A four-degree-of-freedom dynamic control method for coaxial biorthogonal Lorentz force magnetic bearings

Abstract

This invention relates to a four-degree-of-freedom dynamic modeling and control method for a coaxial double orthogonal Lorentz force magnetic bearing. Based on the structural characteristics of a single orthogonal Lorentz force magnetic bearing, an equivalent magnetic circuit analysis is performed. Using Ohm's law for magnetic circuits, a magnetic induction intensity model of the coil air gap is obtained. The mathematical relationship between the orthogonal magnetic bearing parameters and the Lorentz force is derived, and the force analysis of the coil is conducted. After the magnetically levitated rotor is disturbed, a PID controller outputs a control current based on the rotor displacement change, completing the dynamic modeling of two-degree-of-freedom translation and two-degree-of-freedom rotation. The rotor displacement measurement value is decomposed into translational and rotational components to construct a decoupling control law for the translational-rotational coupled motion, thereby achieving closed-loop control of the four-degree-of-freedom translational-rotational coupled motion. This invention solves the problem of dynamic modeling and motion control of double orthogonal Lorentz force magnetic bearings and has broad application prospects in the field of attitude control technology for novel spacecraft.

Description

Technical Field

[0001] This invention relates to a dynamic modeling and control method for coaxial double orthogonal Lorentz force magnetic bearings, which can realize decoupled control of the translational motion of magnetically levitated rotors and is applicable to the attitude control system of spacecraft based on orthogonal Lorentz force magnetic bearings. Technical Background To meet the performance requirements of ultra-high agility, ultra-high stability, and ultra-high precision for satellites, while suppressing the impact of micro-vibrations on the pointing accuracy, pointing stability, and agility of spacecraft, magnetic levitation technology can be used to suppress vibrations caused by load disturbances. Compared to traditional spacecraft platforms using mechanical vibration isolation and maneuvering mechanisms, magnetic levitation technology has the advantages of being non-contact, resistant to micro-vibrations, and having a long lifespan, making it a hot research topic in the design of ultra-high agility, ultra-stability, and ultra-precision spacecraft platforms.

[0002] Magnetic levitation platforms can be classified into magnetic reluctance and Lorentz force magnetic levitation platforms based on their force mechanisms. Magnetic reluctance magnetic levitation platforms have a large load-bearing capacity and high positioning accuracy. However, their electromagnetic force is quadratically related to the control current, resulting in negative displacement stiffness and a complex control system. Compared to magnetic reluctance magnetic levitation platforms, Lorentz force magnetic levitation platforms offer better linearity, a larger control bandwidth, and the ability to quickly achieve stable levitation. They are an ideal levitation support method in microgravity environments, as the control torque provided to the load is proportional to the current, has no negative displacement stiffness, and offers higher control accuracy. Based on this, this invention utilizes a Lorentz force magnetic levitation omnidirectional stabilization platform developed by a research team at an aerospace engineering university. Employing a full Lorentz force magnetic levitation load support system, it achieves high-dynamic omnidirectional maneuverability based on high-precision levitation control, providing a novel technical approach for ultra-stable, ultra-precise, and ultra-sensitive "three-super" satellite platforms.

[0003] The orthogonal magnetic bearings mentioned in this invention are components used to achieve attitude control of the rotor and load based on a Lorentz force magnetic levitation platform. By designing the dynamics and control laws for a pair of Lorentz force orthogonal magnetic bearings on both sides of the rotor, closed-loop control of the rotor after disturbance can be achieved. This solves the dynamics analysis and attitude control of two-degree-of-freedom translation and two-degree-of-freedom rotation of a Lorentz force magnetic levitation omnidirectional stable platform, as well as the dynamics modeling and motion control problems of dual orthogonal Lorentz force magnetic bearings, and has broad application prospects in the field of attitude control technology for novel spacecraft. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the complexity of the system caused by the square relationship between electromagnetic force and current and the existence of negative displacement stiffness in a magnetic reluctance magnetic levitation platform, as well as the coupling problem in the rotor's translational motion. A Lorentz force orthogonal magnetic bearing control method is proposed. This method uses the Lorentz force to replace magnetic reluctance for stable control of the rotor after disturbance. It decomposes the four-degree-of-freedom translational motion based on the displacement sensor measurement, decoupling the translational motion and solving the attitude stability control problem of the Lorentz force magnetic levitation platform.

[0005] The technical solution of this invention is as follows: After the magnetic bearing rotor is disturbed by two channels, based on the structure of a single orthogonal magnetic bearing, an equivalent magnetic circuit analysis is performed on the magnetic bearing. Using Ohm's law for magnetic circuits, the uniform magnetic field of the coil air gap is obtained. The linear relationship between the Lorentz force on the coil and the coil current is derived, and the force analysis of the coil is performed. After the magnetic bearing rotor is disturbed, based on the change in displacement sensor values, a PID controller outputs control current to complete the dynamic modeling of two-degree-of-freedom translation and two-degree-of-freedom rotation. Since the sensor measurement value can be decomposed into sensor offset values ​​caused by translation and rotation, the decoupling of the two channels of translational-rotational coupled motion can be achieved. Closed-loop control is then performed on the disturbed four-degree-of-freedom translational-rotational coupled motion, specifically including the following steps: (1) Dynamic modeling of a single orthogonal Lorentz force magnetic bearing The reference coordinate system is determined with the center of the magnetic bearing as the origin. The positive Z-axis is to the right along the rotor axis, and the positive Y-axis is upward along the center of the magnetic bearing. The X-axis forms a right-handed system with the Y and Z axes. Ignoring the effects of magnet leakage flux, coil self-induced magnetic field, and edge effects, an equivalent magnetic circuit for a single orthogonal magnetic bearing is established using the equivalent magnetic circuit method. The magnetic circuit includes the magnetomotive force (MOF) of four sets of magnet rings, the corresponding permanent magnet reluctance, and the air gap reluctance passing through the air gap between the inner and outer magnets. The MOF of the magnet rings is linearly related to the tempering length of the magnets. All reluctances are connected in series. The main magnetic flux of the coil is obtained from the magnetic circuit. The mathematical expression for magnetic flux density B is: in, , For the coercivity of the magnet, The magnetization length of the magnet. To correspond to the magnetic reluctance of the magnet, and These are the air gap reluctances between the outer and inner magnets that pass through the rotor coils. and These represent the magnetic flux densities of the air gaps between the inner and outer magnets, respectively. and These are the equivalent cross-sectional areas corresponding to the inner and outer magnetic flux densities, respectively. When no disturbance torque is generated, the Lorentz force experienced by a single orthogonal magnetic bearing in the magnetic field formed by the inner and outer magnets and the magnetic ring is: in, This indicates the strength of the annular magnetic field formed on the rotor by the inner magnet, outer magnet, and magnetic guide ring. This represents the steady current in the tile-shaped coil when no interfering torque is generated. This represents the effective magnetic induction length of the long arc segment of the tile-shaped coil in a circular magnetic field. This represents the effective magnetic induction length of the short arc segment of the tile-shaped coil in a circular magnetic field. and It can be represented as: in, Indicates the opening angle and outer radius of the tile-shaped coil. and l i This indicates the distance from the long arc segment of the tile-shaped coil to the center of the coil, and the inner radius. Representing the distance from the short arc segment of the tile-shaped coil to the center of the coil, combining equation (3) with equations (2) and (4) yields the dynamic model of a single Lorentz force orthogonal magnetic bearing: in, and Let Y and X represent the output forces of the orthogonal magnetic bearings in the Y and X channels, respectively. Under normal operating conditions, the magnetization length, equivalent magnetic reluctance, and equivalent cross-sectional area corresponding to the internal and external magnetic flux remain basically unchanged. It can be assumed that the magnetic bearing output force and the coil current are linearly related. Equation (5) can be equivalently represented as: Where H is the coil current stiffness coefficient; (2) Translational dynamics modeling of a pair of coaxial orthogonal Lorentz force magnetic bearings When the magnetic bearing rotor is disturbed, the four displacement sensors on the two channels at both ends of the rotor will generate a shift. , , , The control currents generated by the PID controller are respectively , , , : in, The control coils responsible for rotor translation are designed to have equal and opposite control currents in the bearing coils at both ends of each channel when only considering rotor translation. This results in equal and opposite Lorentz forces. Assuming the initial current in the bearing coils of both magnetic bearings is zero, the equation of motion for rotor translation can be expressed as: Combining equation (7), the rotor translational dynamics equations can be simplified to: Applying the Laplace transform to both sides of the equation, we obtain the transfer function considering only the rotor translation: in, and The control current on both channels is the input quantity. and It represents the displacement change of the rotor after the coil generates a control current; it is the output quantity. (3) Rotational dynamics modeling of a pair of coaxial orthogonal Lorentz force magnetic bearings When only considering the rotor's rotational motion, the control currents of the coils in the magnetic bearings at both ends of each channel are equal in magnitude and opposite in direction, resulting in equal in magnitude and opposite in direction of the Lorentz forces. When the output force of the left magnetic bearing is positive and the output force of the right magnetic bearing is negative, the rotor rotates clockwise; when the output force of the right magnetic bearing is positive and the output force of the left magnetic bearing is negative, the rotor rotates counterclockwise. During the actual rotation of the rotor, the rotation angle is relatively small, and the rotation arc can be approximated by the displacement sensor's sensitive offset. in, These represent the rotor offset angles on the Y and X channels, respectively. This represents the distance from the center of the orthogonal magnetic bearing to the center of the shaft. The control current generated by the PID controller after the displacement sensor measurement is... : in, Responsible for controlling the rotor's rotation, assuming the initial current in the two magnetic bearing coils is 0, the equation of motion for the rotor's rotation can be expressed as: in, and These represent the moments of inertia of the magnetically levitated rotor along the Y-axis and X-axis, respectively. and The rotational angular accelerations generated by the Lorentz force produced by the control current in the tile-shaped coil on the rotor in the two channels can be simplified to: Applying the Laplace transform to both sides of the equation yields the transfer function considering only rotor rotation: in, and This represents the control current on both channels; it is an input quantity. and This represents the angular change in rotor rotation caused by the control current generated by the coil; it is the output quantity. In the formula... All use PID control: Based on the above force analysis of rotor translation and rotation, the control force and control torque generated by the magnetic bearing can be obtained as follows: in, and , and This represents the projection of the control force and torque provided by the orthogonal magnetic bearing to the rotor onto the Y and X channels; (4) Design of translational-rotational coupling motion and control law for orthogonal Lorentz force magnetic bearing When considering translational-rotational coupled motion, based on the algebraic relationship between the translational and rotational displacements in the two channels after being disturbed in any direction, the sensitive offset of the displacement sensor is decomposed into translational and rotational displacements, thus achieving decoupling in the dynamic modeling process of translational-rotational coupled motion. The algebraic relationship between the translational and rotational displacements and the total offset is as follows: in, and These represent the translational displacement offset of the magnetically levitated rotor in the two channels, respectively. and These represent the rotational displacement of the magnetically levitated rotor in the two channels, respectively. Based on the decomposition of the displacement sensor's sensitive offset in the two motion modes, the current in the tile-shaped coil also generates a control current under the action of the PID controller, which can be expressed as: in, and These represent the control currents in the two channels controlling the translational motion during the translational-rotational coupled motion. and Let represent the control currents in the two channels controlling rotation during translational-rotational coupled motion. By decomposing the obtained translational and rotational control currents at the orthogonal magnetic bearings at the left and right ends, we can obtain: Combining equations (17)(18)(19)(20), we can obtain: The above equation is the decoupled control law after decomposing the rotor translation and rotation of the displacement sensor using the sensor measurement principle, where H is the current stiffness coefficient, and G... P (s) and G Z (s) represents the control of the current during translation and rotation.

[0006] The principle of this invention is as follows: After the magnetic bearing rotor is disturbed by two channels, the equivalent magnetic circuit of the magnetic bearing is analyzed based on the structure of a single orthogonal magnetic bearing. Using Ohm's law for magnetic circuits, the uniform magnetic field of the air gap of the coil is obtained. The linear relationship between the Lorentz force on the coil and the coil current is derived, and the force analysis of the coil is performed. After the magnetic bearing rotor is disturbed, the control current is output by the PID controller based on the change of displacement sensor, and the dynamic modeling of two degrees of freedom translation and two degrees of freedom rotation is completed. Since the sensor measurement value can be decomposed into the sensor offset value caused by translation and rotation, the decoupling of the two channels of translational-rotational coupled motion can be realized, and closed-loop control of the four-degree-of-freedom translational-rotational coupled motion after disturbance can be performed. Attached Figure Description

[0007] Figure 1. Control scheme diagram of orthogonal Lorentz force magnetic bearing; Figure 2. Structure diagram of orthogonal Lorentz force magnetic bearing; Figure 3. Schematic diagram of orthogonal Lorentz force magnetic bearing structure; Figure 4. Equivalent magnetic circuit diagram of orthogonal Lorentz force magnetic bearing; Figure 5. Force diagram of the orthogonal Lorentz force magnetic bearing coil; Figure 6. Cross-sectional view of a pair of coaxial orthogonal Lorentz force magnetic bearings; Detailed Implementation The overall control scheme of the present invention is as follows: Figure 1 As shown, the three-dimensional model of the orthogonal magnetic bearing is as follows: Figure 2 As shown, the forces acting on the magnetic bearing during coil and rotor rotation are as follows: Figure 5 and Figure 6 As shown, after the magnetic bearing rotor is disturbed by two channels, an equivalent magnetic circuit analysis is performed on the magnetic bearing based on the structure of a single orthogonal magnetic bearing. Using Ohm's law for magnetic circuits, the uniform magnetic field of the coil air gap is obtained. The linear relationship between the Lorentz force on the coil and the coil current is derived, and the force analysis of the coil is performed. After the magnetic bearing rotor is disturbed, the control current is output by a PID controller based on the change in displacement sensor readings to complete the dynamic modeling of two-degree-of-freedom translation and two-degree-of-freedom rotation. Since the sensor measurement value can be decomposed into the sensor offset value caused by translation and rotation, the decoupling of the two channels of translational-rotational coupled motion can be achieved. Closed-loop control is then performed on the disturbed four-degree-of-freedom translational-rotational coupled motion, specifically including the following steps: (1) Dynamic modeling of a single orthogonal Lorentz force magnetic bearing The reference coordinate system is determined with the center of the magnetic bearing as the origin. The positive Z-axis is to the right along the rotor axis, and the positive Y-axis is upward along the center of the magnetic bearing. The X-axis forms a right-handed system with the Y and Z axes. Ignoring the effects of magnet leakage flux, coil self-induced magnetic field, and edge effects, an equivalent magnetic circuit for a single orthogonal magnetic bearing is established using the equivalent magnetic circuit method. The magnetic circuit includes the magnetomotive force (MOF) of four sets of magnet rings, the corresponding permanent magnet reluctance, and the air gap reluctance passing through the air gap between the inner and outer magnets. The MOF of the magnet rings is linearly related to the tempering length of the magnets. All reluctances are connected in series. The main magnetic flux of the coil is obtained from the magnetic circuit. The mathematical expression for magnetic flux density B is: in, , For the coercivity of the magnet, The magnetization length of the magnet. To correspond to the magnetic reluctance of the magnet, and These are the air gap reluctances between the outer and inner magnets that pass through the rotor coils. and These represent the magnetic flux densities of the air gaps between the inner and outer magnets, respectively. and These are the equivalent cross-sectional areas corresponding to the inner and outer magnetic flux densities, respectively. When no disturbance torque is generated, the Lorentz force experienced by a single orthogonal magnetic bearing in the magnetic field formed by the inner and outer magnets and the magnetic ring is: in, This indicates the strength of the annular magnetic field formed on the rotor by the inner magnet, outer magnet, and magnetic guide ring. This represents the steady current in the tile-shaped coil when no interfering torque is generated. This represents the effective magnetic induction length of the long arc segment of the tile-shaped coil in a circular magnetic field. This represents the effective magnetic induction length of the short arc segment of the tile-shaped coil in a circular magnetic field. and It can be represented as: in, Indicates the opening angle and outer radius of the tile-shaped coil. and This indicates the distance from the long arc segment of the tile-shaped coil to the center of the coil, and the inner radius. Representing the distance from the short arc segment of the tile-shaped coil to the center of the coil, combining equation (3) with equations (2) and (4) yields the dynamic model of a single Lorentz force orthogonal magnetic bearing: in, and Let Y and X represent the output forces of the orthogonal magnetic bearings in the Y and X channels, respectively. Under normal operating conditions, the magnetization length, equivalent magnetic reluctance, and equivalent cross-sectional area corresponding to the internal and external magnetic flux remain basically unchanged. It can be assumed that the magnetic bearing output force and the coil current are linearly related. Equation (5) can be equivalently represented as: Where H is the coil current stiffness coefficient; (2) Translational dynamics modeling of a pair of coaxial orthogonal Lorentz force magnetic bearings When the magnetic bearing rotor is disturbed, the four displacement sensors on the two channels at both ends of the rotor will generate a shift. , , , The control currents generated by the PID controller are respectively , , , : in, The control coils responsible for rotor translation are designed to have equal and opposite control currents in the bearing coils at both ends of each channel when only considering rotor translation. This results in equal and opposite Lorentz forces. Assuming the initial current in the bearing coils of both magnetic bearings is zero, the equation of motion for rotor translation can be expressed as: Combining equation (7), the rotor translational dynamics equations can be simplified to: Applying the Laplace transform to both sides of the equation, we obtain the transfer function considering only the rotor translation: in, and The control current on both channels is the input quantity. and It represents the displacement change of the rotor after the coil generates a control current; it is the output quantity. (3) Rotational dynamics modeling of a pair of coaxial orthogonal Lorentz force magnetic bearings When only considering the rotor's rotational motion, the control currents of the coils in the magnetic bearings at both ends of each channel are equal in magnitude and opposite in direction, resulting in equal in magnitude and opposite in direction of the Lorentz forces. When the output force of the left magnetic bearing is positive and the output force of the right magnetic bearing is negative, the rotor rotates clockwise; when the output force of the right magnetic bearing is positive and the output force of the left magnetic bearing is negative, the rotor rotates counterclockwise. During the actual rotation of the rotor, the rotation angle is relatively small, and the rotation arc can be approximated by the displacement sensor's sensitive offset. in, These represent the rotor offset angles on the Y and X channels, respectively. This represents the distance from the center of the orthogonal magnetic bearing to the center of the shaft. The control current generated by the PID controller after the displacement sensor measurement is... : in, Responsible for controlling the rotor's rotation, assuming the initial current in the two magnetic bearing coils is 0, the equation of motion for the rotor's rotation can be expressed as: in, and These represent the moments of inertia of the magnetically levitated rotor along the Y-axis and X-axis, respectively. and The rotational angular accelerations generated by the Lorentz force produced by the control current in the tile-shaped coil on the rotor in the two channels can be simplified to: Applying the Laplace transform to both sides of the equation yields the transfer function considering only rotor rotation: in, and This represents the control current on both channels; it is an input quantity. and This represents the angular change in rotor rotation caused by the control current generated by the coil; it is the output quantity. All use PID control: Based on the above force analysis of rotor translation and rotation, the control force and control torque generated by the magnetic bearing can be obtained as follows: in, and , and This represents the projection of the control force and torque provided by the orthogonal magnetic bearing to the rotor onto the Y and X channels; (4) Design of translational-rotational coupling motion and control law for orthogonal Lorentz force magnetic bearing When considering translational-rotational coupled motion, based on the algebraic relationship between the translational and rotational displacements in the two channels after being disturbed in any direction, the sensitive offset of the displacement sensor is decomposed into translational and rotational displacements, thus achieving decoupling in the dynamic modeling process of translational-rotational coupled motion. The algebraic relationship between the translational and rotational displacements and the total offset is as follows: in, and These represent the translational displacement offset of the magnetically levitated rotor in the two channels, respectively. and These represent the rotational displacement of the magnetically levitated rotor in the two channels, respectively. Based on the decomposition of the displacement sensor's sensitive offset in the two motion modes, the current in the tile-shaped coil also generates a control current under the action of the PID controller, which can be expressed as: in, and These represent the control currents in the two channels controlling the translational motion during the translational-rotational coupled motion. and Let represent the control currents in the two channels controlling rotation during translational-rotational coupled motion. By decomposing the obtained translational and rotational control currents at the orthogonal magnetic bearings at the left and right ends, we can obtain: Combining equations (17)(18)(19)(20), we can obtain: The above equation is the decoupled control law after decomposing the rotor translation and rotation of the displacement sensor using the sensor measurement principle, where H is the current stiffness coefficient, and G... P (s) and G Z (s) represents the control of the current during translation and rotation.

[0008] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A coaxial double-quadrature Lorentz force magnetic bearing four-degree-of-freedom dynamics control method, characterized in that: Based on the structural characteristics of a single orthogonal Lorentz force magnetic bearing, an equivalent magnetic circuit analysis is performed. Using Ohm's law for magnetic circuits, a magnetic induction intensity model of the coil air gap is obtained. The mathematical relationship between the orthogonal magnetic bearing parameters and the Lorentz force is derived, and the force analysis of the coil is conducted. After the magnetically levitated rotor is disturbed, based on the rotor displacement change, a PID controller outputs control current to complete the dynamic modeling of two-degree-of-freedom translation and two-degree-of-freedom rotation. The rotor displacement measurement value is decomposed into translational and rotational components to construct a decoupling control law for the translational-rotational coupled motion, thereby achieving closed-loop control of the translational-rotational coupled motion. Specifically, the following steps are included: (1) Dynamic modeling of a single orthogonal Lorentz force magnetic bearing The reference coordinate system is determined with the center of the magnetic bearing as the origin. The positive Z-axis is to the right along the rotor axis, and the positive Y-axis is upward along the center of the magnetic bearing. The X-axis forms a right-handed system with the Y and Z axes. Ignoring the effects of magnet leakage flux, coil self-induced magnetic field, and edge effects, an equivalent magnetic circuit for a single orthogonal magnetic bearing is established using the equivalent magnetic circuit method. The magnetic circuit includes the magnetomotive force (MOF) of four sets of magnet rings, the corresponding permanent magnet reluctance, and the air gap reluctance passing through the air gap between the inner and outer magnets. The MOF of the magnet rings is linearly related to the tempering length of the magnets. All reluctances are connected in series. The main magnetic flux of the coil is obtained from the magnetic circuit. The mathematical expression for magnetic flux density B is: in, , For the coercivity of the magnet, The magnetization length of the magnet. To correspond to the magnetic reluctance of the magnet, and These are the air gap reluctances between the outer and inner magnets that pass through the rotor coils. and These represent the magnetic flux densities of the air gaps between the inner and outer magnets, respectively. and These are the equivalent cross-sectional areas corresponding to the inner and outer magnetic flux densities, respectively. When no disturbance torque is generated, the Lorentz force experienced by a single orthogonal magnetic bearing in the magnetic field formed by the inner and outer magnets and the magnetic ring is: in, This indicates the strength of the annular magnetic field formed on the rotor by the inner magnet, outer magnet, and magnetic guide ring. This represents the steady current in the tile-shaped coil when no interfering torque is generated. This represents the effective magnetic induction length of the long arc segment of the tile-shaped coil in a circular magnetic field. This represents the effective magnetic induction length of the short arc segment of the tile-shaped coil in a circular magnetic field. and Represented as: in, Indicates the opening angle and outer radius of the tile-shaped coil. This indicates the distance from the long arc segment of the tile-shaped coil to the center of the coil, and the inner radius. Representing the distance from the short arc segment of the tile-shaped coil to the center of the coil, combining equation (3) with equations (2) and (4) yields the dynamic model of a single Lorentz force orthogonal magnetic bearing: in, and Let Y and X represent the output forces of the orthogonal magnetic bearings in the Y and X channels, respectively. Under normal operating conditions, the magnetization length, equivalent magnetic reluctance, and equivalent cross-sectional areas corresponding to the internal and external magnetic fluxes remain basically unchanged. It is assumed that the output force of the magnetic bearing and the coil current are linearly related, and equation (5) is equivalent to: Where H is the coil current stiffness coefficient; (2) Translational dynamics modeling of a pair of coaxial orthogonal Lorentz force magnetic bearings When the magnetic bearing rotor is disturbed, the four displacement sensors on the two channels at both ends of the rotor will generate a shift. , , , The control currents generated by the PID controller are respectively , , , : in, The control coils responsible for rotor translation are considered only when considering rotor translational motion. The control currents in the coils of the magnetic bearings at both ends of each channel are equal in magnitude and direction, resulting in equal and same Lorentz forces. Assuming the initial current in the coils of the two magnetic bearings is 0, the equation of motion for rotor translation is expressed as: Combining equation (7), the rotor translational dynamics equations simplify to: Applying the Laplace transform to both sides of the equation, we obtain the transfer function considering only the rotor translation motion: in, and The control current on both channels is the input quantity. and It represents the displacement change of the rotor after the coil generates a control current; it is the output quantity. (3) Rotational dynamics modeling of a pair of coaxial orthogonal Lorentz force magnetic bearings When only considering the rotor's rotational motion, the control currents of the coils in the magnetic bearings at both ends of each channel are equal in magnitude and opposite in direction, resulting in equal in magnitude and opposite in direction of the Lorentz forces. When the output force of the left magnetic bearing is positive and the output force of the right magnetic bearing is negative, the rotor rotates clockwise; when the output force of the right magnetic bearing is positive and the output force of the left magnetic bearing is negative, the rotor rotates counterclockwise. During the actual rotation of the rotor, the rotation angle is relatively small, and the rotation arc is approximately equal to the displacement sensor's sensitive offset. in, These represent the rotor offset angles on the Y and X channels, respectively. This represents the distance from the center of the orthogonal magnetic bearing to the center of the shaft. The control current generated by the PID controller after the displacement sensor measurement is... : in, Responsible for controlling the rotor's rotation, assuming the initial current in the two magnetic bearing coils is 0, the equation of motion for the rotor's rotation is expressed as: in, and These represent the moments of inertia of the magnetically levitated rotor along the Y-axis and X-axis, respectively. and These represent the rotational angular accelerations generated by the Lorentz force produced by the control current in the tile-shaped coil on the rotor in the two channels, respectively. The rotor rotational dynamics equation simplifies to: Applying the Laplace transform to both sides of the equation yields the transfer function considering only rotor rotation: in, and This represents the control current on both channels; it is an input quantity. and This represents the angular change in rotor rotation caused by the control current generated by the coil; it is the output quantity. In the formula... All use PID control: Based on the above force analysis of rotor translation and rotation, the control force and control torque generated by the magnetic bearing can be obtained as follows: in, and , and This represents the projection of the control force and torque provided by the orthogonal magnetic bearing to the rotor onto the Y and X channels; (4) Design of translational-rotational coupling motion and control law for orthogonal Lorentz force magnetic bearing When considering translational-rotational coupled motion, based on the algebraic relationship between the translational and rotational displacements in the two channels after being disturbed in any direction, the sensitive offset of the displacement sensor is decomposed into translational and rotational displacements, thus achieving decoupling in the dynamic modeling process of translational-rotational coupled motion. The algebraic relationship between the translational and rotational displacements and the total offset is as follows: in, and These represent the translational displacement offset of the magnetically levitated rotor in the two channels, respectively. and These represent the rotational displacement of the magnetically levitated rotor in the two channels, respectively. Based on the decomposition of the displacement sensor's sensitive offset in the two motion modes, the current in the tile-shaped coil also generates a control current under the action of the PID controller, expressed as: in, and These represent the control currents in the two channels controlling the translational motion during the translational-rotational coupled motion. and Let represent the control currents in the two channels controlling rotation during translational-rotational coupled motion. By decomposing the obtained translational and rotational control currents at the orthogonal magnetic bearings at the left and right ends, we can obtain: Combining equations (17)(18)(19)(20), we can obtain: The above formula is a decoupling control law for the rotor translation and rotation of the displacement sensor after decomposition using sensor measurement principle, wherein H is a current stiffness coefficient, G P (s) and G Z (s) represent the control of the current in the process of translation and rotation.

2. The four-degree-of-freedom dynamic control method for a coaxial double orthogonal Lorentz force magnetic bearing according to claim 1, characterized in that, Orthogonal magnetic bearings use magnetically conductive materials to coat the inner and outer magnets, which can concentrate the magnets and generate a constant, uniform, vertical magnetic field along the axial direction in the air gap. Through equivalent magnetic circuit analysis, the magnetic flux in the air gap can be calculated according to Ohm's law for magnetic circuits, ensuring the linearity between the Lorentz force and the coil current.

3. The four-degree-of-freedom dynamic control method for a coaxial double orthogonal Lorentz force magnetic bearing according to claim 1, characterized in that, When analyzing the force on a single tile-shaped coil, since the magnetic field is perpendicular to the coil plane, by projecting and integrating the Lorentz force on the coil in the Y and X directions, the force on a single orthogonal Lorentz force magnetic bearing tile-shaped coil can be obtained as follows: in, The angle of the coil, Then the length is The electromagnetic force experienced by the current element is .

4. The four-degree-of-freedom dynamic control method for a coaxial double orthogonal Lorentz force magnetic bearing according to claim 1, characterized in that, When the orthogonal Lorentz force magnetic bearing is subjected to a disturbance, the output of the displacement sensor generates a control current in the vortex coil through the control circuit, forming a closed-loop control of the rotor motion. This control current is the current that realizes the rotor motion.

5. The four-degree-of-freedom dynamic control method for a coaxial double orthogonal Lorentz force magnetic bearing according to claim 4, characterized in that, This control circuit utilizes a PID controller to form a closed-loop control. The PID controller is represented as follows: The control parameters differ for translational and rotational control, and the transfer functions are expressed as follows: and .

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