Control method and system of hybrid magnetic suspension bearing system

Abstract

The invention relates to the technical field of magnetic suspension bearings, in particular to a control method and system of a hybrid magnetic suspension bearing system. The method comprises the following steps: acquiring a rigid rotor kinetic equation of an HMB system; selecting a plurality of feature working points in the whole working interval, and performing linearization processing on each feature working point to obtain a linear stiffness matrix of each feature working point; establishing a linear steady state space model structure of each characteristic working point based on a rigid rotor kinetic equation and a linear stiffness matrix; the HMB system is operated in the experiment platform, and the rotor is suspended to different characteristic working points; performing subspace identification and parameter estimation at each feature working point to obtain model parameters of the linear steady state space model structure, and obtaining a local target linear model at each feature working point; the global controller in the full working interval is constructed based on the plurality of local target linear models, and the robustness and adaptability of the HMB system in the full working interval are improved.

Description

Technical Field

[0001] This application relates to the field of magnetic levitation bearing technology, and in particular to a control method and system for a hybrid magnetic levitation bearing system. Background Technology

[0002] Hybrid magnetic bearing (HMB) systems have broad application prospects in high-end equipment fields such as aero engines, high-speed electric spindles, and blowers due to their advantages such as high speed, non-contact operation, and low power consumption.

[0003] For example, patent application CN117291014A discloses a predictive control method and system for a hybrid magnetic levitation bearing displacement model. The method includes: constructing the dynamic equation of the rotor of the hybrid magnetic levitation bearing in the mechanical model coordinate system; constructing a closed-loop controller for controlling the hybrid magnetic levitation bearing; obtaining the rotor's displacement velocity at the current moment; calculating the predicted displacement velocity of the rotor at the next moment based on the dynamic equation and the rotor's displacement velocity at the current moment within the first control cycle of the closed-loop controller; calculating the output result of the closed-loop controller in the first control cycle based on the predicted displacement velocity of the rotor at the next moment and the rotor's displacement velocity at the current moment; and predicting the target displacement velocity and target displacement acceleration of the rotor in the second and third control cycles based on the output result.

[0004] However, existing HMB systems generally employ Taylor expansion and linearization of the nonlinear model at the system equilibrium point, and then design a controller based on the resulting linear model. The applicability of such controllers is severely limited. When the HMB system deviates significantly from the equilibrium point, the accuracy of the linearized model will decrease or even fail, resulting in low practicality. Summary of the Invention

[0005] The main objective of this application is to provide a control method and system for a hybrid magnetic levitation bearing system. To solve the aforementioned technical problems, this application specifically adopts the following technical solution: A first aspect of this application is to provide a control method for a hybrid magnetic levitation bearing system, the method comprising: S101, Obtain the rigid rotor dynamics equation of the hybrid magnetic levitation bearing system; S102, select multiple characteristic working points in the entire working range, and linearize the nonlinear hybrid magnetic force of each characteristic working point to obtain the linear stiffness matrix of each characteristic working point. S103, Based on the rigid rotor dynamics equation and the linear stiffness matrix, establish the linear steady state space model structure for each characteristic operating point; S104, The hybrid magnetic levitation bearing system is run in a pre-built experimental platform, and the rotor is levitated to different characteristic operating points; S105, perform subspace identification and parameter estimation at each characteristic operating point to obtain the model parameters of the linear time-invariant state-space model structure, and obtain the local target linear model at each characteristic operating point. S106, Construct a global controller for the entire working range based on multiple local target linear models.

[0006] In some embodiments, selecting multiple characteristic operating points in the entire operating range includes: obtaining the operating requirements of the hybrid magnetic levitation bearing system, and determining the selection range and / or distribution density of the characteristic operating points based on the operating requirements; and selecting multiple characteristic operating points in the entire operating range based on the selection range and / or distribution density.

[0007] In some embodiments, S101 further includes: describing the small-amplitude vibration of the rotor using the translation and tilt data of the rotor's center of mass in the reference coordinate system, and establishing the dynamic equation of the rigid rotor based on a preset mechanical algorithm, wherein the preset mechanical algorithm includes at least one of the Newton-Euler method and the Lagrange method.

[0008] In some embodiments, S102 includes: analyzing the magnetic circuit of the hybrid magnetic levitation bearing system based on the equivalent magnetic circuit method, calculating the target expression for the magnetic flux and magnetic force of each magnetic pole, wherein the target expression is used to describe the nonlinear hybrid magnetic force at different positions within the entire operating range; and performing linearization of the nonlinear hybrid magnetic force at different characteristic operating points based on Taylor expansion linearization and the target expression to obtain the linear stiffness matrix at the characteristic operating points.

[0009] In some embodiments, the experimental platform includes a hybrid magnetic levitation bearing motion experimental platform, and S104 includes: S1041, based on the voltage signal measured by the displacement sensor, and based on the preset calculation algorithm, the voltage signal is calculated into a rotor displacement signal in the sensor coordinate system; S1042, Based on the first coordinate transformation algorithm, the rotor position signal is converted into a centroid position signal in the rotor centroid coordinate system; S1043, Generate a first control parameter based on the error between the centroid position signal and the reference position signal; S1044, based on the second coordinate transformation algorithm, converts the first control parameters in the rotor centroid coordinate system into the second control parameters in the magnetic bearing coordinate system; S1045, based on the second control parameter, the pre-built hybrid magnetic levitation bearing motion experimental platform outputs the corresponding current signal so that the rotor is suspended at the characteristic working point.

[0010] In some embodiments, the linear time-invariant state-space model structure of the characteristic operating point is as follows: ; in, Let be the state variable at time t, where the state variable is the rotor displacement signal and the derivative of the rotor displacement signal; The rate of change of the state variable; Let be the current signal at time t; Let be the rotor displacement signal at time t; For the system matrix; The input matrix; This is the output matrix; Let be the rotor displacement vector in the magnetic bearing coordinate system.

[0011] In some embodiments, S105 further includes: constructing input / output data Hankel matrices, obtaining a first Hankel matrix of the first control parameters, a second Hankel matrix of the centroid position signal, and a third Hankel matrix of the reference position signal; performing orthogonal projection on the third Hankel matrix based on the first and second Hankel matrices to convert closed-loop identification into open-loop identification; calculating the generalized observability matrix and the generalized state sequence using an oblique projection algorithm, and solving for the generalized observability matrix and the generalized state sequence based on the weight matrix; and calculating a matrix based on the generalized observability matrix and the generalized state sequence. , , , ,in, It is a feedforward matrix.

[0012] In some embodiments, the method further includes: iteratively solving the matrix based on the least squares algorithm. , , , Alternatively, the matrix can be calculated based on the generalized observability matrix. , Solving based on the least squares algorithm , .

[0013] In some embodiments, S106 further includes: determining a local controller for each feature working point based on a local target linear model for each feature working point; and interpolating the local controllers for different feature working points based on a preset linear interpolation algorithm to obtain a global controller for the entire working range.

[0014] A second aspect of this application is to provide a hybrid magnetic levitation bearing system, the system comprising: a magnetic levitation bearing structure, a displacement sensor, a current sensor, and a global controller; The magnetic levitation bearing structure includes a stator equipped with a permanent magnet and a control coil, and a rotor that can be levitated and rotated. The controller is obtained based on the steps of the control method for the hybrid magnetic levitation bearing system provided in any embodiment of this application.

[0015] Beneficial effects: This application provides a control method and system for a hybrid magnetic levitation bearing system. By combining theoretical modeling and experimental identification at finite operating points, it effectively balances computational efficiency and control accuracy, highly adapts to the variable dynamic characteristics of HMB, and improves the robustness and adaptability of the HMB system across the entire operating range.

[0016] Specifically, based on the rigid rotor dynamics equations, a multi-point local linearization method is used to construct a linear steady-state-space model structure for each characteristic operating point. Then, an initial linear stiffness matrix is ​​obtained through Taylor expansion, completing the model structure for each characteristic operating point. This theoretical modeling process involves low computational cost, a clear theoretical foundation, and low computational power requirements. Furthermore, experimental identification is conducted by precisely suspending the rotor at each characteristic operating point on an experimental platform. Measured data is used to refine the model parameters, ensuring the model's accuracy at actual operating points. Compared to purely theoretical modeling, experimental identification fully considers non-ideal factors in the actual system (such as magnetic circuit saturation, sensor deviation, and power amplifier delay) and nonlinear factors (such as structural parameter errors), improving the model's accuracy and reliability.

[0017] Furthermore, a corresponding local controller is designed based on multiple local target linear models, and a global controller is generated under the entire working range using a linear interpolation algorithm, thereby reducing computing power requirements while achieving precise motion control in the entire working range.

[0018] Furthermore, this application embodiment also provides a mechanism for adjusting the distribution density of feature working points according to operational requirements. The selection of feature working points does not blindly cover the entire physically feasible range, but is closely combined with the actual operational requirements of the system. By reasonably determining the selection range and distribution density, modeling efficiency is improved while ensuring control accuracy. For example, according to the system's operational requirements, the density of working points is increased in frequently used working areas. In most areas, the corresponding local controller can be directly called. Even if control is achieved through linear interpolation in other areas, higher local control accuracy can be obtained based on more information from neighboring working points. In less frequently used areas, the density of working points is appropriately reduced, and basic control performance is maintained by relying on linear interpolation. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. The elements or parts in the drawings are not necessarily drawn to scale. Obviously, the drawings described below are some embodiments of this application; for those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0020] Figure 1 This is a schematic flowchart of a control method for a hybrid magnetic levitation bearing system provided in an embodiment of this application; Figure 2 This application provides a feature operating point variable parameter model. Figure 3 This is a flowchart illustrating a closed-loop debugging method for an experimental platform provided in an embodiment of this application. Figure 4 This is a flowchart illustrating another closed-loop debugging method for an experimental platform provided in the embodiments of this application; Figure 5 This is a block diagram of a global linear variable parameter control algorithm for a hybrid magnetic levitation bearing provided in an embodiment of this application; Figure 6 This is a schematic diagram of a hybrid magnetic levitation bearing system provided in an embodiment of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0022] The flowchart shown in the attached diagram is for illustrative purposes only and does not necessarily include all content and operations / steps, nor does it necessarily have to be performed in the order described. For example, some operations / steps can be broken down, combined, or partially merged, so the actual execution order may change depending on the actual situation.

[0023] In this document, suffixes such as “module,” “part,” or “unit” used to denote elements are used only for illustrative purposes and have no specific meaning in themselves. Therefore, “module,” “part,” or “unit” can be used interchangeably.

[0024] In this document, the terms "upper," "lower," "inner," "outer," "front," "rear," "one end," and "the other end," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0025] In this document, unless otherwise explicitly specified and limited, the terms "installed," "equipped with," and "connected," etc., should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, a direct connection, or an indirect connection through an intermediate medium; it can be a connection within two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0026] In this document, the term “and / or” includes any and all combinations of one or more of the listed related items.

[0027] In this article, the term "multiple" means two or more, that is, it includes two, three, four, five, etc.

[0028] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0029] Hybrid magnetic bearing (HMB) systems combine permanent magnets and electromagnetic coils, providing bias and control fluxes in a hybrid manner to achieve rotor levitation while reducing power consumption. The coupling between the permanent magnets and the electromagnetic field in the magnetic circuit results in a strongly nonlinear magnetic force. This nonlinearity manifests as a nonlinear change in magnetic force with rotor displacement and control current, giving the system's dynamic characteristics significant displacement and current dependence.

[0030] During HMB system operation, the permanent magnet first provides a stable bias magnetic field, bearing the main static weight of the rotor and achieving efficient, low-power initial levitation. Displacement sensors collect rotor displacement signals in real time to monitor rotor position. When the rotor deviates from its equilibrium position due to disturbance, the control system adjusts the current signal in the electromagnetic coil through a power amplifier based on the deviation signal between the rotor position and the reference position, outputting a control current. At this time, the additional magnetic field generated by the electromagnet superimposes with the permanent magnet magnetic field, producing a precise dynamic control force that pulls the rotor back to the set position.

[0031] As the application scenarios of HMB systems expand, this displacement dependence and current dependence severely restrict the promotion and application of HMB systems.

[0032] For example, in the field of high-end ultra-precision machining, the magnetically levitated electric spindle of a machine tool is no longer merely a component providing stable rotational power, but has evolved into an intelligent actuator integrating precision support and high-frequency micro-motion excitation functions. It is widely used in the final finishing processes of parts such as optical molds, complex aerospace components, and medical implants. In such vibration-assisted machining processes, any control deviation of the tool can directly affect the machining quality. Insufficient control precision of the control algorithm may lead to unstable amplitude or frequency drift, which not only disrupts the stability of the cutting process and exacerbates tool wear, but may even cause surface damage or chipping of the workpiece. Furthermore, phase lag, amplitude attenuation, or path deformation in trajectory control will be directly "copied" onto the workpiece surface, turning the desired mirror effect into chaotic vibration patterns, and distorting the shape of the designed microstructure. For another example, although the rotor has undergone fine dynamic balancing before leaving the factory, residual unbalanced forces can still be generated during high-speed operation due to factors such as material inhomogeneity and thermal deformation, causing harmful vibrations. Moreover, the amount of unbalance will dynamically change under time-varying conditions (such as rotor deformation caused by temperature rise). Traditional dynamic balancing relies on adding or adjusting counterweights after the machine stops, which is difficult to handle dynamic changes. Therefore, it is necessary to adjust the virtual balance position of the rotor in real time to actively and accurately shift the rotor's center of mass to a new position, so that the centrifugal force generated by its rotation around the geometric center can cancel out the residual unbalanced force.

[0033] It is evident that in current application scenarios, the rotor often needs to dynamically adjust its suspension position according to external working conditions (such as responding to cutting force fluctuations or suppressing unbalanced vibrations), and does not always operate at a fixed equilibrium point. The control algorithm of the HMB system needs to have extremely high dynamic response speed and trajectory tracking accuracy.

[0034] Based on this, the embodiments of this application provide a control method and system for a hybrid magnetic levitation bearing system. By combining theoretical modeling and experimental identification at finite operating points, it effectively balances computational efficiency and control accuracy, highly adapts to the variable dynamic characteristics of HMB, and improves the robustness and adaptability of the HMB system in the entire operating range.

[0035] The following detailed description of some embodiments of this application is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0036] Please see Figure 1 , Figure 1 This is a schematic flowchart illustrating a control method for a hybrid magnetic levitation bearing system provided in an embodiment of this application, such as... Figure 1 As shown in the figure, this application provides a control method for a hybrid magnetic levitation bearing system.

[0037] S101, Obtain the rigid rotor dynamic equation of the hybrid magnetic levitation bearing system.

[0038] Specifically, based on the principles of mechanics, the force balance relationship of the rotor in the radial and axial degrees of freedom is analyzed. Combining the nonlinear relationship between electromagnetic force, current, and air gap, a rigid rotor dynamic equation is established. This rigid rotor dynamic equation is a mathematical model describing the dynamic relationship between the rotor's displacement, velocity, acceleration, and external forces under the action of electromagnetic force. For details on the modeling process, please refer to relevant technical documentation.

[0039] In some embodiments, S101 further includes: describing the small-amplitude vibration of the rotor using translational and tilting data of the rotor's center of mass in a reference coordinate system, and establishing a rigid rotor dynamic equation based on a preset mechanical algorithm. Specifically, the small-amplitude vibration of the rotor is described by the translational and tilting of the rotor's center of mass in the reference coordinate system XYZ, and based on this motion description, a preset mechanical algorithm is used to establish a rigid rotor dynamic equation.

[0040] In some embodiments, the preset mechanical algorithm includes at least one of the Newton-Euler method and the Lagrange method. The Newton-Euler method is a modeling method based on classical mechanics. It establishes the dynamic equations of the translational motion of the rigid body's center of mass using Newton's second law, and simultaneously uses the Euler equations to describe the relationship between the angular acceleration of the body's rotation about its center of mass and the external torque. It is suitable for dynamic modeling of multi-degree-of-freedom rigid body systems. The Lagrange method is a modeling method based on energy principles. It constructs the Lagrange function of the system to model the dynamic equations, calculates partial derivatives with respect to generalized coordinates and generalized velocities, and substitutes them into the Lagrange equations to derive the system's differential equations of motion. It is suitable for the dynamic analysis of complex constrained systems. In high-speed applications, a flexible rotor modeling method can also be used to comprehensively consider flexible modes. For specific modeling processes, please refer to relevant technologies.

[0041] In some embodiments, S101 further includes: simplifying the hybrid magnetic levitation bearing rotor structure. The simplification includes: ignoring the coupling effect of forces between the radial and axial degrees of freedom; simplifying the uniformly distributed electromagnetic force of the axial magnetic levitation bearing on the rotor disk into a concentrated force along the rotor axis, and ignoring the resultant torque. It should be understood that ignoring the coupling effect of the axial to radial electromagnetic force has a relatively small impact on subsequent experimental results and can effectively improve modeling efficiency.

[0042] S102, select multiple characteristic working points in the entire working range, and linearize the nonlinear hybrid magnetic force of each characteristic working point to obtain the linear stiffness matrix of each characteristic working point.

[0043] The full working range refers to the range that the rotor in a hybrid magnetic levitation bearing system may reach during normal operation, and can be the physical gap (also known as the air gap) between the bearing stator and the rotor.

[0044] Specifically, several typical operating points are selected within the entire operating range, namely characteristic operating points. Each characteristic operating point corresponds to a specific set of rotor positions and currents, which will be used later to reflect the local dynamic characteristics of the system at different locations. At each characteristic operating point, the nonlinear electromagnetic force is locally linearized to obtain the linear stiffness matrix for that characteristic operating point. It should be understood that the linear stiffness matrix is ​​used to describe the linear relationship between rotor displacement, control current, and electromagnetic force near the current characteristic operating point; it is a linearized expression of the rigid rotor dynamics equations within a local region.

[0045] In some embodiments, S102 includes: analyzing the magnetic circuit of the hybrid magnetic levitation bearing system based on the equivalent magnetic circuit method, calculating the target expression for the magnetic flux and magnetic force of each magnetic pole, wherein the target expression is used to describe the nonlinear hybrid magnetic force at different positions within the entire operating range; and performing linearization of the nonlinear hybrid magnetic force at different characteristic operating points based on Taylor expansion linearization and the target expression to obtain the linear stiffness matrix at the characteristic operating points.

[0046] Specifically, the equivalent magnetic circuit method is used to analyze the magnetic circuit, and the specific expressions for the magnetic flux and magnetic force of each magnetic pole (i.e., the target expressions) are calculated. Based on the target expressions, the nonlinear hybrid magnetic force near each characteristic operating point can be determined. At different characteristic operating points, the nonlinear hybrid magnetic force is linearized using Taylor expansion linearization, thereby extracting the linear relationship between the electromagnetic force and the changes in rotor displacement and control current at each characteristic operating point, thus obtaining the linear stiffness matrix of the corresponding characteristic operating point. It should be noted that the equivalent magnetic circuit method and Taylor expansion linearization are existing algorithms; for specific implementation details, please refer to relevant technologies.

[0047] S103. Based on the rigid rotor dynamics equation and the linear stiffness matrix, establish a linear steady state-space model structure for each characteristic operating point.

[0048] Specifically, for each characteristic operating point, the nonlinear electromagnetic force term in the original rigid rotor dynamics equation is replaced based on the corresponding linear stiffness matrix, thereby constructing a linear steady state-space model structure under that characteristic operating point, providing a fixed structural basis for subsequent identification of model parameters through experimental data.

[0049] The Linear Time-Invariant State-Space (LTI-SS) model structure is a mathematical model framework used to describe the dynamic behavior of linear time-invariant systems. It consists of a basic framework of state equations and output equations. Furthermore, the LTI-SS model structure includes four coefficient state-space matrices: the system matrix, input matrix, output matrix, and feedforward matrix. These matrices remain invariant at each characteristic operating point and are used to represent the linear relationship between the system state, input, and output.

[0050] In some embodiments, the state variables are made directly measurable rotor displacement signals through linear transformation. In the LTI-SS model structure, the rotor displacement and velocity (such as the acquired rotor displacement signal and the derivative of the rotor displacement signal) are used as state variables, and the control current signal or voltage signal is used as input variable.

[0051] In some embodiments, the linear time-invariant state-space model structure of the characteristic operating point is as follows: ; in, Let be the state variable at time t, where the state variable is the rotor displacement signal and the derivative of the rotor displacement signal; The rate of change of the state variable; Let be the current signal at time t; Let be the rotor displacement signal at time t; For the system matrix; The input matrix; This is the output matrix; The scheduling variable is the rotor displacement vector in the magnetic bearing coordinate system.

[0052] In some embodiments, the LTI-SS model structure for all characteristic operating points constitutes a set of models related to the control current and rotor displacement, i.e., a variable parameter model. Please refer to [link to relevant documentation]. Figure 2 , Figure 2 This is a characteristic operating point variable parameter model provided in an embodiment of this application. For example... Figure 2As shown, multiple characteristic operating points are selected within each HMB system, resulting in multiple LTI-SS model structures. Each LTI-SS model structure is associated with the control current and rotor displacement, as shown below. Figure 2 middle, , This represents the current supplied by the radial magnetic levitation bearing in the magnetic bearing coordinate system, where XY represents the rotor displacement in the magnetic bearing coordinate system, which can be converted from state variables. This theoretical modeling process involves low computational cost, has a clear theoretical foundation, and requires relatively low computational power.

[0053] S104, The hybrid magnetic levitation bearing system is run in a pre-built experimental platform, and the rotor is levitated to different characteristic operating points.

[0054] Specifically, a hybrid magnetic levitation bearing system is operated in a pre-built experimental platform. A controller applies specific bias current and control voltage, gradually adjusting the electromagnetic force to allow the rotor to smoothly rise from its initial state and stably levitate at various preset characteristic operating points. For example, existing control strategies are used, combined with displacement sensor feedback, to manually or automatically position the rotor point-by-point, providing accurate operating status identification for subsequent experiments. In some embodiments, the experimental platform refers to a pre-built physical testing device for testing and verifying the performance of the hybrid magnetic levitation bearing system. It can be a complete hybrid magnetic levitation bearing system, and the controller's control algorithm requires further optimization and adjustment.

[0055] In some embodiments, the experimental platform includes a hybrid magnetic levitation bearing motion experimental platform; please refer to [link to relevant documentation]. Figures 3 to 4 , Figure 3 This is a flowchart illustrating a closed-loop debugging method for an experimental platform provided in an embodiment of this application. Figure 4 This is a flowchart illustrating another closed-loop debugging method for an experimental platform provided in this application embodiment. For example... Figure 3 As shown, S104 includes: S1041, based on the voltage signal measured by the displacement sensor, and based on the preset calculation algorithm, the voltage signal is calculated into a rotor displacement signal in the sensor coordinate system; S1042, Based on the first coordinate transformation algorithm, the rotor position signal is converted into a centroid position signal in the rotor centroid coordinate system; S1043, Generate a first control parameter based on the error between the centroid position signal and the reference position signal; wherein, the centroid position signal is the actual rotor centroid position in the rotor centroid coordinate system; and the reference position signal is the target rotor centroid position in the rotor centroid coordinate system.

[0056] S1044, based on the second coordinate transformation algorithm, converts the first control parameters in the rotor centroid coordinate system into the second control parameters in the magnetic bearing coordinate system; S1045, based on the second control parameter, the pre-built hybrid magnetic levitation bearing motion experimental platform outputs the corresponding current signal so that the rotor is suspended at the characteristic working point.

[0057] Specifically, such as Figure 4 As shown, a displacement sensor (such as an eddy current displacement sensor) acquires the voltage signal on the rotor surface in real time, and calculates it into a rotor position signal in the sensor coordinate system using a preset calculation algorithm (such as a preset mapping algorithm between voltage and displacement signals), such as x. a x b y a y b Based on the sensor installation position and the rotor's center of mass position, a first coordinate transformation algorithm is pre-calibrated to convert the rotor position signal into a center of mass position signal in the rotor's center of mass coordinate system. This center of mass position signal is then used as the system output data Y. The error is calculated based on the center of mass position signal and the reference position signal r corresponding to the characteristic operating point. The controller (e.g., a PID controller) generates a first control parameter to eliminate the error, and a second control parameter is used as the system output data U. To match the physical layout of the magnetic bearing, the first control parameter is then converted into a second control parameter in the magnetic bearing coordinate system using a pre-calibrated second coordinate transformation algorithm. This second control parameter represents the desired current input to the magnetic bearing, such as ixa*, ixb*, iya*, iyb*, and iz*. Finally, the power amplifier or driver outputs the corresponding current signals ixa, ixb, iya, iyb, and iz* to adjust the electromagnetic force of each magnetic pole, ensuring the rotor is precisely and stably suspended at the target characteristic operating point.

[0058] In some embodiments, based on the constructed hybrid magnetic levitation bearing motion experimental platform and the acquired LTI-SS model structure, five sets of PID control algorithms are manually adjusted to achieve initial rotor levitation. The rotor displacement signal measured by the sensor is output as an initial setting displacement signal. After coordinate transformation, the sensor coordinate displacement signal is converted to the rotor centroid coordinate. The control quantity of the centroid coordinate system is output by five sets of PID control. After coordinate transformation to the magnetic bearing coordinate system, the actual control current is output by the driver.

[0059] It should be understood that magnetic levitation bearing systems inherently possess open-loop instability and cannot be directly identified in the open-loop manner. Parameter identification must be carried out under closed-loop operating conditions. In the absence of prior data, the controller parameters are manually adjusted to enable the rotor to stably levitate at the equilibrium position or characteristic operating point, forming an effective feedback control closed loop, which provides support for subsequent closed-loop identification.

[0060] Based on the aforementioned linear steady-state-space model structure, the system identification method is used to obtain accurate model parameters at each characteristic operating point. Compared with pure theoretical modeling, experimental identification fully considers non-ideal factors (such as magnetic circuit saturation, sensor deviation and power amplifier delay) and nonlinear factors (such as structural parameter errors) in the actual system, thus improving the accuracy and reliability of the model.

[0061] S105, perform subspace identification and parameter estimation at each characteristic operating point to obtain the model parameters of the linear time-invariant state-space model structure, and obtain the local target linear model at each characteristic operating point.

[0062] Specifically, after the rotor is stably suspended at each characteristic operating point, input and output data from displacement and current sensors are collected. Based on this data, a subspace identification method is used to estimate the parameters of the linear time-invariant state-space model structure, solving for model parameters such as the system matrix, input matrix, output matrix, and feedforward matrix. For each characteristic operating point, the accurate linear time-invariant state-space model obtained after experimental data identification is a local target linear model, including complete parameter information of the dynamic characteristics of the local region, which is used to design the local controller. Subspace identification is a modern system identification method based on input and output data to estimate the parameters of the linear system state-space model; for details, please refer to relevant technical documentation.

[0063] In some embodiments, S105 includes direct solution based on closed-loop identification. , , , matrix.

[0064] In some embodiments, S105 further includes: constructing input / output data Hankel matrices, obtaining a first Hankel matrix of the first control parameters, a second Hankel matrix of the centroid position signal, and a third Hankel matrix of the reference position signal; performing orthogonal projection on the third Hankel matrix based on the first and second Hankel matrices to convert closed-loop identification into open-loop identification; calculating the generalized observability matrix and the generalized state sequence using an oblique projection algorithm, and solving for the generalized observability matrix and the generalized state sequence based on the weight matrix; and calculating a matrix based on the generalized observability matrix and the generalized state sequence. , , , ,in, It is a feedforward matrix.

[0065] Among them, the Hankel matrix is ​​a type of square or rectangular matrix in which all elements on each subdiagonal are equal, and it has important applications in mathematics, digital signal processing, numerical computation, system identification and control theory.

[0066] Specifically, the rotor centroid displacement (i.e., centroid position signal) is obtained by transforming the output data of the controller (i.e., the first control signal) and the output data of the sensor (i.e., the rotor displacement signal) through the first coordinate transformation algorithm. The first Hankel matrix of the first control signal and the second Hankel matrix of the centroid position signal are orthogonally projected onto the third Hankel matrix of the reference input data (i.e., the reference position signal) to convert the data identified by the closed loop into data that can be used by the open loop identification.

[0067] Furthermore, the generalized observability matrix and the generalized state sequence are calculated using an oblique projection algorithm. The expression is: ; in, This represents past input data. Indicates future input data; This represents past output data. This indicates future output data; Represents the generalized observability matrix; The specific definitions of the generalized state sequence, generalized observability matrix, and generalized state sequence can be found in relevant technical documents. This expression is used to describe... Along The direction is The oblique projection onto the (i.e., the past input-output matrix).

[0068] Furthermore, in conjunction with the weight matrix, the SVD algorithm is used to determine and solve the generalized observability matrix and the generalized state sequence. In subspace identification, the weight matrix is ​​used to perform weighted projection on the data. The SVD algorithm, also known as the singular value decomposition algorithm, is used for matrix decomposition. The left singular matrix obtained by decomposition corresponds to the generalized observability matrix, and the right singular matrix is ​​combined with the weight matrix to reconstruct the generalized state sequence.

[0069] Finally, the coefficient state space matrix is ​​calculated based on the generalized observability matrix and the generalized state sequence. , , , .

[0070] In some embodiments, the matrix is ​​solved iteratively using the least squares algorithm. , , , Alternatively, the matrix can be calculated based on the generalized observability matrix. , Solving based on the least squares algorithm , .

[0071] Specifically, the least squares algorithm is used to iteratively solve the problem. , , , The matrix can be solved using the following formula: ; in, This represents least squares, which minimizes the sum of squared prediction errors; Represents the system output vector; Represents a generalized sequence of states; Indicates time; Indicates the next moment.

[0072] Specifically, based on Define the computation matrix , The calculation formula is as follows: ; Next, the least squares algorithm is used to solve the problem. , The solution formula is as follows: ; in, Indicates the number of columns / rows in the matrix; Represents the identity matrix; The first parameter sequence is represented, and the Hankel matrix formed by it is used to characterize the dynamic properties of the system. The output projection sequence is the result sequence obtained by performing orthogonal projection operations on the input and output data.

[0073] S106, Construct a global controller for the entire working range based on multiple local target linear models.

[0074] Specifically, a corresponding local controller is designed for the local target linear model at each feature working point, forming a controller parameter set to realize the global controller function for operation across the entire working range. For example, during actual system operation, the current state of the rotor (such as position) is monitored in real time, its location is determined, and several nearby feature working points are identified. The local controller corresponding to the nearest feature working point is then invoked for control, thereby reducing computing power requirements while achieving precise motion control across the entire operating range.

[0075] In some embodiments, S106 further includes: S1061, determining a local controller for each feature working point based on a local target linear model for each feature working point; S1062, interpolating the local controllers for different feature working points based on a preset linear interpolation algorithm to obtain a global controller for the entire working range.

[0076] Specifically, based on the local target linear models obtained through experimental identification at each characteristic operating point, corresponding local controllers are designed using controller design methods from modern control theory such as pole placement, LQR, or H∞ to improve the dynamic performance and stability of the system near each local operating point. For non-characteristic operating points, parameters are fused among multiple known local controllers using a preset linear interpolation algorithm based on the actual location of the current characteristic operating point. For example, local controllers for several neighboring characteristic operating points are selected, and weighted calculations are performed based on the spatial distance between the characteristic operating points and the current location to generate controllers suitable for non-characteristic points. Thus, a global controller covering the entire operating range can be formed without complex modeling of the entire system, improving the system's adaptability and control accuracy under wide operating conditions.

[0077] In some embodiments, the preset linear interpolation algorithm is a cubic spline linear interpolation algorithm.

[0078] In some embodiments, after executing S1061 to obtain the local controller for each characteristic operating point, S1062 can be executed directly to obtain the global controller. Alternatively, when the rotor is actually operating at a non-calibrated characteristic operating point, a preset linear interpolation algorithm can be used to fuse parameters among multiple known local controllers based on the current actual position.

[0079] In some embodiments, the global controller is a linear variable-parameter global controller whose parameters are continuously adjusted according to changes in the real-time system state (such as rotor position and control current), enabling stable and high-performance closed-loop control across the entire operating range. Please refer to [link to relevant documentation]. Figure 5 , Figure 5 This is a block diagram of a global linear variable parameter control algorithm for a hybrid magnetic levitation bearing provided in an embodiment of this application, such as... Figure 5 As shown, w is the exogenous input, including the reference trajectory, measurement noise, and input disturbance; z is the system index vector output; H(p) represents the linear variable parameter state-space model of the system; K(p) is the linear variable parameter optimal robust controller (i.e., the linear variable parameter global controller); p represents the scheduling variable; F represents the entire closed-loop system; y represents the system input; and u represents the system input.

[0080] In some embodiments, selecting multiple characteristic operating points in the entire operating range includes: obtaining the operating requirements of the hybrid magnetic levitation bearing system, and determining the selection range and / or distribution density of the characteristic operating points based on the operating requirements; and selecting multiple characteristic operating points in the entire operating range based on the selection range and / or distribution density.

[0081] Specifically, the operational requirements of the hybrid magnetic levitation bearing system in practical application scenarios are analyzed to determine the range and density of selection points. For example, in dynamic balancing adaptive adjustment applications requiring large-scale rotor position adjustments, the selection range of characteristic operating points should be expanded to approximately 60% of the air gap interval, with equal distribution density within the selected range to achieve uniform point selection and fully cover the nonlinear characteristics under large displacement conditions. As another example, in applications requiring only micro-amplitude vibration, such as ultra-precision vibration machining, the rotor's operating range is typically concentrated within a specific area. In this case, the selection range can be limited to within 30% of the air gap interval, with higher distribution density closer to the center of the specific area to avoid redundant modeling in peripheral areas with no practical value.

[0082] In some embodiments, the specific value of the distribution density is set based on accuracy and computational burden. For example, in regions with high control accuracy requirements or drastic nonlinear changes, the operating point density can be appropriately increased, such as by using a first distribution density; while in regions with smoother response or low-frequency use, the density is reduced, such as by using a second distribution density, where the first distribution density is higher than the second distribution density. It should be understood that if too many feature operating points are selected, it will not only increase the experimental identification time but also lead to an increase in the subsequent controller interpolation calculation, affecting real-time performance. Therefore, the distribution density of feature operating points can be increased in the high-frequency operating region of the system or in a preset region with high control accuracy requirements, and the distribution density can be reduced in low-frequency or edge regions. Based on the selection range and distribution density, multiple feature operating points are selected uniformly or non-uniformly throughout the entire operating range.

[0083] It should be understood that the selection of feature operating points is not about blindly covering the entire physically feasible region, but rather about closely integrating with the actual operational requirements of the system. By rationally determining the selection range and distribution density, modeling efficiency can be improved while ensuring control accuracy. For example, based on system operational requirements, the density of operating points can be increased in frequently used operating areas. In most areas, the corresponding local controller can be directly invoked. Even in other areas where control is achieved through linear interpolation, higher local control accuracy can be obtained based on more information from neighboring operating points. In less frequently used areas, the density of operating points can be appropriately reduced, relying on linear interpolation to maintain basic control performance. This adaptive distribution mechanism effectively captures the nonlinear characteristics of the system while avoiding the computational burden caused by oversampling, thus optimizing resource allocation.

[0084] In some embodiments, selecting multiple characteristic operating points across the entire operating range includes: selecting a first preset number of characteristic operating points across the entire operating range based on typical system operating conditions and safe operating boundaries to obtain a preliminary local model set, and designing an initial controller based on the preliminary local model set; evaluating the control response performance of the HMB system in different regions through closed-loop operation testing on an experimental platform or simulation environment, wherein the control response performance is determined based on trajectory tracking error and / or vibration suppression capability; if the control response performance in any region exceeds a preset tolerance threshold, a second preset number of new characteristic operating points are added to the corresponding region to update the preliminary local model, achieving iterative optimization of the model set, and finally optimizing to obtain a global controller. It should be understood that the feedback mechanism based on control performance verification can specifically identify weak areas in the modeling and avoid oversampling in low-sensitivity areas.

[0085] In some embodiments, multiple feature working points are selected in the entire working range, including: the closed-loop operation test includes simulating load disturbance or executing a predetermined trajectory motion, and judging whether the model accuracy meets the requirements by comparing the error between the actual control output and the expected response; when the error exceeds a preset error threshold, a local model update mechanism is triggered to automatically or manually add new feature working points in the corresponding working area.

[0086] In some embodiments, multiple characteristic operating points are selected in the entire operating range, including: acquiring rotor suspension position information collected during the actual operation of the system within a preset time period; analyzing the rotor dwell frequency or displacement distribution density in each region based on the rotor suspension position information to identify high-frequency use areas; increasing the distribution density of characteristic operating points in the high-frequency use areas to improve model accuracy and control performance under common operating conditions; and maintaining a low density for rarely reached extreme positions, which are only used to ensure stability boundary coverage.

[0087] It should be understood that the selection of feature working points can be one-time and static, or it can be dynamically adjusted based on operational needs, control performance and actual data. The initial layout should be based on the conservative principle of saving computing power (such as setting the first preset number to a low level), and then feature working points should be added as needed, so as to reduce the computational burden to a certain extent while ensuring the accuracy of global control.

[0088] This application also provides a hybrid magnetic levitation bearing system, the system comprising: a magnetic levitation bearing structure, a displacement sensor, a current sensor, and a global controller; the magnetic levitation bearing structure includes a stator with a permanent magnet and a control coil, and a rotor capable of levitation and rotation; the controller is based on a control method for the hybrid magnetic levitation bearing system provided in any embodiment of this application.

[0089] Please see Figure 6 , Figure 6 This is a schematic diagram of a hybrid magnetic levitation bearing system provided in an embodiment of this application. Figure 6 As shown, the hybrid magnetic levitation bearing system includes core components such as a magnetic levitation bearing structure (e.g., a 5-DOF hybrid magnetic levitation bearing), displacement sensors, current sensors, and a global controller. The magnetic levitation bearing structure includes a stator and a levitable rotor. The stator is equipped with permanent magnets and control coils. The permanent magnets provide static bias flux to bear constant loads such as the rotor's own weight. The control coils are supplied with a controllable current to generate dynamically adjustable flux, enabling active control of the rotor's position. The displacement sensor detects the rotor's displacement relative to its equilibrium position in real time and outputs a rotor displacement signal, which is transmitted to an analog input board for feedback to the controller. The current sensor collects the actual current value in the control coil and outputs a current signal, which is also transmitted to the analog input board for feedback to the controller. The global controller is based on the control method of the hybrid magnetic levitation bearing system provided in any embodiment of this application. By establishing and identifying local linear models at multiple characteristic operating points, an interpolation algorithm is used to construct a linear variable parameter controller covering the entire operating range, achieving high-precision and high-stability control of the rotor under different operating conditions.

[0090] In addition, such as Figure 6 As shown, the hybrid magnetic levitation bearing system may also include: a driver, analog input / output boards, an industrial computer, a power supply module, a router, and other supporting components. The driver receives command signals from the controller and converts them into drive current output to each coil; the industrial computer communicates with the controller through the router's network cable interface to monitor system status and configure controller parameters; the power supply module includes sub-modules such as power supplies, relays, air switches, and push-button switches to ensure safe power supply for the hybrid magnetic levitation bearing system.

[0091] In some embodiments, the magnetic levitation bearing structure may be a 5-DOF hybrid magnetic levitation bearing, a 4-DOF hybrid magnetic levitation bearing, etc., and is not limited thereto.

[0092] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A control method of a hybrid magnetic bearing system, characterized by, The method comprises: S101, acquiring a rigid rotor dynamics equation of a hybrid magnetic bearing system; S102, selecting a plurality of characteristic working points in a full working range, and respectively linearizing a nonlinear hybrid magnetic force of each characteristic working point to obtain a linear stiffness matrix of each characteristic working point; S103, establishing a linear constant state space model structure of each characteristic working point based on the rigid rotor dynamics equation and the linear stiffness matrix; S104, running the hybrid magnetic bearing system in a pre-built experimental platform, and suspending the rotor to different characteristic working points; S105, performing subspace identification and parameter estimation at each characteristic working point to obtain model parameters of the linear constant state space model structure, and obtaining a local target linear model at each characteristic working point; S106, constructing a global controller under the full working range based on a plurality of the local target linear models.

2. The method of claim 1, wherein, The selecting a plurality of characteristic working points in the full working range comprises: acquiring a running requirement of the hybrid magnetic bearing system, and determining a selection range and / or distribution density of the characteristic working points according to the running requirement; selecting a plurality of the characteristic working points in the full working range according to the selection range and / or distribution density.

3. The method of claim 1, wherein, The S101 further comprises: small amplitude vibration of the rotor is described by translation and tilt data of the rotor mass center in a reference coordinate system, and the rigid rotor dynamics equation is established based on a preset mechanical algorithm, the preset mechanical algorithm comprising at least one of Newton-Euler method and Lagrange method.

4. The method of claim 1, wherein, S102 comprises: magnetic circuit of the hybrid magnetic bearing system is analyzed based on equivalent magnetic circuit method, and a target expression of magnetic flux and magnetic force of each magnetic pole is calculated, the target expression being used to describe the nonlinear hybrid magnetic force at different positions in the full working range; linearization of the nonlinear hybrid magnetic force is performed at different characteristic working points based on Taylor expansion linearization and the target expression to obtain a linear stiffness matrix at the characteristic working point.

5. The method of claim 1, wherein, The experimental platform comprises a hybrid magnetic bearing motion experimental platform, and S104 comprises: S1041, measuring a voltage signal based on a displacement sensor, and calculating the voltage signal into a rotor displacement signal in a sensor coordinate system based on a preset calculation algorithm; S1042, converting the rotor position signal into a mass center position signal in a rotor mass center coordinate system based on a first coordinate transformation algorithm; S1043, generating a first control parameter based on an error between the mass center position signal and a reference position signal; S1044, converting the first control parameter in the rotor mass center coordinate system into a second control parameter in a magnetic bearing coordinate system based on a second coordinate transformation algorithm; S1045, controlling the pre-built hybrid magnetic bearing motion experimental platform to output a corresponding current signal based on the second control parameter, so that the rotor is suspended at the characteristic working point.

6. The method of claim 5, wherein, The linear constant state space model structure of the characteristic working point is: ； wherein is a state variable at time t, the state variable being a rotor displacement signal and a derivative of the rotor displacement signal; is a rate of change of the state variable; is a current signal at time t; is a rotor displacement signal at time t; is a system matrix; is an input matrix; is an output matrix; is a rotor displacement vector of the rotor in a magnetic bearing coordinate system.

7. The method of claim 6, wherein, The S105 further comprises: A Hankel matrix of input and output data is constructed, and a first Hankel matrix of a first control parameter, a second Hankel matrix of a centroid position signal, and a third Hankel matrix of a reference position signal are obtained respectively; Orthogonal projection is performed on the third Hankel matrix based on the first Hankel matrix and the second Hankel matrix to convert from closed-loop identification to open-loop identification; A generalized observability matrix and a generalized state sequence are calculated by using a oblique projection algorithm, and the generalized observability matrix and the generalized state sequence are solved based on a weight matrix; calculating a generalized observability matrix based on the generalized state sequence calculation matrix , , , wherein, is a feedforward matrix.

8. The method of claim 7, wherein, The method further comprises: iterative solution of the matrix based on the least squares algorithm , , , ; or, calculation of the matrix based on the generalized observability matrix , ; solution of , .

9. The method of claim 1, wherein, The S106 further comprises: A local controller of each feature working point is determined based on a local target linear model of each feature working point; The local controllers of different feature working points are interpolated based on a preset linear interpolation algorithm to obtain a global controller of the full working interval.

10. A hybrid magnetic bearing system, characterized by The system comprises a magnetic suspension bearing structure device, a displacement sensor, a current sensor, and a global controller. The magnetic suspension bearing structure device comprises a stator provided with a permanent magnet and a control coil and a rotatable rotor that can be suspended. The controller is obtained based on the control method of the hybrid magnetic suspension bearing system according to any one of claims 1-9.

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