processing to calculate the second mode frequency and the second mode vibration shape of each order.

[0146] (4) Based on the error between the theoretical and experimental results, the simulated annealing algorithm is used to optimize the parameters of the magnetic bearing model of multiple modes, including: steps S4 to S6;

[0147] Step S4: obtaining the modal frequency error of each order according to the difference between the first modal frequency of each order and the second modal frequency of each order;

[0148] Step S5: obtaining the modal vibration error of each order according to the difference between the first modal vibration shape of each order and the second modal vibration shape of each order;

[0149] Step S6: Optimizing the fractional-order transfer function model according to the modal frequency errors and modal vibration shape errors of each order to obtain an optimal fractional-order transfer function model;

[0150] In this embodiment, based on the modal parameters solved in step S2 and step S3, a simulated annealing algorithm is used to further optimize the model parameters of the fractional-order model in the flexible range, specifically including:

[0151] The fractional-order transfer function model is optimized according to the modal frequency errors and modal vibration shape errors of each order to obtain the optimal fractional-order transfer function model, such as Figure 5 Shown, including:

[0152] Step S6.1: setting the initialization temperature of the simulated annealing algorithm, and randomly generating an initial solution of the simulated annealing algorithm, using the initial solution as the current solution, and using the initialization temperature as the current temperature;

[0153] In this embodiment, the initial temperature and initial solution are given, including: setting the initialization temperature , and randomly generate an initial solution , take the initial solution as the current solution and the initialization temperature as the current temperature, and iterate.

[0154] Step S6.2: Perform random perturbations on the current solution to generate a new solution;

[0155] In this embodiment, a new solution is generated according to the current temperature, including: Based on this, random perturbations are performed to generate new solutions .

[0156] Step S6.3: setting the objective function based on the modal frequency error of each order and the modal shape error of each order;

[0157] In this embodiment, the objective function is set according to the optimization object and the optimization goal. , where the optimization objects are the modal frequencies and modal vibration shapes of each order, and the optimization targets are the modal frequency errors and modal vibration shape errors of each order, including:

[0158] Step S6.3.1: Take the modal frequency and modal vibration shape as the correction targets, where the correction error function of the modal frequency is , the calculation formula is as follows:

[0159] ;

[0160] in, is the first modal frequency of the i-th order solved by finite element modal analysis, is the second mode frequency of the i-th order obtained by the hammer test;

[0161] Step S6.3.2: Corrected Error Function for Mode Shapes , the calculation formula is as follows:

[0162] ;

[0163] in, is the correlation coefficient between the first mode shape of the i-th order and the second mode shape of the i-th order. The definition of MAC is: ,in, is the first mode shape of the i-th order, is the j-th order second mode vibration shape matched with it;

[0164] Step S6.3.2: Select the first four modal parameters and set the objective function as:

[0165] ;

[0166] in, is the weight value of the modal frequency error, is the weight value of the mode shape error.

[0167] Step S6.4: Calculate the objective function value of the current solution and the objective function value of the new solution;

[0168] In this embodiment, the current solution is calculated and new solutions The objective function value of and .

[0169] Step S6.5: Calculate the increment of the evaluation function based on the objective function value of the current solution and the objective function value of the new solution;

[0170] In this embodiment, according to the objective function value of the current solution And the objective function value of the new solution The difference between the two is used to calculate the increment of the evaluation function ;

[0171] Step S6.6: Based on the objective function value of the current solution , the objective function value of the new solution and the current temperature , calculate the acceptance probability;

[0172] The calculation formula for the acceptance probability P is as follows:

[0173] ;

[0174] in, is the current solution in the i-th iteration process, is the current temperature during the i-th iteration;

[0175] Step S6.7: If the increment of the evaluation function is less than zero, the new solution is accepted and used as the current solution for the next iteration, i.e. ;

[0176] Step S6.8: When the increment of the evaluation function is greater than or equal to zero, determine whether the acceptance probability is greater than a preset probability threshold rand;

[0177] Step S6.9: If the acceptance probability is greater than the preset probability threshold, the new solution is accepted and used as the current solution for the next iteration, i.e. , the preset probability threshold rand is a random number between 0 and 1;

[0178] Step S6.10: If the acceptance probability is less than or equal to the preset probability threshold, the new solution is not accepted and the current solution is retained;

[0179] Step S6.11: Lower the current temperature according to the preset cooling strategy;

[0180] In this embodiment, the current temperature is lowered according to a certain cooling strategy. , linear cooling and exponential cooling can be used.

[0181] Step S6.12: When the current temperature drops to a preset temperature threshold and the current number of iterations is greater than a preset maximum number of iterations, the iteration is stopped and the optimal fractional-order transfer function model (i.e., the optimal solution) is output;

[0182] In this embodiment, it is ensured that the search is sufficient at the current temperature. If the search is not sufficient, the process returns to step S6.2 and continues the iteration.

[0183] Step S6.13: If the current temperature has not dropped to the preset temperature threshold or the current number of iterations is not greater than the preset maximum number of iterations, the lowered temperature is used as the current temperature, and the process returns to step S6.2 to continue iteration.

[0184] Finally, the controller design includes three aspects:

[0185] (1) Design a fractional-order PID controller based on the fractional-order magnetic bearing switching system model;

[0186] (2) Using genetic algorithm to tune the parameters of fractional-order PID;

[0187] (3) Under the control of fractional-order PID, the rotor of the magnetic levitation motor (i.e., pressure difference generator) is stably suspended.

[0188] The detailed description is as follows:

[0189] (1) Design a fractional-order PID controller based on the fractional-order magnetic bearing switching system model;

[0190] Step S7: performing multi-mode switching PID control on the integer-order transfer function model and the optimal fractional-order transfer function model respectively to achieve control of the magnetic bearing, including:

[0191] Step S7.1: Obtaining the rotational speed of the rotor of the pressure difference generator;

[0192] Step S7.2: When the speed of the rotor is greater than a preset speed threshold, a fractional-order PID controller is used to control the rotor based on the optimal fractional-order transfer function model, and parameters of the fractional-order PID controller are tuned using a genetic algorithm;

[0193] Step S7.3: When the rotational speed of the rotor is less than or equal to a preset rotational speed threshold, a traditional PID controller is used to perform control based on an integer-order transfer function model.

[0194] In this embodiment, since the rotor presents a rigid mode when the rotor speed is low and the eddy current effect is weak, the model accuracy of the magnetic bearing is relatively high. It can be directly controlled by taking the integer-order transfer function model as the object and adopting the traditional PID controller. When the rotor speed rises to about 70% of the first-order bending speed, the rotor presents a flexible mode, the amplitude of each node cannot be ignored, and the eddy current effect is strong, which has a greater impact on the model, so it is necessary to switch the parameters of the control model of the magnetic bearing here.

[0195] like Figure 6As shown, when the magnetic levitation motor system operates in a low speed range, the model parameters of the rigid rotor (i.e., an integer-order transfer function model is used as the object) are used for control, and the rotor displacement signal is collected in real time by an eddy current displacement sensor to detect the speed. When the rotor vibrates violently as the speed continues to increase, a threshold for switching the model parameters is set for the collected displacement signal. When the rotor displacement exceeds the threshold, it indicates that the rotor enters the flexible modal range (i.e., the speed reaches 70% of the next critical speed). At this time, the model parameters are switched (i.e., the model parameters of the next mode are switched), and the magnetic bearing model parameters of the flexible modal range optimized by simulated annealing (i.e., the optimal fractional-order transfer function model is used as the object, and a fractional-order PID controller is used for control) are used for control.

[0196] If the speed continues to increase and reaches the third-order or higher modal resonance point, the same method is used to switch the parameters of the control model to express the dynamic characteristics of the current speed range and achieve precise control.

[0197] According to the fractional-order open-loop transfer function of the single-degree-of-freedom magnetic bearing derived in step 3, a fractional-order PID controller is designed to control the fractional-order model;

[0198] In this embodiment, Figure 7 This is a diagram of the rotor and magnetic bearing differential control structure of a magnetic levitation motor. The circle on the right is a cross-section of the rotor. The upper and lower electromagnets simulate the electromagnetic bearings. It can be seen that the rotor is affected by the two electromagnets, but the magnitude of the electromagnetic force applied to the rotor by these two electromagnets is different. This depends on the placement of the motor. If it is a horizontal motor, the electromagnet below the radial magnetic bearing needs to provide more electromagnetic force to balance the gravity of the rotor itself. If it is a vertical motor, the electromagnet below the axial magnetic bearing needs to provide more electromagnetic force to balance the gravity of the rotor. Figure 7 middle, To control the current, is the bias current, x is the rotor displacement, is the rotor mass, The electromagnetic force on the rotor. In differential control, the current of each electromagnet coil consists of two parts, one is the bias current , one for controlling current The two currents are summed on one side and subtracted on the other side. After passing through the power amplifier, two electromagnets with symmetrical positions provide two electromagnetic forces of different magnitudes to push the rotor to the center position.

[0199] A fractional-order PID controller is built using the FOTF toolbox based on the Oustaloup filter approximation method. The modules of the fractional-order transfer function model and the fractional-order PID controller provided by the toolbox are introduced into Simulink. Then, the five control parameters (including integral order parameter, differential order parameter, proportional control coefficient, integral control coefficient and differential control coefficient) are set using the trial-and-error method combined with the rules of prior knowledge. The step response effect is observed and the adjustment is repeated until the response curve has the best effect.

[0200] (2) Using genetic algorithm to tune the parameters of fractional-order PID;

[0201] Figure 8 This is the genetic algorithm flow chart. The genetic algorithm is used to tune the parameters of the fractional-order PID controller, seek the optimal fractional-order PID control parameters, and improve the performance of the fractional-order PID controller.

[0202] The parameters of the fractional-order PID device are tuned using a genetic algorithm, including:

[0203] Step S7.2.1: Set the value range of the parameters in the fractional-order PID device, and use a set of parameters in the fractional-order PID device as an individual in the genetic algorithm. The set of parameters in the fractional-order PID device includes: integral order parameter, differential order parameter, proportional control coefficient, integral control coefficient and differential control coefficient; wherein, Figure 9 It is the structural block diagram of the fractional-order PID controller;

[0204] Figure 9 where s is a complex domain variable, is the integration order parameter, is the differential order parameter, is the proportional control coefficient, is the integral control coefficient, is the differential control coefficient. In this embodiment, it is necessary to set the value range of the parameters in the fractional-order PID device. If the value range is not set in the genetic algorithm, the search will be carried out within the entire range of real numbers, which will greatly increase the calculation time and reduce efficiency. Therefore, it is necessary to set an appropriate value range to reduce the search area.

[0205] Step S7.2.2: Initialize all individuals in the genetic algorithm, randomly generate different values ​​within the parameter range, encode each individual, and obtain the initial population, which is used as the current population;

[0206] In this embodiment, all individuals are initialized, and different numerical values ​​are randomly generated within the value range to form individuals. Each individual represents a set of parameters in the fractional-order PID device, and the encoding method is decimal encoding;

[0207] Step S7.2.3: Initialize the parameters of the population in the genetic algorithm, which include: the number of individuals in the population, the number of iterations, the probability of crossover, and the probability of mutation;

[0208] Step S7.2.4: Determine a fitness function using the error, adjustment time, overshoot, and control variable of the fractional-order PID controller. The fitness function determines the probability that each individual can survive during the iteration process.

[0209] In this embodiment, the system error, adjustment time, overshoot and control amount of the fractional-order PID controller are used as the main components of setting the fitness function. The fitness function J is the fitness function when the system has no overshoot, and the calculation formula is as follows:

[0210] ;

[0211] When the system has overshoot, the fitness function J is calculated as follows:

[0212] ;

[0213] in, is the system output, Expressed as the systematic error, represents the rise time of the system, is the first weight, is the second weight, is the third weight, is the fourth weight, y(t) represents the rotor displacement value at time t, and y(t-1) represents the rotor displacement value at time t-1.

[0214] Step S7.2.5: Iteratively evolve the current population, including: calculating the fitness value of the current population using the fitness function, calculating the crossover probability of each individual, randomly selecting two individuals for crossover, performing numerical perturbations on the randomly selected individuals based on the mutation probability, and evolving to a new generation, wherein the crossover between two individuals involves exchanging a parameter from one set of encoded parameters with a parameter from another set of encoded parameters;

[0215] Step S7.2.6: When the number of iterations reaches the initial set value or the value of the fitness function is less than the preset fitness threshold, stop the iteration and output the optimal fractional-order PID parameters;

[0216] Step S7.2.7: When the number of iterations reaches the initial set value or the value of the fitness function is greater than or equal to the preset fitness threshold, return to step S7.2.5 and continue iterating with the new generation as the current population.

[0217] (3) Under the control of fractional-order PID, the rotor of the magnetic levitation motor (i.e., pressure difference generator) is stably suspended.

[0218] In this embodiment, the rotor of the magnetic levitation motor is stably suspended under the control of the optimal fractional-order PID controller parameters; the output of the displacement sensor and the reference displacement are used as the input of the fractional-order PID controller, and the output of the fractional-order PID controller is used to control the current of the magnetic levitation bearing electromagnet through the power amplifier, thereby achieving stable suspension of the magnetic levitation bearing. Figure 10 As shown, input is a given reference rotor displacement position, the output It is the rotor displacement value after adjustment by the controller. During the operation of the motor, when the actual displacement deviates from the given reference value, the fractional-order PID controller will quickly correct the electromagnetic force, and then output the current to the magnetic bearing through the power amplifier to make the rotor stably suspended; when the system is interfered by an external excitation signal or a sinusoidal disturbance signal, it will also act on the magnetic bearing through the power amplifier, but after the displacement sensor detects the actual displacement offset, it will also pass through the fractional-order PID controller to restore the rotor to the given reference displacement. After the control current adjusted by the fractional-order PID acts on the magnetic bearing, the signal of the change in rotor position (i.e., the output signal) is detected by the displacement sensor and obtained.

[0219] This embodiment proposes a control method for a magnetic bearing of a pressure-differential generator based on multi-mode switching. To address the problems of large errors in the current magnetic bearing model and a single control object model that cannot accurately represent the rotor dynamic characteristics within the full speed range, a magnetic bearing model is first established. Then, finite element modal analysis and hammer test analysis are performed on the magnetic levitation motor rotor to calculate the modal parameters. Then, the parameters of the magnetic bearing model are optimized based on the theoretical experimental errors. Finally, a fractional-order PID controller and its parameter tuning method are designed.

[0220] Example 2:

[0221] This embodiment proposes an electronic device, comprising: one or more processors, and a memory, wherein the memory is used to store instructions. When the instructions are executed by the one or more processors, the one or more processors execute the method for controlling a pressure difference generator magnetic bearing based on multi-mode switching.

[0222] The electronic device may be a mobile phone, computer, or tablet computer, and includes a memory and a processor. The memory stores a computer program that, when executed by the processor, implements a method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching, as described in the embodiments. It is understood that the electronic device may also include an input / output (I / O) interface and a communication component.

[0223] The processor is configured to execute all or part of the steps of the method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching as described in the above embodiment. The memory is configured to store various types of data, such as instructions for any application or method in the electronic device, as well as data related to the application.

[0224] The processor can be an application specific integrated circuit (ASIC), a digital signal processor (DSP), a programmable logic device (PLD), a field programmable gate array (FPGA), a controller, a microcontroller, a microprocessor or other electronic components, and is used to execute the pressure difference generator magnetic suspension bearing control method based on multi-mode switching described in the above embodiment.

[0225] Example 3:

[0226] This embodiment provides a computer-readable storage medium storing executable instructions. When the instructions are executed, if they are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0227] The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of a pressure difference generator magnetic levitation bearing control method based on multi-mode switching described in various embodiments of the present application.

[0228] The aforementioned storage media include: flash memory, hard disk, multimedia card, card-type memory (for example, SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR abbreviation, memory data register) memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, CD, server, APP (Application, abbreviation of application software) application store and other media that can store program verification codes, on which a computer program is stored. When the computer program is executed by the processor, it can implement the above-mentioned various steps of the pressure difference generator magnetic suspension bearing control method based on multi-mode switching.

[0229] Example 4:

[0230] This embodiment provides a computer program product, including a computer program or instructions. When the computer program or instructions are executed by a processor, the method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching is implemented.

[0231] Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a computer program product.

[0232] The various embodiments in this application are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments.

[0233] The scope of protection of this application is not limited to the above-described embodiments. Obviously, those skilled in the art may make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of the claims of this disclosure and their equivalents, the disclosure is intended to include such modifications and variations.

Claims

1. A method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching, characterized in that: include: The integer-order transfer function model and fractional-order transfer function model of the magnetic bearing of the pressure-differential generator are established respectively; Based on the three-dimensional solid model of the pressure difference generator, the finite element modal analysis of the rotor of the pressure difference generator is performed to obtain the first modal frequency and the first modal vibration shape of each order; The hammer modal experiment is carried out on the pressure difference generator to obtain the second mode frequency and the second mode vibration shape of each order; According to the difference between the first modal frequency of each order and the second modal frequency of each order, the modal frequency error of each order is obtained; According to the difference between the first mode vibration shape of each order and the second mode vibration shape of each order, the mode vibration shape error of each order is obtained; Optimizing the fractional-order transfer function model according to the modal frequency errors and modal vibration shape errors of each order to obtain an optimal fractional-order transfer function model; Taking integer-order transfer function model and optimal fractional-order transfer function model as objects, multi-mode switching PID control is performed to realize the control of magnetic suspension bearings. The steps of respectively establishing an integer-order transfer function model and a fractional-order transfer function model of the magnetic bearing of the pressure-differential generator include: The electromagnetic force exerted by two single-degree-of-freedom magnetic bearings on the rotor is calculated by magnetic circuit analysis. The electromagnetic forces of the two magnetic bearings on the rotor are linearized, and the single-degree-of-freedom integer-order transfer function model of the magnetic bearings of the pressure-differential generator is derived based on the dynamic equations of the rotor. Based on the integer-order transfer function model and considering the influence of eddy current effect on magnetic bearings, a fractional-order transfer function model is established; According to the integer-order transfer function model and considering the influence of eddy current effect on the magnetic suspension bearing, a fractional-order transfer function model is established, including: According to the angular frequency of the rotor, the expression of the magnetic flux changing with the angular frequency of the rotor is obtained; Among them, φ(ω g ) is the magnetic flux of the pressure difference generator, ω g is the angular frequency of the pressure difference generator, l m The length of the ferromagnetic material of the pressure difference generator, μ0 is the magnetic permeability of air, μ r is the relative magnetic permeability of the ferromagnetic material of the magnetic levitation motor, i is the current in the coil of the pressure difference generator; ɑ is the first intermediate parameter, Where σ is the conductivity of the ferromagnetic material of the magnetic levitation motor, A is the cross-sectional area of ​​the magnetic pole, N is the number of turns of the electromagnetic coil, and b is the height of the magnetic pole; Based on the expression of magnetic flux changing with the angular frequency of the rotor, the expression of effective magnetic resistance in time-varying magnetic field is derived; For the convenience of expression, the constant term in the above formula is represented by an intermediate parameter c, that is, Therefore, the effective magnetic resistance when the rotor is in the equilibrium position is calculated as follows: R=R0+R t ; Where R0 is the effective magnetic resistance of the static magnetic field, which is calculated as follows: Where x0 is the air gap distance between the stator and the rotor when the rotor is in the equilibrium position; According to the effective magnetic resistance expression in the time-varying magnetic field, the relationship between electromagnetic force, rotor displacement and control current is modified; Perform Laplace transformation on the relationship between the corrected electromagnetic force, rotor displacement, and control current, take the control current as input and the rotor displacement as output, and obtain a fractional-order transfer function model; The method of performing multi-mode switching PID control on an integer-order transfer function model and an optimal fractional-order transfer function model to realize control of a magnetic bearing includes: Obtaining the rotational speed of the rotor of the pressure difference generator; When the speed of the rotor is greater than a preset speed threshold, a fractional-order PID controller is used to control the rotor based on an optimal fractional-order transfer function model, and parameters of the fractional-order PID controller are tuned using a genetic algorithm; When the rotation speed of the rotor is less than or equal to a preset rotation speed threshold, a traditional PID controller is used to perform control with an integer-order transfer function model as the object.

2. A pressure difference generator magnetic bearing control method based on multi-mode switching according to claim 1, characterized in that: The method of performing finite element modal analysis on the rotor of the pressure difference generator based on the three-dimensional solid model of the pressure difference generator to obtain the first modal frequency and the first modal vibration shape of each order includes: Based on the three-dimensional solid model of the pressure difference generator, the finite element modal analysis is performed on the rotor of the pressure difference generator to obtain the motion equation in the finite element analysis; Simplifying the motion equation, setting the damping matrix and the dynamic excitation force to zero, and obtaining a simplified motion equation; The simplified motion equation is solved using differential equations to obtain the relationship between the rotor displacement and the amplitude vector and natural frequency of the pressure difference generator. Substituting the relationship between the rotor displacement, the amplitude vector matrix of the pressure differential generator, and the natural frequency of the pressure differential generator into the simplified motion equation, it is found that the only condition for the simplified motion equation to have a non-zero solution is that the coefficient is zero; When the coefficient is zero, the simplified motion equation is solved to obtain the amplitude vector and eigenvalue of each order of the pressure difference generator. The amplitude vector of each order of the pressure difference generator is used as the first modal vibration shape of each order, and the eigenvalue is used as the first modal frequency of each order.

3. The method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching according to claim 1, characterized in that: The method of optimizing the fractional-order transfer function model according to the modal frequency errors and modal vibration shape errors of each order to obtain the optimal fractional-order transfer function model includes: Step S6.1: setting the initialization temperature of the simulated annealing algorithm, and randomly generating an initial solution of the simulated annealing algorithm, using the initial solution as the current solution, and using the initialization temperature as the current temperature; Step S6.2: Perform random perturbations on the current solution to generate a new solution; Step S6.3: setting the objective function based on the modal frequency error of each order and the modal shape error of each order; Step S6.4: Calculate the objective function value of the current solution and the objective function value of the new solution; Step S6.5: Calculate the increment of the evaluation function based on the objective function value of the current solution and the objective function value of the new solution; Step S6.6: Calculate the acceptance probability based on the objective function value of the current solution, the objective function value of the new solution, and the current temperature; Step S6.7: If the increment of the evaluation function is less than zero, the new solution is accepted and used as the current solution for the next iteration; Step S6.8: When the increment of the evaluation function is greater than or equal to zero, determine whether the acceptance probability is greater than a preset probability threshold; Step S6.9: If the acceptance probability is greater than a preset probability threshold, the new solution is accepted and used as the current solution for the next iteration. The preset probability threshold is a random number between 0 and 1. Step S6.10: If the acceptance probability is less than or equal to the preset probability threshold, the new solution is not accepted and the current solution is retained; Step S6.11: Lower the current temperature according to the preset cooling strategy; Step S6.12: When the current temperature drops to a preset temperature threshold and the current number of iterations is greater than a preset maximum number of iterations, stop the iteration and output the optimal fractional-order transfer function model; Step S6.13: If the current temperature has not dropped to the preset temperature threshold or the current number of iterations is not greater than the preset maximum number of iterations, the lowered temperature is used as the current temperature, and the process returns to step S6.2 to continue iteration.

4. The method for controlling a magnetic bearing of a pressure-differential generator based on multi-mode switching according to claim 1, characterized in that: The parameters of the fractional-order PID device are tuned using a genetic algorithm, including: Step S7.2.1: Setting a value range for the parameters of the fractional-order PID controller, using a set of parameters of the fractional-order PID controller as an individual in the genetic algorithm, wherein the set of parameters of the fractional-order PID controller includes: an integral order parameter, a differential order parameter, a proportional control coefficient, an integral control coefficient, and a differential control coefficient; Step S7.2.2: Initialize all individuals in the genetic algorithm, randomly generate different values ​​within the parameter range, encode each individual, and obtain the initial population, which is used as the current population; Step S7.2.3: Initialize the parameters of the population in the genetic algorithm, which include: the number of individuals in the population, the number of iterations, the probability of crossover, and the probability of mutation; Step S7.2.4: Determine a fitness function using the error, adjustment time, overshoot, and control variable of the fractional-order PID controller. The fitness function determines the probability of each individual surviving during the iteration process. Step S7.2.5: Iteratively evolve the current population, including: calculating the fitness value of the current population using the fitness function, calculating the crossover probability of each individual, randomly selecting two individuals for crossover, performing numerical perturbations on the randomly selected individuals based on the mutation probability, and evolving to a new generation, wherein the crossover between two individuals involves exchanging a parameter from one set of encoded parameters with a parameter from another set of encoded parameters; Step S7.2.6: When the number of iterations reaches the initial set value or the value of the fitness function is less than the preset fitness threshold, stop the iteration and output the optimal fractional-order PID parameters; Step S7.2.7: When the number of iterations reaches the initial set value or the value of the fitness function is greater than or equal to the preset fitness threshold, return to step S7.2.5 and continue iterating with the new generation as the current population.

5. An electronic device, characterized in that: include: One or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the pressure difference generator magnetic levitation bearing control method based on multi-mode switching as described in any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that It stores executable instructions, which, when executed, enable the processor to execute the pressure difference generator magnetic suspension bearing control method based on multi-mode switching as described in any one of claims 1 to 4.

7. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the method for controlling a magnetic bearing of a pressure difference generator based on multi-mode switching as described in any one of claims 1 to 4 is implemented.

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