Position sensorless control method for magnetic suspension bearing

Abstract

The invention discloses a sensorless control method for a magnetic suspension bearing, and the method specifically comprises the steps: constructing a buoyancy function of radial magnetic suspension bearing electromagnetic force and air gap as well as coil excitation power and a magnetic suspension bearing kinetic model, and rewriting the kinetic model into a state equation; taking multi-frequency disturbance as a bounded variable to be expanded into a state equation, and obtaining a nonlinear expansion state observer; tracking the nutation mode, and compensating the following nutation mode in the nonlinear extended state observer to obtain an extended state displacement observer; and finally, position information is estimated through the excitation current of the magnetic suspension bearing by adopting an extended state displacement observer, the difference between the position information and the ideal air gap position is obtained, the difference is input into a PID controller, and position sensorless control is realized. The magnetic suspension bearing solves the problems of strong gyroscopic effect and vibration suppression of the magnetic suspension bearing in the prior art.

Description

Technical Field

[0001] The present invention belongs to the technical field of radial magnetic levitation bearing control, and particularly relates to a position-sensorless control method for magnetic levitation bearings. Background Art

[0002] Due to the characteristics of no friction and no need for lubrication, magnetic levitation bearings are applied in fields such as flywheel energy storage, control moment gyroscopes, artificial hearts, and molecular pumps. At the same time, they also have excellent characteristics of adjustable damping and stiffness. However, since a magnetic levitation bearing is naturally an unstable system, there are multi-frequency vibrations in the magnetic levitation bearing rotor system, and its frequency is the same frequency as the rotor frequency and its integer multiples. At the same time, there are also fractional-frequency nutation modes.

[0003] On the one hand, at high speeds of rotation, the magnetic levitation bearing rotor will generate a strong gyroscopic effect. At the same time, as the rotor speed increases, the gyroscopic effect will be further enhanced. The gyroscopic effect will be manifested through relatively slow precession modes and very strong nutation modes, where the nutation mode is the main vibration, and the frequency is the rotation frequency multiplied by the ratio of the moment of inertia of the inertial principal axis of the magnetic levitation bearing rotor to the moment of inertia of the secondary inertial principal axis.

[0004] On the other hand, due to the different concentricities on the surface of the magnetic levitation bearing rotor and the interference of the surrounding electromagnetic characteristics, the eddy current sensors of the magnetic levitation bearing will drift, and then multi-frequency harmonics will be generated in the current signal. After being amplified by the power amplifier and passing through the coils of the magnetic levitation bearing, the multi-frequency harmonics will generate strong vibrations, further affecting the stability of the rotor. In addition, the imbalance of the magnetic levitation rotor mass will also cause the rotor co-frequency component of the sensor current, thereby causing synchronous vibration. The suppression of the vibration of the active magnetic levitation bearing can actually be achieved by suppressing the harmonics in the current signal.

[0005] Currently, the methods for suppressing the vibration of the active magnetic levitation bearing include using a notch filter method or using a resonator for filtering. However, the methods of using a notch filter and a resonator can only suppress the harmonics of one frequency and are not applicable to the control under variable speeds. Moreover, when using a notch filter for filtering, it will affect the stability of the system. Specifically, it will cause a phase delay on the root locus of the system. Therefore, phase compensation is required to give the system sufficient phase margin, and the phase margins required for different frequency harmonics are also different. Summary of the Invention

[0006] The object of the present invention is to provide a position-sensorless control method for magnetic levitation bearings, which solves the problems of strong gyroscopic effect and vibration suppression in the prior art for magnetic levitation bearings.

[0007] The technical solution adopted by the present invention is a position sensorless control method for a magnetic levitation bearing, which specifically includes the following steps: Step 1: Construct a buoyancy function of the electromagnetic force of the radial magnetic levitation bearing with respect to the air gap and the coil excitation power, and based on the buoyancy function, construct a single-degree-of-freedom dynamic model of the magnetic levitation bearing, and rewrite the dynamic model into a state equation; Step 2: Consider the multi-frequency disturbance as a bounded variable and expand it into the state equation, design a new NAFal function to replace the Fal function for compensation, and obtain a nonlinear extended state observer; Step 3: Construct a plug-in fractional-order repetitive controller to track the nutation mode, and compensate the followed nutation mode in the nonlinear extended state observer to obtain an extended state displacement observer; Step 4: Use the extended state displacement observer to estimate the position information through the excitation current of the magnetic levitation bearing, subtract it from the ideal air gap position, and input it into the PID controller to achieve position sensorless control.

[0008] The present invention is further characterized in that Step 1 specifically includes the following steps: Step 1.1: Construct a buoyancy function of the electromagnetic force of the radial magnetic levitation bearing with respect to the air gap and the coil excitation power, as shown in the following formula: ; In the formula, is the magnetic permeability in vacuum; is the number of turns of the winding; is the unilateral air gap length, is the excitation current; is the magnetic induction intensity in the air gap; is the cross-sectional area of the air gap in the magnetic circuit; Step 1.2: Linearize the electromagnetic force model, perform a binary Taylor expansion in the neighborhood of the operating point of the bearing, and regard the higher-order partial derivatives as remainders; Step 1.3: Construct a single-degree-of-freedom dynamic model of the magnetic levitation bearing, as shown in the following formula: ; In the formula, is the lumped disturbance during the rotation of the rotor; Step 1.4: Rewrite the single-degree-of-freedom dynamic model of the radial magnetic levitation bearing into the form of a state equation, as shown in the following formula: .

[0009] The linearization process of the buoyancy function in Step 1.2 is as shown in the following formula: ; Among them, ; ; Convert the electromagnetic force into a differential form as shown in the following equation: .

[0010] Step 2 specifically includes the following steps: Step 2.1, construct a nonlinear extended state observer for the single-degree-of-freedom magnetic levitation bearing model; Regard the disturbance as an extended state and assume that the disturbance change rate is bounded, that is , as shown in the following equation: ; In the formula, is a nonlinear function that needs to be tuned. When a suitable one is selected, tracks , tracks , tracks , contains disturbance information; Step 2.2, construct the NAFal function as shown in the following equation: ; In the formula, α is an adjustable parameter with a value between 0 and 1; has a value greater than 0; Step 2.3, replace the Fal function of the nonlinear extended state observer in Step 2.1 with the NAFal function to obtain a new nonlinear extended state observer as shown in the following equation: .

[0011] The expression of the nonlinear function in Step 2.1 is as follows: ; In the formula, is the sign function, determines the magnitude of the nonlinearity and takes values in the range (0, 1), represents the order; determines the size of the nonlinear interval.

[0012] Step 3 specifically includes the following steps: Step 3.1, construct a plug-in fractional-order repetitive controller. The internal model order N of the repetitive controller is as shown in the following equation: ; In the formula, R represents the integer part, represents the fractional part; Step 3.2, based on the Farrow structure, design a fractional-order delay filter using the Taylor series, as shown in the following formula: ; In the formula, is the order of the Taylor expansion, is the high-order remainder of the Taylor expansion with respect to is the fractional-order of the fractional-order delay filter, is the order of the fractional-order delay filter, is the i-th sub-filter (i = 0, 1, 2,..., M), and all W + 1 sub-filters can be expressed as a constant coefficient M-order polynomial with M ≥ W; Step 3.3, construct the discrete transfer function of the plug-in fractional-order repetitive controller, as shown below: ; In the formula, is the control gain of the repetitive controller; The value of the low-pass filter is less than 1; is the time delay corresponding to the disturbance; is the phase compensation; Assume that the nutation is a jump in the direction perpendicular to the torque around the x-axis, then the expression of the nutation frequency is as follows: ; In the formula, is the rotational frequency of the rotor, is the moment of inertia of the rotor about the z-axis, is the moment of inertia of the rotor about the x-axis; according to the nutation frequency in the above formula, the delay calculation expression of the repetitive controller corresponding to the nutation is obtained, as shown below: ; In the formula, is the sampling duration; is the sampling frequency; Step 3.4, use the output of the plug-in fractional-order repetitive control as the correction term for the disturbance estimation, and correct the nonlinear extended state observer to obtain the extended state displacement observer, as shown in the following formula: ; In the formula, is the extended disturbance correction factor.

[0013] In step 4, the exciting current of the magnetic levitation bearing is collected using a Hall current sensor.

[0014] Step 4 specifically includes the following steps: Step 4.1, collect the exciting current signal in the active radial magnetic levitation bearing, and use the extended state displacement observer obtained in step 3 to observe the position signal through the current signal; Step 4.2: Subtract the obtained position signal from the ideal reference air-gap position signal to get the error signal e, and input the error signal e into the PID controller for following the ideal position, thus completing the sensorless control, as shown in the following formula: 。

[0015] The beneficial effects of the present invention are as follows: The sensorless control method for a magnetic levitation bearing of the present invention observes the position signal of the magnetic levitation bearing by using an extended state displacement observer for the excitation current signal on the magnetic levitation bearing. After subtracting it from the reference air-gap position signal, PID control is used to achieve following of the ideal air-gap position, realizing sensorless control of the magnetic levitation bearing. The adopted extended state displacement observer can suppress current harmonic signals and enhance the robustness of the magnetic levitation bearing. Description of the Drawings

[0016] Figure 1 is a schematic flow chart of the sensorless control method for a magnetic levitation bearing of the present invention; Figure 2 is a block diagram of the plug-in fractional-order repetitive controller in the extended state position observer (ESDO) of the present invention Figure 3 is a block diagram of the extended state position observer of the present invention; Figure 4 is a control block diagram of the sensorless control method for a magnetic levitation bearing of the present invention. Detailed Embodiments

[0017] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0018] Embodiment 1 The sensorless control method for a magnetic levitation bearing of the present invention, as Figure 1 shown, specifically includes the following steps: Step 1: Construct a buoyancy function of the electromagnetic force, air gap, and coil excitation power of the radial magnetic levitation bearing, and based on the buoyancy function, construct a single-degree-of-freedom dynamic model of the magnetic levitation bearing, and rewrite the dynamic model into a state equation; Step 2: Regard the multi-frequency disturbance as a bounded variable and expand it into the state equation, design a new NAFal function to replace the Fal function for compensation, and obtain a nonlinear extended state observer; Step 3: Construct an insertion fractional-order repetitive controller to track the nutation mode, and compensate the followed nutation mode in a nonlinear extended state observer to obtain an extended state displacement observer (ESDO). Step 4: Use the extended state displacement observer to estimate the position information through the excitation current of the magnetic levitation bearing, subtract it from the ideal air gap position, and input it into the PID controller to achieve sensorless control.

[0019] In the present invention, the excitation current signal on the magnetic levitation bearing is observed by using the extended state displacement observer to obtain the position signal of the magnetic levitation bearing. After subtracting it from the reference air gap position signal, PID control is used to achieve following the ideal air gap position, realizing sensorless control of the magnetic levitation bearing. The adopted extended state displacement observer can suppress current harmonic signals and enhance the robustness of the magnetic levitation bearing.

[0020] As Figure 2 shown, in the present invention, the excitation current collected from the magnetic levitation bearing coil is observed by the ESDO to estimate the bearing position signal, which is input into the PID after subtraction to achieve sensorless control.

[0021] Embodiment 2 Based on the above Embodiment 1, Step 1 of the method for sensorless control of a magnetic levitation bearing in the present invention constructs a dynamic model of a single-degree-of-freedom magnetic levitation bearing by deriving the function of the electromagnetic force of the radial magnetic levitation bearing with respect to the air gap and the coil excitation current, and derives the state equation form of the single-degree-of-freedom dynamic model, mainly including the following steps: Step 1.1: According to the working principle of the magnetic levitation bearing and combined with the basic theory of electromagnetic fields, assuming that the magnetic permeability of the iron core is infinite and ignoring the influence of edge effects, etc., the magnetic induction intensity B is as shown in formula (1): (1); In the formula, is the magnetic permeability in vacuum; is the number of winding turns; is the unilateral air gap length, is the excitation current; According to the Maxwell suction formula, the electromagnetic force of the electromagnet on the rotor is as shown in formula (2): (2); In the formula, is the electromagnetic force of the electromagnet on the rotor; is the magnetic induction intensity in the air gap; is the cross-sectional area of the air gap in the magnetic circuit; Substituting Equation (1) into Equation (2) gives the buoyancy function of the electromagnetic force of the radial magnetic levitation bearing with respect to the air gap and the coil excitation power, as shown in Equation (3): (3).

[0022] Step 1.2, it can be seen from Equation (3) that the electromagnetic force of the radial magnetic levitation bearing is a binary function of the excitation current and the rotor position. For the convenience of controller design, it is necessary to linearize it; let the operating point of the bearing be and , and perform a binary Taylor expansion in the neighborhood of the operating point, as shown in Equation (4) specifically (4); At the excitation current and the rotor displacement , when small changes occur in a very small neighborhood of the operating point , partial derivatives higher than the first-order partial derivatives can be regarded as remainders and ignored. Therefore, Equation (4) can be simplified as shown in Equation (5): (5); Among them, ; ; Convert the electromagnetic force into a differential form, as shown in Equation (6): (6).

[0023] Step 1.3, construct the dynamic model of the single-degree-of-freedom magnetic levitation bearing, as shown in Equation (7): (7); In the formula, is the gravitational acceleration, approximately ; is the lumped disturbance during the rotation of the rotor; Since the influence of the gravity on the suspended magnetic levitation rotor on its system is very small, the influence of gravity can be ignored, and Equation (7) can be simplified as shown in Equation (8): (8); Step 1.4, rewrite the single-degree-of-freedom dynamic model of the radial magnetic levitation bearing into the form of a state equation, as shown in Equation (9): (9).

[0024] Example 3 Based on the above Embodiment 2, Step 2 of the sensorless control method for a magnetic levitation bearing of the present invention, based on the state equation of the constructed single-degree-of-freedom magnetic levitation bearing dynamics model, regards the external disturbance of the system as a bounded variable, expands it into the state equation, and uses the Fal function for compensation to obtain a non-linear extended state observer, which mainly includes the following steps: Step 2.1, construct a non-linear extended state observer (NESO) for the single-degree-of-freedom magnetic levitation bearing model; regard the disturbance as an extended state, assume that the disturbance change rate is bounded, that is as shown in formula (10): (10); In the formula, is a non-linear function that needs to be tuned. After selecting a suitable it tracks , it tracks , it tracks , contains disturbance information; The expression of the non-linear function is as shown in formula (11): (11); In the formula, is the sign function, determines the magnitude of the non-linearity and takes values in the range (0, 1), represents the order; determines the size of the non-linear interval.

[0025] Step 2.2, due to the characteristics of itself, high-frequency oscillation phenomena will occur near the origin, resulting in poor anti-interference performance. The existence of the Fal function is the essence that enables the NESO to have the engineering characteristics of "small error, large gain, large error, small gain". Therefore, in order to ensure this engineering advantage of the NESO and at the same time solve the chattering problem caused by the Fal function of the NESO, a new function, the NAFal function, is constructed. The NAFal function absorbs the normal distribution function, and the function value is larger the closer it is to the center of the normal distribution, and smaller the farther it is from the center of the normal distribution. At the same time, the normal distribution function curve has good continuity, convergence, and smoothness characteristics; at the same time, it combines the arctangent function which has the good characteristics of an odd function, smooth transition and convergence, and solves the problem of excessive jumps caused by the sign.

[0026] The expression of the NAFal function is as shown in formula (12): (12); Wherein, α is an adjustable parameter, and its value ranges from 0 to 1, ensuring the characteristic of small gain of the NAFal function when there is a large error; δ takes a value greater than 0, which determines the thickness of the function boundary layer and is also a filtering factor. The larger δ is, the worse the anti-disturbance ability is.

[0027] Step 2.3: Replace the Fal function of the nonlinear extended state observer in Step 2.1 with the NAFal function to obtain a new nonlinear extended state observer, as shown in the following formula (13): (13); Wherein, is the compensation gain.

[0028] Embodiment 4 Based on the above Embodiment 3, in this embodiment, for the problem that the nutation effect on the magnetic levitation bearing is obvious in Step 3 of the sensorless control method of the present invention for magnetic levitation bearings, and considering that the frequency of the nutation effect is often a fractional multiple of the revolution frequency of the magnetic levitation bearing, an inserted fractional-order repetitive controller is designed to track the disturbance of the nutation mode and perform compensation in the nonlinear extended state observer to obtain an extended state displacement observer, which mainly includes the following steps: Step 3.1: Construct an inserted fractional-order repetitive controller for compensating the disturbance; the internal model order N of the repetitive controller is as shown in the formula (14): (14); Wherein, R represents the integer part, represents the fractional part; Step 3.2: Based on the Farrow structure, design a fractional-order delay filter using the Taylor series. The block diagram of the Farrow structure filter is as Figure 2 shown; the fractional-order delay can be expressed as a polynomial containing using the Taylor expansion, as shown in the formula (15): (15); Wherein, is the order of the Taylor expansion, is the higher-order remainder term of the Taylor expansion with respect to Here, it is an infinitesimal of higher order and can be ignored. A polynomial function with respect to can be obtained, as shown in the formula (16): (16); Furthermore, the fractional-order delay The expression is as shown in formula (17): (17); Wherein, is the order of the fractional delay filter. Substituting the above formula (16) into formula (17), the fractional delay link of the filter based on the Farrow structure can be obtained The expression is as shown in formula (18): (18); Wherein, is the i-th sub-filter (i = 0, 1, 2,..., M). All W + 1 sub-filters can be expressed as a constant coefficient M-order polynomial with M ≥ W. Usually, M = W is selected

[0029] Step 3.3, the coefficients of the sub-filter based on the Lagrange interpolation method are as shown in the following formulas (19) to (21): (19); (20); (21); From the above formula, the discrete transfer function of the plug-in fractional order repetitive controller can be obtained, as shown in formula (22): (22); Wherein, is the control gain of the repetitive controller; The value of the low-pass filter is less than 1; is the delay corresponding to the disturbance; is the phase compensation; The constructed plug-in fractional order repetitive controller is as Figure 2 shown, and the fractional order effect is realized through the Farrow filter constructed in step 3.2

[0030] The magnetic levitation bearing will face a very strong gyroscopic effect during high-speed rotation. The gyroscopic effect affects the stability of the magnetic levitation bearing in two aspects

[0031] On the one hand, it is the precession effect. This part is manifested as periodic disturbances on the plane of the rotor's stable torque. At the same time, as the rotor speed continues to increase, the periodic rotation frequency of the precession will gradually decrease

[0032] On the other hand, it is manifested through the nutation effect. Specifically, it is a rapid periodic jump around the vertical direction of the rotor's stable torque-breaking moment. As the speed increases, the frequency of the nutation will also increase

[0033] Assume that the nutation is a jump around the vertical direction of the torque on the x-axis. Then the expression of the nutation frequency is as shown in formula (23): (23); Wherein, is the rotational frequency of the rotor, is the moment of inertia of the rotor about the z-axis, is the moment of inertia of the rotor about the x-axis; According to the nutation frequency of the above formula, the delay calculation expression of the repetitive controller corresponding to nutation is obtained, as shown in formula (24): (24); Wherein, is the sampling duration; is the sampling frequency.

[0034] Step 3.4, take the output of the plug-in fractional-order repetitive control as the correction term of the disturbance estimation, and correct the estimated value of the disturbance by the nonlinear extended state observer, as shown in formula (25): (25); Substitute the corrected formula into the nonlinear extended state observer obtained in step 2.1 to obtain the extended state displacement observer strengthened by the plug-in fractional-order repetitive controller, as shown in formula (26): (26); Wherein, is the extended disturbance correction factor. The complete structural block diagram of the extended state displacement observer is as Figure 3 shown, where the RC part is the plug-in fractional-order repetitive controller.

[0035] Embodiment 5 Based on the above Embodiment 4, in step 4 of the present invention, the excitation current of the magnetic levitation bearing is collected and detected by a Hall sensor, and the current signal is transmitted to the extended state displacement observer to estimate the air gap position of the magnetic levitation bearing, and the difference is made with the ideal air gap position, and then the error signal is transmitted to the PID controller to realize the tracking of the ideal air gap position. Furthermore, in the case of not using an eddy current sensor, the sensorless control of the magnetic levitation bearing, the disturbance term compensation in the extended state displacement sensor, and the compensation of the nutation mode by the plug-in fractional-order repetitive controller are realized, enhancing the robustness of the sensorless control system of the magnetic levitation bearing and realizing the suppression of multi-frequency disturbances.

[0036] As Figure 4 shown, the excitation current collected from the magnetic levitation bearing coil by the present invention is observed by the ESDO, the bearing position signal is estimated, and after making a difference, it is input into the PID to realize sensorless control.

[0037] Embodiment 6 Based on the above-mentioned Embodiment 5, Step 4 of the sensorless control method of the present invention for a magnetic levitation bearing specifically includes the following steps: Step 4.1: Collect the excitation current signal in the active radial magnetic levitation bearing, and use the extended state displacement observer obtained in Step 3 to observe the position signal through the current signal; Specifically: The disturbance of the active radial magnetic levitation bearing is taken as an extended term in the extended state displacement observer, extended into the observer, and compensated to suppress current fluctuations caused by various reasons; Furthermore, in order to enhance the robustness of the extended state displacement observer and suppress the nutation mode that has the greatest impact on the stable operation of the active radial magnetic levitation bearing, a plug-in fractional-order repetitive controller is used to perform specific compensation for the current fluctuations caused by this special vibration of the nutation mode, so that the current harmonics become smaller and the system robustness is enhanced; Step 4.2: Subtract the obtained position signal from the ideal reference air gap position signal to obtain an error signal e, and input the error signal e to the PID controller to follow the ideal position, thereby completing the sensorless control, as shown in Equation (27): (27); The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other.

[0038] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A sensorless control method for a magnetic levitation bearing, characterized in that Specifically, it includes the following steps: Step 1: Construct a buoyancy function of the electromagnetic force of the radial magnetic levitation bearing, the air gap, and the coil excitation power, construct a dynamic model of the magnetic levitation bearing with a single degree of freedom based on the buoyancy function, and rewrite the dynamic model into a state equation; Step 2: Regard the multi-frequency disturbance as a bounded variable and expand it into the state equation, design a new NAFal function to replace the Fal function for compensation, and obtain a nonlinear extended state observer; Step 3: Construct a plug-in fractional-order repetitive controller to track the nutation mode, and compensate the following nutation mode in the nonlinear extended state observer to obtain an extended state displacement observer; Step 4: Use the extended state displacement observer to estimate the position information through the excitation current of the magnetic levitation bearing, subtract it from the ideal air gap position, and input it into the PID controller to achieve sensorless position control.

2. The sensorless control method for a magnetic levitation bearing according to claim 1, characterized in that, The specific content of Step 1 includes the following steps: Step 1.1: Construct a buoyancy function of the electromagnetic force of the radial magnetic levitation bearing, the air gap, and the coil excitation power, as shown in the following formula: ； Wherein, is the magnetic permeability in vacuum; is the number of turns of the winding; is the unilateral air-gap length, is the exciting current; is the magnetic induction intensity in the air gap; is the cross-sectional area of the air gap in the magnetic circuit; Step 1.2: Linearize the electromagnetic force model, perform a binary Taylor expansion in the neighborhood of the working point of the bearing, and regard the higher-order partial derivatives as remainders; Step 1.3: Construct a dynamic model of the magnetic levitation bearing with a single degree of freedom, as shown in the following formula: ； In the formula, is the lumped disturbance during the rotation of the rotor; Step 1.4: Rewrite the single-degree-of-freedom dynamic model of the radial magnetic levitation bearing into the form of a state equation, as shown in the following formula: 。 3. The sensorless control method for a magnetic levitation bearing according to claim 1, wherein The linearization process of the buoyancy function in Step 1.2 is as shown in the following formula: ； Among them, ; ; The electromagnetic force is converted into a differential form as shown in the following formula: 。 4. The sensorless control method for a magnetic levitation bearing according to claim 1, wherein The specific content of Step 2 includes the following steps: Step 2.1, construct a non-linear extended state observer for the single-degree-of-freedom magnetic levitation bearing model; regard the disturbance as an extended state, assume that the disturbance change rate is bounded, that is , as shown in the following formula: ； In the formula, is a non-linear function that needs to be tuned. After selecting the appropriate one, tracks , tracks , tracks , contains disturbance information; Step 2.2: Construct the NAFal function, as shown in the following formula: ； Where α is an adjustable parameter with a value between 0 and 1; The value is greater than 0; Step 2.3: Replace the Fal function in the nonlinear extended state observer in Step 2.1 with the NAFal function to obtain a new nonlinear extended state observer, as shown in the following formula: 。 5. The sensorless control method for a magnetic levitation bearing according to claim 4, characterized in that, The non-linear function in step 2.1 has the following expression: ； In the formula, is the sign function, determines the magnitude of the non-linearity and takes values in the range (0, 1), represents the order; determines the size of the non-linear interval.

6. The sensorless control method for a magnetic levitation bearing according to claim 1, characterized in that The specific content of Step 3 includes the following steps: Step 3.1: Construct a plug-in fractional-order repetitive controller, and the internal model order N of the repetitive controller is as shown in the following formula: ； wherein, R represents the integer part, represents the fractional part; Step 3.2: Based on the Farrow structure, design a fractional-order delay filter using the Taylor series, as shown in the following formula: ； In the formula, is the order of Taylor expansion, is the high-order remainder of Taylor expansion with respect to The high-order remainder of Taylor expansion, is the order of the fractional delay filter, is the i-th sub-filter (i = 0, 1, 2, …, M), and all W + 1 sub-filters can be expressed as M-order polynomials with constant coefficients where M ≥ W; Step 3.3: Construct the discrete transfer function of the plug-in fractional-order repetitive controller, as shown below: ； In the formula, is the control gain of the repetitive controller; is the value of the low-pass filter less than 1; is the delay corresponding to the disturbance; is the phase compensation; Assume that the nutation is a jump in the direction perpendicular to the torque around the x-axis, then the expression of the nutation frequency is as shown in the following formula: ； In the formula, is the rotational frequency of the rotor, is the moment of inertia of the rotor about the z-axis, is the moment of inertia of the rotor about the x-axis; according to the nutation frequency of the above formula, the delay calculation expression of the repetitive controller corresponding to nutation is obtained as follows: ； In the formula, is the sampling duration; is the sampling frequency; Step 3.4: Use the output of the plug-in fractional-order repetitive control as a correction term for the disturbance estimation to correct the nonlinear extended state observer to obtain an extended state displacement observer, as shown in the following formula: ； In the formula, is the extended perturbation correction factor.

7. The sensorless control method for a magnetic levitation bearing according to claim 1, characterized in that In Step 4, the excitation current of the magnetic levitation bearing is collected using a Hall current sensor.

8. The sensorless control method for a magnetic levitation bearing according to claim 1, characterized in that, The specific content of Step 4 includes the following steps: Step 4.1: Collect the excitation current signal in the active radial magnetic levitation bearing, and use the extended state displacement observer obtained in Step 3 to observe the position signal through the current signal; Step 4.2: Subtract the obtained position signal from the ideal reference air gap position signal to obtain an error signal e, and input the error signal e into the PID controller to follow the ideal position, completing sensorless position control, as shown in the following formula: 。

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