A method for modeling dynamics of a rotating lorentz force magnetic bearing

Abstract

The application relates to a rotating Lorentz force magnetic bearing dynamics modeling method. Based on equivalent magnetic circuit method, the stator magnetic circuit of the rotating Lorentz force magnetic bearing is analyzed, and a rotating air gap magnetic induction strength mathematical model is constructed; based on Kirchhoff's law, the Lorentz force rotor winding circuit is analyzed, and a relationship equation of angular displacement, working voltage and working current is constructed; based on the Lorentz force electromagnetism principle, the force characteristics of the Lorentz force magnetic bearing rotor are analyzed, and then a rotor dynamics model is constructed; aiming at the high-frequency commutation characteristics of the rotating Lorentz force magnetic bearing rotor, a Lorentz force magnetic bearing controller is designed based on current feedback, and then high-dynamic and high-precision reciprocating control of the rotating Lorentz force magnetic bearing in 1pi space is realized. The application has wide application prospects in the application fields of high-precision, high-stability and high-dynamic pointing of satellite load systems.

Description

Technical fields:

[0001] This invention relates to a dynamic modeling method for rotating Lorentz magnetic bearings, which is applicable to application scenarios where rotating Lorentz magnetic bearings are used as drive mechanisms to achieve high dynamic and large-range agile maneuvers of spacecraft payloads. Technical background:

[0002] Magnetic bearings, as a force / torque output mechanism, play a crucial role in servo control. Based on their working principle, they can be categorized into reluctance magnetic bearings and Lorentz force magnetic bearings: reluctance magnetic bearings work by using a coil wound around an iron core to generate a magnetic field, which magnetically attracts the rotor; Lorentz force magnetic bearings work by using a current-carrying coil in a magnetic field, where the Lorentz force generates force and torque to control rotor movement. Based on function, they can be classified into linear magnetic bearings and rotary magnetic bearings, controlling the rotor's linear motion and rotational motion around an axis. The magnetic bearing discussed in this method is a rotary Lorentz force magnetic bearing, which uses the Lorentz force as its working principle to control rotor rotation. Rotary Lorentz force magnetic bearings can achieve load rotation. Because the output torque of the magnetic bearing is linearly related to the coil current, magnetic bearings offer advantages such as high precision, high dynamics, and fast response. The magnetic bearing is equipped with a non-contact angular displacement sensor, which converts the angular displacement signal into an electrical signal. This signal is then processed by conditioning and differential circuits to become the controller input signal. Finally, the controller outputs a voltage signal, which, after passing through a D / A module and an amplifier module, outputs a control current. The control current and the input current work together to provide the operating current for the magnetic bearing, ensuring its high-precision output.

[0003] Based on the above-mentioned working principle of magnetic bearings, this invention provides a transfer function from output angular displacement to input voltage, based on the establishment of equivalent magnetic circuit model, equivalent circuit model and rotor dynamics model of magnetic bearings. Summary of the Invention:

[0004] This invention proposes a dynamic modeling method for rotating Lorentz magnetic bearings, specifically for their application in platform vibration isolation and omnidirectional deflection. The method establishes equivalent magnetic circuit models, equivalent circuit models, and rotor dynamic models for the bearing, and provides the transfer function from output angular displacement to input voltage. By changing the voltage input signal of the rotating Lorentz magnetic bearing, the output angular displacement is altered, achieving servo control. This method effectively improves the modeling accuracy of magnetic bearings and shortens the distance between model application and engineering practice. Furthermore, it effectively alleviates the contradiction between torque output accuracy and response speed in magnetic bearings.

[0005] The technical solution of this invention:

[0006] Based on the equivalent magnetic circuit method, the stator magnetic circuit of the rotating Lorentz force magnetic bearing is analyzed, and a mathematical model of the rotating air gap magnetic induction intensity is constructed. Based on Kirchhoff's laws, the rotor winding circuit of the Lorentz force is analyzed, and the relationship equations between angular displacement, operating voltage, and operating current are constructed. Based on the electromagnetic principle of Lorentz force, the force characteristics of the Lorentz force magnetic bearing rotor are analyzed, and a rotor dynamics model is constructed. Considering the high-frequency commutation characteristics of the rotating Lorentz force magnetic bearing rotor, a Lorentz force magnetic bearing controller is designed based on current feedback, thereby achieving high-dynamic and high-precision reciprocating control of the rotating Lorentz force magnetic bearing in 1π space. The specific steps are as follows:

[0007] (1) Modeling of magnetic circuit parameters of rotating Lorentz force magnetic bearing based on equivalent magnetic circuit method

[0008] The rotating Lorentz magnetic bearing is disc-shaped. Its magnetic circuit, radially from the outside in, consists of an outer magnetic ring, an outer magnet, a working air gap, an inner magnet, and an inner magnetic ring. It has one outer magnet and one inner magnet, symmetrical about the radial direction. Both the outer and inner magnets are radially magnetized in the same direction. Ignoring magnetic leakage and the magnetic field generated by the coil, its magnetic flux can be expressed as follows, based on the equivalent magnetic circuit method:

[0009]

[0010] In the formula, F O- ,F O+ ,F I- ,F I+ R represents the magnetomotive force of four permanent magnets; R1 and R2 represent the working air gap reluctance; R 内 ,R 外 R represents the magnetic reluctance of the inner and outer magnetic rings. O- ,R O+ ,R I- ,R I+ The magnetic reluctance of four permanent magnets; H c Coercivity of radially magnetized permanent magnets

[0011] Magnetic flux density can be expressed as:

[0012] B=φ / S (2)

[0013] Substituting into equation (1), we get:

[0014]

[0015] In the formula, l p1 , l p2 l1 and l2 are the magnetization lengths of the inner and outer permanent magnets; l1 and l2 are the thicknesses of the inner and outer permanent magnets; S1 and S2 are the circumferential surface areas of the magnetic rings surrounding the inner and outer permanent magnets; δ is the length of the working air gap magnetic field; S is the circumferential surface area of ​​the coil; S p1 S p2The circumferential surface area of ​​the inner and outer permanent magnets; μ0, μ r The permeability of air and the relative permeability of soft magnetic materials

[0016] (2) Equivalent circuit modeling of rotating Lorentz magnetic bearing based on Kirchhoff's laws

[0017] The electromagnetic principle of a rotating Lorentz force magnetic bearing is that a current-carrying conductor moves under the influence of the Lorentz force in a magnetic field. The main part of the magnetic bearing circuit is a coil. Based on Kirchhoff's laws, the voltage balance in the circuit can be analyzed, and its equivalent circuit can be represented by the following equation:

[0018]

[0019] A charged conductor moving in a magnetic field, cutting magnetic field lines, generates a back electromotive force. In a magnetic bearing, the charged conductor is a coil, and the equation is expressed as:

[0020]

[0021] In the formula, u is the operating voltage, which is generated by the PWM signal output by the DSP chip and then amplified to form the driving voltage of the magnetic bearing; R is the equivalent resistance of the rotating Lorentz magnetic bearing; L is the equivalent inductance of the rotating Lorentz magnetic bearing, i.e., the inductance of the coil; e is the back electromotive force, generated by the motion of the coil cutting magnetic field lines in the magnetic field; L a θ is the working length of the coil; θ is the angular displacement of the rotating Lorentz force magnetic bearing coil; B is the magnetic flux density; i(t) is the operating current in the equivalent circuit.

[0022] (3) High-precision, high-dynamic rotating Lorentz magnetic bearing rotor dynamics modeling

[0023] In a rotating Lorentz force magnetic bearing, the stator consists of inner and outer magnets and a magnetic ring, while the rotor is composed of coils and their supports. When the coils are energized, they experience a Lorentz force in the magnetic field.

[0024] Lorentz force is:

[0025] F(t) = BL a i1(t) (6)

[0026] A rotating Lorentz force magnetic bearing has a pair of inner and outer magnets. The coil is connected in series and passes through two working air gaps. It is subjected to a pair of Lorentz forces of equal magnitude and opposite direction, generating torque.

[0027] The torque is:

[0028] T(t) = BL a Di1(t) (7)

[0029] D is the rotation diameter of the rotor (coil); i1(t) is the current in the coil, which is different from the equivalent current in equation (4). In the rotating Lorentz force magnetic bearing, the coil support and the output shaft adopt a mechanical transmission structure. When the coil is energized and subjected to the Lorentz force to generate torque, it drives the output shaft of the coil support to rotate, that is, to achieve fixed-axis rotation around the axial direction. In this process, three kinds of torques are overcome: inertial torque T m Frictional torque T f Elastic torque T e The inertial torque is related to the rotational inertia and angular acceleration of the rotor, transmission structure, and load; the frictional torque is generated by the frictional force in the mechanical transmission structure; and the elastic torque is related to the material of the output shaft itself. The rotor torque balance equation is expressed as:

[0030]

[0031] In the formula, J is the moment of inertia of the rotating Lorentz force magnetic bearing rotor assembly and the load; K f K is the friction torque coefficient. e The elastic moment coefficient

[0032] (4) Design of a 1π-space rotation controller for a rotating Lorentz magnetic bearing based on current feedback

[0033] In the rotor section of the rotating Lorentz magnetic bearing, the sensor is a non-contact eddy current angular displacement sensor. The sensor converts the rotor's angular displacement signal into an electrical signal, which is then conditioned by a conditioning circuit, averaged by an adder, and input to the controller. The controller ultimately generates a control current. When the angular displacement θ = ±90°, the controller output current remains constant, and the rotor maintains θ = ±90°. When the next angular displacement signal is input, |θ| ≤ 90°, operation continues, thus ensuring commutation at the endpoints. Therefore, the angular displacement range of the rotating Lorentz magnetic bearing is -90° to 90°, ensuring high-precision, high-dynamic tracking capability within a 1π space.

[0034] Based on the above working principle of the magnetic bearing, PID parameters are designed to achieve stable control of the magnetic bearing. The equation is expressed as:

[0035]

[0036] Among them, K p K is the proportionality coefficient. d K is the differential coefficient. I Let i1(t) be the integral coefficient and i2(t) be the feedback current. After introducing current feedback, the actual operating current is i1(t) - i2(t), that is:

[0037] i(t)=i1(t)-i2(t) (10)

[0038] Combining equations (4), (5), (5), (7), (8), (9), and (10), we obtain the transfer function from the magnetic bearing output angular displacement to the input voltage:

[0039]

[0040] Expanding equation (11), we get

[0041]

[0042] Equation (12) shows that changing the driving voltage of the magnetic bearing can change the output angular displacement of the magnetic bearing. The driving voltage of the magnetic bearing is the voltage signal output by the controller, which is formed after passing through the A / D module and the power amplification module. Therefore, the transfer function between the output angular displacement and the input voltage should be given for the modeling of the magnetic bearing. Based on the equivalent magnetic circuit method, the stator magnetic circuit of the rotating Lorentz force magnetic bearing is analyzed, and a mathematical model of the magnetic induction intensity of the rotating air gap is constructed; based on Kirchhoff's law, the rotor winding circuit of the Lorentz force is analyzed, and the relationship equations of angular displacement, working voltage and working current are constructed; based on the electromagnetic principle of Lorentz force, the force characteristics of the Lorentz force magnetic bearing rotor are analyzed, and then the rotor dynamics model is constructed; for the high-frequency commutation characteristics of the rotating Lorentz force magnetic bearing rotor, a Lorentz force magnetic bearing controller is designed based on current feedback, and then the high dynamic and high-precision reciprocating control of the rotating Lorentz force magnetic bearing in 1π space is realized.

[0043] Each parameter in equation (12) has a practical physical meaning, and the rotating Lorentz force magnetic bearing is a linear time-invariant system. Simplifying equation (12) by combining the coefficients of each order, we have:

[0044]

[0045] Equations of state:

[0046]

[0047] Output equation:

[0048]

[0049] According to the controllability criterion of linear time-invariant systems:

[0050]

[0051] Rank M = 4, so the system is completely controllable.

[0052] The above mathematically proves the necessity of stable magnetic bearing control. Therefore, the structural parameters can be designed correctly, the program design in the controller can be adjusted, and high-precision, high-dynamic tracking capability in 1π space can be achieved. Attached Figure Description

[0053] Figure 1 Detailed implementation plan diagram;

[0054] Figure 2 Magnetic circuit schematic diagram;

[0055] Figure 3 Equivalent magnetic circuit diagram of a rotating Lorentz force magnetic bearing;

[0056] Figure 4 Equivalent circuit diagram of a rotating Lorentz force magnetic bearing;

[0057] Figure 5 Control current diagram of a rotating Lorentz force magnetic bearing;

[0058] Figure 6 Cross-sectional structural diagram of a rotating Lorentz force magnetic bearing;

[0059] Figure 7 Schematic diagram of the coordinate system of a rotating Lorentz force magnetic bearing;

[0060] Figure 8 Vector diagram of magnetic field lines of a rotating Lorentz force magnetic bearing; Detailed Implementation Plan

[0061] The specific implementation scheme of the present invention is as follows: Figure 1 As shown, the equivalent magnetic circuit, equivalent circuit, and feedback circuit are as follows: Figure 3 As shown in Figures 4 and 5, the specific implementation steps are as follows:

[0062] (1) Modeling of magnetic circuit parameters of rotating Lorentz force magnetic bearing based on equivalent magnetic circuit method

[0063] The rotating Lorentz magnetic bearing is disc-shaped. Its magnetic circuit, radially from the outside in, consists of an outer magnetic ring, an outer magnet, a working air gap, an inner magnet, and an inner magnetic ring. It has one outer magnet and one inner magnet, symmetrical about the radial direction. Both the outer and inner magnets are radially magnetized in the same direction. Ignoring magnetic leakage and the magnetic field generated by the coil, its magnetic flux can be expressed as follows, based on the equivalent magnetic circuit method:

[0064]

[0065] In the formula, F O- ,F O+ ,F I- ,F I+ R represents the magnetomotive force of four permanent magnets; R1 and R2 represent the working air gap reluctance; R 内 ,R 外 R represents the magnetic reluctance of the inner and outer magnetic rings. O- ,R O+ ,R I- ,R I+ The magnetic reluctance of four permanent magnets; H cCoercivity of radially magnetized permanent magnets

[0066] Magnetic flux density can be expressed as:

[0067] B=φ / S (2)

[0068] Substituting into equation (1), we get:

[0069]

[0070] In the formula, l p1 , l p2 L1 and L2 are the magnetization lengths of the inner and outer permanent magnets; L1 and L2 are the thicknesses of the inner and outer permanent magnets; S1 and S2 are the circumferential surface areas of the magnetic rings surrounding the inner and outer permanent magnets; δ is the length of the working air gap magnetic field; S is the circumferential surface area of ​​the coil; S p1 S p2 The circumferential surface area of ​​the inner and outer permanent magnets; μ0, μ r The permeability of air and the relative permeability of soft magnetic materials

[0071] (2) Equivalent circuit modeling of rotating Lorentz magnetic bearing based on Kirchhoff's laws

[0072] The electromagnetic principle of a rotating Lorentz force magnetic bearing is that a current-carrying conductor moves under the influence of the Lorentz force in a magnetic field. The main part of the magnetic bearing circuit is a coil. Based on Kirchhoff's laws, the voltage balance in the circuit can be analyzed, and its equivalent circuit can be represented by the following equation:

[0073]

[0074] A charged conductor moving in a magnetic field, cutting magnetic field lines, generates a back electromotive force. In a magnetic bearing, the charged conductor is a coil, and the equation is expressed as:

[0075]

[0076] In the formula, u is the operating voltage, which is generated by the PWM signal output by the DSP chip and then amplified to form the driving voltage of the magnetic bearing; R is the equivalent resistance of the rotating Lorentz magnetic bearing; L is the equivalent inductance of the rotating Lorentz magnetic bearing, i.e., the inductance of the coil; e is the back electromotive force, generated by the motion of the coil cutting magnetic field lines in the magnetic field; L a θ is the working length of the coil; θ is the angular displacement of the rotating Lorentz force magnetic bearing coil; B is the magnetic flux density; i(t) is the operating current in the equivalent circuit.

[0077] (3) High-precision, high-dynamic rotating Lorentz magnetic bearing rotor dynamics modeling

[0078] In a rotating Lorentz force magnetic bearing, the stator consists of inner and outer magnets and a magnetic ring, while the rotor is composed of coils and their supports. When the coils are energized, they experience a Lorentz force in the magnetic field.

[0079] Lorentz force is:

[0080] F(t) = BL a i1(t) (6)

[0081] A rotating Lorentz force magnetic bearing has a pair of inner and outer magnets. The coil is connected in series and passes through two working air gaps. It is subjected to a pair of Lorentz forces of equal magnitude and opposite direction, generating torque.

[0082] The torque is:

[0083] T(t) = BL a Di1(t) (7)

[0084] D is the rotation diameter of the rotor (coil); i1(t) is the current in the coil, which is different from the equivalent current in equation (4). In the rotating Lorentz force magnetic bearing, the coil support and the output shaft adopt a mechanical transmission structure. When the coil is energized and subjected to the Lorentz force to generate torque, it drives the output shaft of the coil support to rotate, that is, to achieve fixed-axis rotation around the axial direction. In this process, three kinds of torques are overcome: inertial torque T m Frictional torque T f Elastic torque T e The inertial torque is related to the rotational inertia and angular acceleration of the rotor, transmission structure, and load; the frictional torque is generated by the frictional force in the mechanical transmission structure; and the elastic torque is related to the material of the output shaft itself. The rotor torque balance equation is expressed as:

[0085]

[0086] In the formula, J is the moment of inertia of the rotating Lorentz force magnetic bearing rotor assembly and the load; K f K is the friction torque coefficient. e The elastic moment coefficient

[0087] (4) Design of a 1π-space rotation controller for a rotating Lorentz magnetic bearing based on current feedback

[0088] In the rotor section of the rotating Lorentz magnetic bearing, the sensor is a non-contact eddy current angular displacement sensor. The sensor converts the rotor's angular displacement signal into an electrical signal, which is then conditioned by a conditioning circuit, averaged by an adder, and input to the controller. The controller ultimately generates a control current. When the angular displacement θ = ±90°, the controller output current remains constant, and the rotor maintains θ = ±90°. When the next angular displacement signal is input, |θ| ≤ 90°, operation continues, thus ensuring commutation at the endpoints. Therefore, the angular displacement range of the rotating Lorentz magnetic bearing is -90° to 90°, ensuring high-precision, high-dynamic tracking capability within a 1π space.

[0089] Based on the above working principle of the magnetic bearing, PID parameters are designed to achieve stable control of the magnetic bearing. The equation is expressed as:

[0090]

[0091] Among them, K p K is the proportionality coefficient. d K is the differential coefficient. I Let i1(t) be the integral coefficient and i2(t) be the feedback current. After introducing current feedback, the actual operating current is i1(t) - i2(t), that is:

[0092] i(t)=i1(t)-i2(t) (10)

[0093] Combining equations (4), (5), (5), (7), (8), (9), and (10), we obtain the transfer function from the magnetic bearing output angular displacement to the input voltage:

[0094]

[0095] Expanding equation (11), we get

[0096]

[0097] like Figure 6 , Figure 7 The rotating Lorentz magnetic bearing structure mainly includes an inner magnetic ring, an outer magnetic ring, a coil support, and a coil. Two pairs of inner and outer magnetic rings are symmetrically distributed about the Z-axis. The outer magnetic ring is placed outside the coil support, and the inner magnetic ring is placed inside the coil. The inner and outer magnetic rings are radially magnetized, and their magnetization directions are the same. The magnetization direction of the inner magnetic ring in the negative Z-axis direction is the same as that in the positive Z-axis direction, and the magnetization direction of the outer magnetic ring in the negative Z-axis direction is the same as that in the positive Z-axis direction. The coil is wound on the coil support and fixed to a rotating axis of a double-frame float. When the coil is energized, a pair of torques are generated in a uniform magnetic field perpendicular to the coil, causing the coil to deflect axially between the inner and outer magnetic rings. Figure 8 The magnetic circuit of the rotating Lorentz force magnetic bearing is closed, and the magnetic density at the working air gap is uniform. By reasonably designing the parameters of the inner magnet, outer magnet, inner and outer magnetic rings, etc., through formula (3), the magnetic induction intensity B is configured to the desired value.

[0098] The contents not described in detail in this invention are existing technologies known to those skilled in the art.

Claims

1. A method for dynamic modeling of a rotating Lorentz force magnetic bearing, characterized in that: The stator magnetic circuit of the rotating Lorentz force magnetic bearing is analyzed based on the equivalent magnetic circuit method, and a mathematical model of the rotating air gap magnetic induction intensity is constructed. The rotor winding circuit of the Lorentz force is analyzed based on Kirchhoff's laws, and the relationship equations between angular displacement, operating voltage, and operating current are constructed. The force characteristics of the Lorentz force magnetic bearing rotor are analyzed based on the electromagnetic principles of Lorentz force, and a rotor dynamics model is constructed. Considering the high-frequency commutation characteristics of the rotating Lorentz force magnetic bearing rotor, a Lorentz force magnetic bearing controller is designed based on current feedback, thereby achieving high-dynamic and high-precision reciprocating control of the rotating Lorentz force magnetic bearing in 1π space. Specifically, the following steps are included: (1) Modeling of magnetic circuit parameters of rotating Lorentz force magnetic bearing based on equivalent magnetic circuit method The rotating Lorentz magnetic bearing is disc-shaped. Its magnetic circuit, radially from the outside in, consists of an outer magnetic ring, an outer magnet, a working air gap, an inner magnet, and an inner magnetic ring. Symmetrically arranged radially, it has an outer and an inner magnet. Both the outer and inner magnets are radially magnetized in the same direction. Ignoring magnetic leakage and the influence of the magnetic field generated by the coil, its magnetic flux is expressed as follows, based on the equivalent magnetic circuit method: (1) In the formula, The magnetomotive force of four permanent magnets; For working air gap magnetic reluctance; The magnetic reluctance of the inner and outer magnetic rings; The magnetic resistance of four permanent magnets; The coercivity of a radially magnetized permanent magnet; Magnetic induction intensity is expressed as (2) Substituting into equation (1), we can obtain (3) In the formula, , The magnetization length of the inner and outer permanent magnets; , The thickness of the inner and outer permanent magnets; , The circumferential surface area of ​​the magnetic ring surrounding the inner and outer permanent magnets; The length of the working air gap magnetic field; This refers to the circumferential surface area of ​​the coil. , The circumferential surface area of ​​the inner and outer permanent magnets; The permeability of air and the relative permeability of soft magnetic materials (2) Equivalent circuit modeling of rotating Lorentz magnetic bearing based on Kirchhoff's laws The electromagnetic principle of a rotating Lorentz force magnetic bearing is that a current-carrying conductor moves under the influence of the Lorentz force in a magnetic field. The main part of the magnetic bearing circuit is a coil. Based on Kirchhoff's laws, the voltage balance in the circuit is analyzed, and its equivalent circuit is represented by an equation. (4) A charged conductor moving in a magnetic field cuts magnetic field lines and generates a back electromotive force. In a magnetic bearing, the charged conductor is a coil, and the equation is expressed as follows: (5) In the formula, It is the operating voltage, which is generated by the PWM signal output by the DSP chip and then amplified by the power amplifier to form the driving voltage of the magnetic bearing. It is the equivalent resistance of a rotating Lorentz force magnetic bearing; It is the equivalent inductance of a rotating Lorentz force magnetic bearing, i.e., the inductance of a coil; It is a back electromotive force, generated by the motion of a coil cutting magnetic field lines in a magnetic field; This refers to the working length of the coil; The angular displacement of the rotating Lorentz force magnetic bearing coil; It represents the magnetic flux density; This is the operating current in the equivalent circuit. (3) High-precision, high-dynamic rotating Lorentz magnetic bearing rotor dynamics modeling In a rotating Lorentz force magnetic bearing, the stator consists of inner and outer magnets and a magnetic ring, while the rotor is composed of coils and their supports. When the coils are energized, the Lorentz force they experience in the magnetic field is described as follows: (6) A rotating Lorentz force magnetic bearing has a pair of inner and outer magnets. The coil is connected in series and passes through two working air gaps. It is subjected to a pair of equal and opposite Lorentz forces, producing a torque of... (7) The diameter of the rotor is its rotational diameter; the core component of the rotor is the coil. It is the current in the coil, which is different from the equivalent current in equation (4); in the rotating Lorentz force magnetic bearing, the coil support and the output shaft adopt a mechanical transmission structure. When the coil is energized and subjected to the Lorentz force to generate torque, it drives the output shaft of the coil support to rotate, that is, to achieve fixed-axis rotation around the axial direction. In this process, three kinds of torques are overcome: inertial torque. Frictional torque elastic torque The inertial torque is related to the rotational inertia and angular acceleration of the rotor, transmission structure, and load; the frictional torque is generated by the frictional force in the mechanical transmission structure; and the elastic torque is related to the material of the output shaft itself. The rotor torque balance equation is expressed as: (8) In the formula, The moment of inertia of the rotating Lorentz force magnetic bearing rotor assembly and the load; This is the friction torque coefficient; It is the elastic moment coefficient; (4) Design of a 1π-space rotation controller for a rotating Lorentz magnetic bearing based on current feedback In the rotating Lorentz magnetic bearing rotor section, the sensor is a non-contact eddy current angular displacement sensor. The sensor converts the rotor's angular displacement signal into an electrical signal, which is then conditioned by a conditioning circuit, averaged by an adder, and input into the controller. Finally, the controller generates a control current; when the angular displacement... At this time, the control current output by the controller remains constant, and the rotor remains stationary. When the next angle displacement signal is input, It continues to work, thus ensuring reversal at the endpoint; therefore, the angular displacement range of the rotating Lorentz magnetic bearing is -90° to 90°, ensuring high-precision and high-dynamic tracking capability within a 1π space. Based on the above working principle of the magnetic bearing, a PID controller is designed to achieve stable control of the magnetic bearing. The controller equation is expressed as follows: (9) in, This is the proportionality coefficient. These are the differential coefficients. The integral coefficient is... To provide feedback current, after introducing current feedback, the actual operating current is... ,Right now: (10) Combining equations (4), (5), (7), (8), (9), and (10), we obtain the transfer function from the magnetic bearing output angular displacement to the input voltage: (11) Expanding equation (11), we get (12) In Equation (12), all parameters have practical physical meanings. Each parameter can be designed correctly to improve the control accuracy and dynamic tracking capability of the rotating Lorentz force magnetic bearing. This method starts from the structure of the magnetic bearing, analyzes its electromagnetic and rotor dynamics working principles, fully considers the needs of practical applications, and finally gives the transfer function of the magnetic bearing from input voltage to output angular displacement. According to this method, each structural parameter can be designed correctly, the program design in the controller can be adjusted, and high-precision and high-dynamic tracking capability in 1π space can be achieved.

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