A method for modeling and controlling dynamics of axial lorentz force magnetic bearing of a magnetic levitation platform

Abstract

The application relates to a kind of magnetic suspension platform axial Lorentz force magnetic bearing dynamics modeling and control method. To meet the super-stable, super-static index requirements of magnetic suspension universal stable platform, based on the structural characteristics of axial magnetic bearing, for the single degree of freedom linear motion of magnetic suspension platform load cabin along the axial direction, equivalent magnetic circuit method is used for analysis, the magnetic induction intensity model of energized coil is obtained by using magnetic circuit ohm law, the force analysis of stable platform rotor is carried out, the transfer function relationship between input rotor displacement change and output control current is derived, the sliding surface is designed by using backstepping method, the backstepping sliding mode controller is designed according to the control law model derived, and then the stable closed-loop control of magnetic suspension universal stable platform along the axial direction is realized. The application solves the problem of axial Lorentz force magnetic bearing dynamics modeling and motion control, and has wide application prospect in the field of new spacecraft attitude control technology.

Description

Technical Field

[0001] This invention relates to a dynamic modeling and control method for axial Lorentz force magnetic bearings used in a Lorentz force magnetic levitation universal stabilization platform. It can achieve axial stability control of the rotor and load platform with a single degree of freedom and is suitable for the attitude control system of spacecraft under on-orbit microgravity conditions. Technical Background With the rapid development of aerospace technology, aerospace applications have placed new demands on the high-precision orientation and rapid maneuverability of satellite payloads. Traditional mechanical magnetic bearings suffer from mechanical friction and vibration, affecting the bearing's output torque and service life. Magnetic levitation platforms offer advantages such as non-contact operation, low vibration, and long lifespan. Compared to traditional spacecraft platforms employing vibration isolation mechanisms, using magnetic levitation technology to achieve active vibration control and suppression of payload disturbances can meet the performance requirements of ultra-high agility, ultra-high stability, and ultra-high precision for satellites, while simultaneously suppressing the impact of micro-vibrations on the spacecraft's pointing accuracy, pointing stability, and agility. Therefore, magnetic levitation bearings are a hot technology in the research and design of "three-ultra" spacecraft platforms.

[0002] Existing magnetic levitation platforms physically isolate the base and payload platform using magnetic levitation technology, employing multiple actuators installed in the air gap to achieve vibration isolation. In contrast, the magnetic levitation platform proposed in this project is a three-body structure, capable of controlling the seven-degree-of-freedom omnidirectional maneuverability of the payload platform. The three-module design not only achieves physical isolation between the platform and payload modules, but the three types of Lorentz force magnetic bearings in the frame module provide the forces and torques to control the translation and rotation of the payload platform. This allows the payload mounted on the magnetic levitation platform to not only achieve stable levitation but also rapid maneuverability and precise pointing, overcoming the insufficient maneuverability of existing magnetic levitation platforms, expanding their application range, and showing great promise for many specific missions in space.

[0003] The axial Lorentz force magnetic bearing mentioned in this invention is based on a Lorentz force magnetic levitation universal stabilization platform, achieving on-orbit vibration isolation and stable control of the rotor and load platform. The dynamic modeling of the axial Lorentz force magnetic bearing and the design of the axial drive controller solve the dynamic analysis and attitude control of the Lorentz force magnetic levitation universal stabilization platform with a single degree of freedom along the axial direction. Applying the backstepping sliding mode control method to the multibody dynamics control of the magnetic levitation platform can effectively solve problems such as torque coupling and nonlinearity between magnetic bearings, and has certain research value in the field of attitude control technology for novel spacecraft. Summary of the Invention

[0004] The technical problem solved by this invention is to perform dynamic modeling of the axial magnetic bearing that ensures stable levitation in a magnetically levitated universal platform supported by a full Lorentz force load, and to combine backstepping control and sliding mode control methods into the axial drive system. This method mainly addresses the stability control of the rotor and load platform after disturbance. The design of the axial drive controller solves the attitude stability control problem of the Lorentz force magnetically levitated universal platform.

[0005] The technical solution of this invention is as follows: Based on the structural characteristics of the axial magnetic bearing, and considering the single-degree-of-freedom linear motion of the load compartment of the magnetic levitation platform along the axial direction, the equivalent magnetic circuit method is used for analysis. Ohm's law for magnetic circuits is used to obtain the magnetic induction intensity model of the energized coil. Force analysis is performed on the rotor of the stable platform, and the transfer function relationship between the input rotor displacement change and the output control current is derived. The sliding mode surface is designed using the backstepping method, and a backstepping sliding mode controller is designed based on the derived control law model. This achieves stable closed-loop control of the magnetically levitated omnidirectional stable platform along the axial direction. Specifically, the following steps are included: (1) Establish the magnetic flux density model of the axial Lorentz force magnetic bearing The load coordinate system centered on the load platform is established as follows: with the center of mass of the load platform as the center, the positive direction of the Z-axis is to the right along the rotor axis, and the positive direction of the 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. The axial Lorentz magnetic bearing uses radial magnetization to ensure that the annular coil on the magnetic levitation platform rotor is always subjected to electromagnetic force in the axial direction. At the same time, the structure of the axial Lorentz magnetic bearing adopts the form of three annular magnets clamping two annular coils. Unlike the method of two inner and outer magnets surrounding the coil, the three layers of whole circular magnets can enclose the two sets of winding coils. Under the premise of the same output force, it can ensure that the radial diameter of the magnetic bearing is smaller, which can effectively and directly reduce the enveloping size. Based on the structure of the axial Lorentz force magnetic bearing, which consists of three ring magnets surrounding two ring coils, and ignoring the effects of magnet leakage flux, coil self-induced magnetic field, and edge effects, the equivalent magnetic circuit method is used to model the axial magnetic bearing. The permanent magnet circuit includes three sets of permanent magnet ring magnetomotive forces (GMMFs) and their corresponding permanent magnet reluctances, as well as the air gap reluctance passing through the inner and outer coils. According to Ohm's law for magnetic circuits, the GMMF of the magnetomotive forces is equal to the product of the permanent magnet flux and the permanent magnet reluctance. The magnetic induction intensity of the axial Lorentz force magnetic bearing's energized coil can then be calculated. Represented as: (1) in, The magnetomotive force of the permanent magnet steel ring can be expressed as the product of the coercivity and the magnetization length, i.e. , For the coercivity of the magnet, is the magnetization length of the magnet. The permanent magnet reluctance corresponds to the three sets of magnets. and These are the air gap reluctances of the permanent magnet circuit passing through the outer stator coil and the inner stator coil, respectively. and These are the equivalent cross-sectional areas corresponding to the internal and external magnetic flux, respectively; (2) Establish the electromagnetic force and damping force model of the axial magnetic bearing Without considering the slot fill factor, it can be assumed that the energized coils in the winding coil are uniformly distributed. The Lorentz force on the N-turn coil in the permanent magnet field can be equivalent to N times the electromagnetic force on the circular coil at the center of the coil. The effective length of the axial magnetic bearing stator coil in the permanent magnet field can be expressed as: (2) in, and Representing the distances from the centers of the outer and inner circular coils to the rotor center, respectively, the electromagnetic force generated along the Z-axis by the axial Lorentz magnetic bearing when no disturbance torque is generated can be expressed as: (3) in, The current in the coil corresponding to the electromagnetic force is given. In a vacuum environment, the air damping force can be ignored, and the damping force of the equivalent magnetic circuit is mainly considered. The damping force on the axial Lorentz force magnetic bearing can be expressed as: 4 in, The damping coefficient represents the vibration resistance of the power amplifier's output to the load. It can be represented as ,in and These represent the forward and reverse supply voltages of the power amplifier, respectively. The control force and resistance generated by the axial Lorentz magnetic bearing on the track, representing the coil speed, can be expressed as: (5) in This represents various coupling torques and other disturbances; (3) Design of sliding surface for axial Lorentz force drive system Based on the on-track control force and damping force of the axial magnetic bearing, the dynamic equation of the single-degree-of-freedom axial drive system can be obtained as follows: 6 in To indicate the axial displacement of the rotor, let Indicates axial displacement , Indicates axial motion speed , , If the system is subjected to a disturbance, then the dynamic equation of the single-degree-of-freedom axially driven system can be written as: 7 The backstepping sliding mode controller is established based on the dynamic equations as follows: Assume the system axial displacement tracking error for: (8) (9) in, To represent the input target tracking displacement, the Lyapunov function can be selected as follows: 10 To verify system stability, Taking the first derivative with respect to time, we get: 11 Similar to the synchronous and countersynchronous control process, a dummy variable is introduced. and order The value can be: 12 in For any positive number, the dummy variable Substitution (11) We can obtain: 13 When the tracking error is not zero Taking a positive number yields The system is stable; Assume the system axial velocity tracking error for: 14 12 in, To represent the target tracking speed, the sliding surface can be designed as follows: ⒃ in To represent the Laplace operator, we can choose the Lyapunov function as follows: 14 (4) Design the backstepping sliding mode control law for the axial Lorentz force drive system Will Taking the first derivative with respect to time, we get: 18 The backstepping sliding mode control law of the single-degree-of-freedom axial drive system of the axial magnetic bearing can be obtained from the above formula: 16 Substituting equation (19) into equation (18) yields: 20 in, , , A positive number, we get ,Pick It can be obtained in any time domain range The axial drive system is stable.

[0006] The principle of this invention is as follows: Based on the structural characteristics of the axial magnetic bearing, and considering the single-degree-of-freedom linear motion of the load compartment of the magnetic levitation platform along the axial direction, the equivalent magnetic circuit method is used for analysis. The magnetic induction intensity model of the energized coil is obtained using Ohm's law of magnetic circuits. The force analysis of the stable platform rotor is performed, and the transfer function relationship between the input rotor displacement change and the output control current is derived. Based on the derived control law model, a backstepping sliding mode controller is designed, thereby realizing the stable closed-loop control of the magnetic levitation universal stable platform along the axial direction. Attached Figure Description

[0007] Figure 1. Control scheme diagram for axial Lorentz force magnetic bearing; Figure 2. Cross-sectional structural diagram of the Lorentz force magnetic levitation universal stabilization platform; Figure 3. Cross-sectional structure of the axial Lorentz force magnetic bearing; Figure 4. Schematic diagram of radial magnetization of axial Lorentz force magnetic bearing; Figure 5. Equivalent magnetic circuit diagram of the axial Lorentz force magnetic bearing; Figure 6. Structure diagram of the axial Lorentz force magnetic bearing rotor; Detailed Implementation Plan The overall control scheme of the present invention is as follows: Figure 1 As shown, the cross-sectional view of the 3D model of the maglev platform is as follows: Figure 2 As shown, the cross-sectional view of the axial magnetic bearing 3D model is as follows. Figure 3 As shown, the permanent magnet circuit of the axial magnetic bearing is as follows: Figure 4 and Figure 5 As shown, based on the structural characteristics of the axial magnetic bearing, the equivalent magnetic circuit method is used to analyze the single-degree-of-freedom linear motion of the load cabin of the magnetic levitation platform along the axial direction. The magnetic induction intensity model of the energized coil is obtained using Ohm's law for magnetic circuits. Force analysis is performed on the rotor of the stable platform, and the transfer function relationship between the input rotor displacement change and the output control current is derived. The sliding mode surface is designed using the backstepping method, and a backstepping sliding mode controller is designed based on the derived control law model. This achieves stable closed-loop control of the magnetically levitated omnidirectional stable platform along the axial direction. Specifically, the following steps are included: (2) Establish the magnetic flux density model of the axial Lorentz force magnetic bearing The load coordinate system centered on the load platform is established as follows: with the center of mass of the load platform as the center, the positive direction of the Z-axis is to the right along the rotor axis, and the positive direction of the 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. The axial Lorentz magnetic bearing uses radial magnetization to ensure that the annular coil on the magnetic levitation platform rotor is always subjected to electromagnetic force in the axial direction. At the same time, the structure of the axial Lorentz magnetic bearing adopts the form of three annular magnets clamping two annular coils. Unlike the method of two inner and outer magnets surrounding the coil, the three layers of whole circular magnets can enclose the two sets of winding coils. Under the premise of the same output force, it can ensure that the radial diameter of the magnetic bearing is smaller, which can effectively and directly reduce the enveloping size. Based on the structure of the axial Lorentz force magnetic bearing, which consists of three ring magnets surrounding two ring coils, and ignoring the effects of magnet leakage flux, coil self-induced magnetic field, and edge effects, the equivalent magnetic circuit method is used to model the axial magnetic bearing. The permanent magnet circuit includes three sets of permanent magnet ring magnetomotive forces (GMMFs) and their corresponding permanent magnet reluctances, as well as the air gap reluctance passing through the inner and outer coils. According to Ohm's law for magnetic circuits, the GMMF of the magnetomotive forces is equal to the product of the permanent magnet flux and the permanent magnet reluctance. The magnetic induction intensity of the axial Lorentz force magnetic bearing's energized coil can then be calculated. Represented as: (1) in, The magnetomotive force of the permanent magnet steel ring can be expressed as the product of the coercivity and the magnetization length, i.e. , For the coercivity of the magnet, is the magnetization length of the magnet. The permanent magnet reluctance corresponds to the three sets of magnets. and These are the air gap reluctances of the permanent magnet circuit passing through the outer stator coil and the inner stator coil, respectively. and These are the equivalent cross-sectional areas corresponding to the internal and external magnetic flux, respectively; (2) Establish the electromagnetic force and damping force model of the axial magnetic bearing Without considering the slot fill factor, it can be assumed that the energized coils in the winding coil are uniformly distributed. The Lorentz force on the N-turn coil in the permanent magnet field can be equivalent to N times the electromagnetic force on the circular coil at the center of the coil. The effective length of the axial magnetic bearing stator coil in the permanent magnet field can be expressed as: (2) in, and Representing the distances from the centers of the outer and inner circular coils to the rotor center, respectively, the electromagnetic force generated along the Z-axis by the axial Lorentz magnetic bearing when no disturbance torque is generated can be expressed as: (3) in, The current in the coil corresponding to the electromagnetic force is given. In a vacuum environment, the air damping force can be ignored, and the damping force of the equivalent magnetic circuit is mainly considered. The damping force on the axial Lorentz force magnetic bearing can be expressed as: 4 in, The damping coefficient represents the vibration resistance of the power amplifier's output to the load. It can be represented as ,in and These represent the forward and reverse supply voltages of the power amplifier, respectively. The control force and resistance generated by the axial Lorentz magnetic bearing on the track, representing the coil speed, can be expressed as: (5) in This represents various coupling torques and other disturbances; (3) Design of sliding surface for axial Lorentz force drive system Based on the on-track control force and damping force of the axial magnetic bearing, the dynamic equation of the single-degree-of-freedom axial drive system can be obtained as follows: 6 in To indicate the axial displacement of the rotor, let Indicates axial displacement , Indicates axial motion speed , , If the system is subjected to a disturbance, then the dynamic equation of the single-degree-of-freedom axially driven system can be written as: 7 The backstepping sliding mode controller is established based on the dynamic equations as follows: Assume the system axial displacement tracking error for: (8) (9) in, To represent the input target tracking displacement, the Lyapunov function can be selected as follows: 10 To verify system stability, Taking the first derivative with respect to time, we get: 11 Similar to the synchronous and countersynchronous control process, a dummy variable is introduced. and order The value can be: 12 in For any positive number, the dummy variable Substitution (11) We can obtain: 13 When the tracking error is not zero Taking a positive number yields The system is stable; Assume the system axial velocity tracking error for: 14 12 in, To represent the target tracking speed, the sliding surface can be designed as follows: ⒃ in To represent the Laplace operator, we can choose the Lyapunov function as follows: 14 (4) Design the backstepping sliding mode control law for the axial Lorentz force drive system Will Taking the first derivative with respect to time, we get: 18 The backstepping sliding mode control law of the single-degree-of-freedom axial drive system of the axial magnetic bearing can be obtained from the above formula: 16 Substituting equation (19) into equation (18) yields: 20 in, , , A positive number, we get ,Pick It can be obtained in any time domain range The axial drive system is stable.

[0008] 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 control of an axial Lorentz force magnetic bearing of a magnetic levitation platform, characterized in that: To meet the ultra-stable and ultra-quiet requirements of the magnetic levitation universal stabilization platform, based on the structural characteristics of the axial magnetic bearing, and considering the single-degree-of-freedom linear motion of the load compartment along the axial direction of the maglev platform, the equivalent magnetic circuit method is used for analysis. Using Ohm's law for magnetic circuits, a magnetic induction intensity model of the energized coil is obtained. Force analysis is performed on the stabilization platform rotor, and the transfer function relationship between the input rotor displacement change and the output control current is derived. A sliding mode surface is designed using the backstepping method, and a backstepping sliding mode controller is designed based on the derived control law model. This achieves stable closed-loop control of the magnetic levitation universal stabilization platform along the axial direction, specifically including the following steps: (1) Establish the magnetic flux density model of the axial Lorentz force magnetic bearing The load coordinate system centered on the load platform is established as follows: with the center of mass of the load platform as the center, the positive direction of the Z-axis is to the right along the rotor axis, and the positive direction of the 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. The axial Lorentz magnetic bearing uses radial magnetization to ensure that the annular coil on the magnetic levitation platform rotor is always subjected to electromagnetic force in the axial direction. At the same time, the structure of the axial Lorentz magnetic bearing adopts the form of three annular magnets clamping two annular coils. Unlike the method of two inner and outer magnets surrounding the coil, the three layers of whole circular magnets can enclose the two sets of winding coils. Under the premise of the same output force, it can ensure that the radial diameter of the magnetic bearing is smaller, which can effectively and directly reduce the enveloping size. According to the structure of the axial Lorentz force magnetic bearing that three annular magnetic steel enclose two annular coils, ignoring the magnetic steel leakage, coil self-induction magnetic field and the influence of edge effect, the equivalent magnetic circuit method is used to model the axial magnetic bearing. The permanent magnet magnetic circuit includes three groups of permanent magnet magnetic steel ring magnetic motive force and the corresponding permanent magnet reluctance and the air gap reluctance through the inner and outer coils. According to the Ohm law of magnetic circuit, the magnetic motive force of the magnetic steel ring is equal to the product of the permanent magnet flux and the permanent magnet reluctance. The magnetic induction intensity of the energized coil of the axial Lorentz force magnetic bearing is represented as: ⑴ in, The magnetomotive force of the permanent magnet steel ring can be expressed as the product of the coercivity and the magnetization length, i.e. , For the coercivity of the magnet, The magnetization length of the magnet. The permanent magnet reluctance corresponds to the three sets of magnets. and These are the air gap reluctances of the permanent magnet circuit passing through the outer stator coil and the inner stator coil, respectively. and These are the equivalent cross-sectional areas corresponding to the internal and external magnetic flux, respectively; (2) Establish the electromagnetic force and damping force model of the axial magnetic bearing Without considering the slot fill factor, it can be assumed that the energized coils in the winding coil are uniformly distributed. The Lorentz force on the N-turn coil in the permanent magnet field can be equivalent to N times the electromagnetic force on the circular coil at the center of the coil. The effective length of the axial magnetic bearing stator coil in the permanent magnet field can be expressed as: ⑵ in, and Representing the distances from the centers of the outer and inner circular coils to the rotor center, respectively, the electromagnetic force generated along the Z-axis by the axial Lorentz magnetic bearing when no disturbance torque is generated can be expressed as: ⑶ in, The current in the coil corresponding to the electromagnetic force is given. In a vacuum environment, the air damping force can be ignored, and the damping force of the equivalent magnetic circuit is mainly considered. The damping force on the axial Lorentz force magnetic bearing can be expressed as: ⑷ in, The damping coefficient represents the vibration resistance of the power amplifier's output to the load. It can be represented as ,in and These represent the forward and reverse supply voltages of the power amplifier, respectively. The control force and resistance generated by the axial Lorentz magnetic bearing on the track, representing the coil speed, can be expressed as: ⑸ in This represents various coupling torques and other disturbances; (3) Design of sliding surface for axial Lorentz force drive system Based on the on-track control force and damping force of the axial magnetic bearing, the dynamic equation of the single-degree-of-freedom axial drive system can be obtained as follows: ⑹ in To indicate the axial displacement of the rotor, let Indicates axial displacement , Indicates axial motion speed , , If the system is subjected to a disturbance, then the dynamic equation of the single-degree-of-freedom axially driven system can be written as: ⑺ The backstepping sliding mode controller is established based on the dynamic equations as follows: Assume the system axial displacement tracking error for: ⑻ ⑼ in, To represent the input target tracking displacement, the Lyapunov function can be selected as follows: ⑽ To verify system stability, Taking the first derivative with respect to time, we get: ⑾ Similar to the synchronous and countersynchronous control process, a dummy variable is introduced. and order The value can be: ⑿ in For any positive number, the dummy variable Substitution (11) We can obtain: ⒀ When the tracking error is not zero Taking a positive number yields The system is stable; Assume the system axial velocity tracking error for: ⒁ ⒂ in, To represent the target tracking speed, the sliding surface can be designed as follows: ⒃ in To represent the Laplace operator, we can choose the Lyapunov function as follows: ⒄ (4) Design the backstepping sliding mode control law for the axial Lorentz force drive system Will Taking the first derivative with respect to time, we get: ⒅ The backstepping sliding mode control law of the single-degree-of-freedom axial drive system of the axial magnetic bearing can be obtained from the above formula: ⒆ Substituting equation (19) into equation (18) yields: ⒇ in, , , A positive number, we get ,Pick It can be obtained in any time domain range The axial drive system is stable.

2. The dynamic control method for an axial Lorentz force magnetic bearing of a magnetic levitation platform according to claim 1, characterized in that, The Lorentz force magnetic levitation omnidirectional stabilization platform has a three-body structure. It can achieve seven degrees of freedom omnidirectional motion by two sets of rotary magnetic bearings, two coaxial radial magnetic bearings, and one axial magnetic bearing. The rotary Lorentz force magnetic bearings control two degrees of freedom for agile omnidirectional maneuvering, while the radial and axial Lorentz force magnetic bearings control five degrees of freedom for stable levitation. The three types of magnetic bearings cooperate to complete the complex three-body seven-degree-of-freedom motion. To address the problems of unstable control and slow response of the omnidirectional stabilization platform caused by coupling, various disturbances, and nonlinearity, a backstepping control algorithm and a sliding mode control algorithm are combined to design a backstepping sliding mode controller suitable for Lorentz force magnetic levitation bearings. This can significantly improve the tracking accuracy and disturbance rejection capability of the stabilization platform.

3. The dynamic control method for axial Lorentz force magnetic bearings of a magnetic levitation platform according to claim 1, characterized in that, Since each magnetic bearing can be designed and controlled independently, this invention models the coupling torque and damping torque between the bearings as external disturbances, and then extends them to the entire magnetic levitation platform system.

4. The dynamic control method for an axial Lorentz force magnetic bearing of a magnetic levitation platform according to claim 1, characterized in that, The axial drive control system mainly includes an input / output module, a backstepping sliding mode controller, an axial magnetic bearing, an external disturbance control unit, an encoder, and a power amplifier.

5. The dynamic control method for an axial Lorentz force magnetic bearing of a magnetic levitation platform according to claim 1, characterized in that, A magnetically conductive ring is placed next to the three sets of radially stacked magnetic steel rings and two sets of circular coils. A magnetically insulating ring is placed between the magnets and the magnetically conductive rings to ensure that the magnetic circuit is closed-loop and uniform.

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