A method for multi-frequency vibration suppression of an electromagnetic bearing rotor system

Abstract

This invention provides a method for suppressing multi-frequency vibrations in an electromagnetic bearing rotor system, relating to the field of rotor vibration suppression. The invention introduces a pre-trained machine learning regression model to accurately map the original sensor signal to the actual displacement at the electromagnet's force application point, reducing the residual amplitude of unbalanced vibrations. The invention employs a reduced-order generalized integrator to offset the inherent delay of the digital computing and execution mechanism, and uses cascaded notch filters to accurately intercept second-order and higher-order geometric jumps. Utilizing an improved particle swarm optimization algorithm, the notch filter parameters and master control gain are jointly solved in a high-dimensional space, fundamentally eliminating the complex interference between multi-dimensional parameters. This invention proposes an equivalent space mapping and multi-dimensional vector cancellation method to actively cancel alternating components with the same frequency as the disturbance during current command synthesis. When a phase abrupt change is detected, the guiding source is switched to avoid chattering caused by mismatch, and when the rotor approaches the drop boundary, it is pulled back to a safe linear suspension region.

Description

Technical Field

[0001] This invention relates to the field of rotor vibration suppression, specifically a method for suppressing multi-frequency vibration in an electromagnetic bearing rotor system. Background Technology

[0002] Active magnetic bearings (AMBs) offer advantages such as contactless friction, no lubrication required, and adaptability to ultra-high-speed operation, making them widely used in high-end rotating machinery such as high-speed motors, compressors, and flywheel energy storage systems. However, due to uneven rotor material or machining and assembly errors, rotors inevitably exhibit mass eccentricity, generating periodic centrifugal forces at the same frequency as the rotational speed during high-speed rotation—a dynamic imbalance disturbance. If the controller adopts a zero-displacement strategy, it will instinctively output a high-frequency alternating current to forcibly constrain this disturbance, locking the rotor at its geometric center. This approach not only causes severe overheating and a surge in power consumption in the power amplifier but also transmits the alternating force to the stator frame through the magnetic field, triggering high-frequency resonance throughout the machine. More seriously, when the rotor crosses the critical speed, the physical phase of the unbalanced vibration undergoes a dramatic abrupt change of nearly 180 degrees. Traditional control strategies or fixed-parameter filters are highly susceptible to reference mismatch, causing the signal originally intended to suppress vibration to instantly become positive feedback that exacerbates it, leading to system chattering or even instability and failure. Therefore, high-speed electromagnetic bearing systems must employ specialized vibration control methods to eliminate the alternating component in the drive current, allowing the rotor to rotate around its own inertial axis and achieving zero-current control.

[0003] Notch filters are currently one of the main methods for dealing with unbalanced vibrations. For example, the invention patent "CN113485472A A method for suppressing the same-frequency vibration torque of a magnetic levitation rotor based on a dual-channel notch filter" provides a typical solution: a dual-channel notch filter is connected in series or parallel in the closed-loop circuit of the system to simultaneously process the displacement signals in the X and Y orthogonal directions, extract the vibration component with the same frequency as the rotational speed, introduce a phase compensation angle for adjustment, and generate a compensation signal to cancel the same-frequency vibration torque, thereby reducing the hardware resource consumption while ensuring stability within a certain speed range.

[0004] Although the above solutions alleviate unbalanced vibrations to some extent, they still have significant limitations under real high-speed operating conditions:

[0005] Firstly, the frequency band coverage is limited, making it impossible to differentiate and isolate multi-frequency interference. In actual operation, in addition to the first-order vibration caused by mass eccentricity, processing defects on the sensor's detection surface can induce second-order and higher-order spurious fluctuations. This notch filter only extracts the first-order component, allowing higher-order noise to penetrate the control loop without obstruction, causing the power amplifier to overheat and the chassis to resonate at high frequencies.

[0006] Secondly, the closed-loop feedback topology is prone to instability in the critical speed region. This scheme always uses a signal containing the actual displacement error as the input reference. When crossing the critical speed, the vibration phase flips by 180 degrees. If the feedback loop is not disconnected to reconstruct the reference source, it will cause instantaneous reference mismatch of the notch filter, and the compensation signal will deteriorate into positive feedback excitation, triggering severe chattering.

[0007] Third, the positional deviation between the sensor and the actuator introduces reference distortion. Due to physical space limitations, the sensor probe and the electromagnet's force application point cannot be installed in the same position, resulting in differences in amplitude and phase of the displacements measured by the two. This solution directly uses the sensor's raw data for processing without calibrating this spatial deviation, causing the compensation signal to have a non-negligible error from the source.

[0008] Fourth, the overall control architecture remains a localized compensation for specific operating conditions. The main controller still follows a zero-displacement strategy, with alternating electromagnetic force continuously transmitted to the machine base. It cannot actively cancel the alternating component through the current command synthesis stage, nor does it include dynamic safety intervention when the rotor approaches the protective gap. Therefore, existing technology struggles to block vibration energy transmission at the system level and cannot achieve true zero-current operation. Summary of the Invention

[0009] To address the shortcomings of existing technologies, the present invention aims to propose a method for suppressing multi-frequency vibrations in electromagnetic bearing rotor systems. This method overcomes a series of fundamental defects in existing technologies when dealing with multi-frequency vibrations of high-speed rotors, such as distorted sensing references, single signal stripping, easy instability at critical speeds, strong coupling of multiple parameters, and excessive reliance on idealized models to forcibly suppress disturbances in control strategies.

[0010] This invention proposes a method for suppressing multi-frequency vibration in an electromagnetic bearing rotor system, comprising:

[0011] Step 1: Obtain the reconfiguration displacement of the rotor when the actual electromagnetic bearing rotor system is running;

[0012] Step 2: Construct a reduced-order generalized integrator with a dynamic lead-shifting phase matrix, and then process the reconstructed displacement of the rotor to obtain the discrete first-order true vibration characteristic vector of the same frequency.

[0013] Step 3: Optimize the depth and width parameters of the adaptive cascaded notch filter and the control parameters of the model-free adaptive control (MFAC) algorithm, and then process the reconstructed displacement of the rotor to obtain the discrete Nth order high-frequency spurious jump characteristic vector, the master control feedback current and the DC bias current.

[0014] Step 4: Calculate the integrated drive current based on the discrete first-order same-frequency true vibration characteristic vector, the discrete Nth-order high-frequency false jumping characteristic vector, the main control feedback current, and the DC bias current;

[0015] Step 5: Calculate the rotor eccentricity based on the rotor's reconfigured displacement, then determine the safe drive current in conjunction with the comprehensive drive current, and transmit the safe drive current to the power amplifier to suppress the multi-frequency vibration of the electromagnetic bearing.

[0016] Optionally, step 1 specifically includes:

[0017] Step 1.1: Construct a rotor dynamics finite element model of the electromagnetic bearing rotor system. Input the excitation signals of various potential operating conditions into the rotor dynamics finite element model for simulation. Obtain the displacement data sequence of the preset sensor position as the input feature set and the displacement data sequence of the preset electromagnet force center position as the target label set. Based on the input feature set and the target label set, use the extreme gradient boosting regression algorithm to train the extreme gradient boosting model and obtain the trained extreme gradient boosting regression model.

[0018] Step 1.2: When the actual electromagnetic bearing rotor system is running, collect the original observed displacement of the rotor at the preset sensor position;

[0019] Step 1.3: Input the original observed displacement of the rotor into the trained extreme gradient boosting regression model to obtain the reconstructed displacement of the rotor. .

[0020] Optionally, step 2 specifically includes:

[0021] Constructing a reduced-order generalized integrator with a dynamic lead-shift phase matrix , is represented as:

[0022] ;

[0023] in, Adjust the gain of the integrator as the base; This is the complex rotation transformation matrix used to compensate for physical phase lag, where s is the complex frequency and j is the imaginary unit. ω is the real-time rotational angular frequency of the rotor;

[0024] The frequency domain control equations generated based on the reduced-order generalized integrator are expressed as follows:

[0025] ;

[0026] in, To reconstruct displacement The corresponding frequency domain signal, It is the first-order characteristic vector of the real vibration at the same frequency;

[0027] The frequency domain control equations are discretized using the bilinear transform method to obtain the corresponding frequency domain control equations. Discrete transfer function of the domain, using The time-shift property of the transformation yields the discrete first-order true vibration characteristic vector with the same frequency. , is represented as:

[0028] ;

[0029] Where n is the current discrete sampling sequence number, , and All are discretization coefficients. The reconstructed displacement in the nth discrete sampling sequence; It is the discrete first-order same-frequency true vibration feature vector in the (n-1)th discrete sampling sequence.

[0030] Optionally, step 3 specifically includes:

[0031] Step 3.1: In the offline stage, multiple particle vectors are set. The particle vectors include the depth and width parameters of the adaptive cascaded notch filter and the control parameters of the model-free adaptive control (MFAC) algorithm. An improved particle swarm optimization algorithm is used to process all particle vectors to obtain the offline optimal particle vector.

[0032] Step 3.2: In the online phase, obtain the instantaneous displacement error and error change rate of the rotor; based on the preset rotor dynamics expert experience fuzzy rule base, instantaneous displacement error and error change rate, use fuzzy logic algorithm to perform fuzzy reasoning and defuzzification operation to generate dynamic compensation increment; based on the dynamic compensation increment and offline optimal particle vector, generate online optimal particle vector.

[0033] Step 3.3: Configure the adaptive cascaded notch filter based on the optimal depth and width parameters, and reconstruct the displacement according to the configured adaptive cascaded notch filter. After processing, the discrete Nth-order high-frequency spurious pulsation feature vector is obtained. ;

[0034] Step 3.4: Configure the MFAC algorithm based on the optimal control parameters of MFAC, and reconstruct the displacement according to the configured MFAC algorithm. The process is performed to obtain the main control feedback current. and DC bias current .

[0035] Optionally, step 3.3 specifically includes:

[0036] Set a speed threshold, collect the rotor speed in real time, and when the rotor speed is less than the speed threshold, calculate the reference tracking angular frequency based on the reconstructed displacement. Specifically, this is achieved through the following formula:

[0037] ;

[0038] in, To reconstruct displacement The physical phase;

[0039] When the rotor speed is greater than or equal to the speed threshold, obtain the absolute mechanical angle of the shaft. Then calculate the reference tracking angular frequency. Specifically, this is achieved through the following formula:

[0040] ;

[0041] Based on the optimal depth and width parameter configuration of the adaptive cascaded notch filter, the configured adaptive cascaded notch filter is obtained. For each high-frequency harmonic in the multi-order high-frequency harmonics contained in the reconstructed displacement, the angular frequency is tracked based on the reference. The continuous-domain transfer function corresponding to the configured adaptive cascaded notch filter is expressed as:

[0042] ;

[0043] in, For the first The continuous domain transfer function corresponding to the first-order high-frequency harmonics. To reconstruct the frequency domain signal corresponding to the displacement; This is the Nth order high-frequency spurious jump feature vector; For the set higher harmonic orders, k is the highest harmonic order; This refers to the dynamic gain coefficient.

[0044] The continuous domain transfer function is discretized using the bilinear transform method to obtain its corresponding... Discrete transfer function of the domain, using The time-shift property of the transformation yields the discrete Nth-order high-frequency spurious hopping characteristic vector. ;

[0045] ;

[0046] in, , , , , , These are the discretization coefficients. Let n be the reconstructed displacement in the nth discrete sampling sequence. It is the discrete Nth-order high-frequency spurious jump feature vector in the (n-1)th discrete sampling sequence.

[0047] Optionally, step 4 specifically includes:

[0048] Define the equivalent transformation gain matrix , is represented as:

[0049] ;

[0050] in, This is the rotor's displacement-stiffness coefficient. The current-suction coefficient;

[0051] Based on the equivalent transformation gain matrix Discrete first-order true vibration characteristic vector with the same frequency Discrete Nth order high-frequency spurious pulsation feature vector Main control feedback current and DC bias current Calculate the overall drive current Specifically, this is achieved through the following formula:

[0052] .

[0053] Optionally, step 5 specifically includes:

[0054] Step 5.1: Obtain the physical clearance of the protective bearing, calculate the ratio of the reconstructed displacement to the physical clearance of the protective bearing, and obtain the eccentricity;

[0055] Step 5.2: When the eccentricity is less than the preset threshold, the comprehensive drive current is transmitted to the power amplifier as a safe drive current to suppress the multi-frequency vibration of the electromagnetic bearing; when the eccentricity is greater than or equal to the preset threshold, proceed to step 5.3.

[0056] Step 5.3: Calculate the instantaneous motion phase angle Specifically, this is achieved through the following formula:

[0057] ;

[0058] in, and They are respectively Displacement components along the Y and X axes;

[0059] Based on the instantaneous motion phase angle Identify the target coil that provides the reverse restoring force, and calculate the physical limiting current and DC bias current of the power amplifier. The difference is used to obtain the residual current capacity of the target coil. ;

[0060] Calculate the nonlinear gain function Specifically, this is achieved through the following formula:

[0061] ;

[0062] in, This is the steepness coefficient. This is the trigger threshold;

[0063] Based on the comprehensive drive current Nonlinear gain function and residual current capacity Calculate the safe drive current of the target coil. Specifically, it is calculated using the following formula:

[0064] ;

[0065] Safety drive current The signal is transmitted to a power amplifier to suppress multi-frequency vibrations of the electromagnetic bearing.

[0066] The beneficial effects of adopting the above technical solution are as follows:

[0067] 1. Eliminate observation errors at their physical source and reshape high-precision control benchmarks.

[0068] The misalignment of the sensor and electromagnet introduces spatial phase and amplitude observation biases, causing traditional strategies to compensate based on erroneous "pseudo-displacements." This invention introduces a pre-trained machine learning regression model into the sensing stage. Through nonlinear state reconstruction, it accurately maps the original sensing signal to the true displacement at the electromagnet's force application point. This mechanism overcomes the physical limitations of hardware spatial layout, providing a unique and reliable data source for subsequent higher-order algorithms, thus reducing the residual amplitude of unbalanced vibrations at their source.

[0069] 2. Overcame the challenge of multi-frequency interference stripping, achieving zero-delay tracking across the entire speed domain.

[0070] Rotor mass eccentricity and sensor scratches couple together, generating multi-order complex noise. This invention abandons the series filtering structure that easily leads to instability and pioneers a dual-channel parallel cleaning architecture. The reduced-order generalized integrator utilizes a dynamic lead-shifting mechanism to offset the inherent delay of the digital computing and execution mechanisms, achieving absolute phase-locking and zero-delay extraction of the same-frequency vibration characteristics. Simultaneously, a cascaded notch filter is responsible for accurately intercepting second-order and higher-order geometrical jumps. Working together, these two components filter out multi-frequency interference components for subsequent processing stages.

[0071] 3. Overcoming the dilemma of strong coupling of multidimensional parameters, endowing the system with high robustness and adaptive capability.

[0072] When multi-order filters are cascaded with the main controller, the interplay between parameters can easily lead to a rapid deterioration of the system's phase margin. This invention employs a purely data-driven model-free adaptive control, eliminating the reliance on a precise analytical model of the rotor, and constructs a two-layer parameter tuning architecture combining offline global optimization with online fuzzy fine-tuning. This architecture utilizes an improved particle swarm optimization algorithm to jointly solve for the notch filter parameters and the main controller gain in a high-dimensional space, fundamentally eliminating the complex interference between multi-dimensional parameters and ensuring that the system maintains good control stiffness and dynamic response under load changes or operating condition transitions.

[0073] 4. Breaking away from the traditional rigid disturbance rejection, achieving zero current control and power amplifier power consumption reduction.

[0074] Faced with the unbalanced excitation force generated by high-speed rotation, traditional solutions tend to output high-frequency alternating current to forcibly constrain the rotor position. This approach not only causes severe overheating of the power amplifier but also induces strong resonance in the stator frame. This invention proposes an equivalent spatial mapping and multidimensional vector cancellation method to actively cancel the alternating component with the same frequency as the disturbance during the current command synthesis stage. After the alternating electromagnetic pull is removed, the rotor can rotate smoothly around the inertial axis in accordance with its own dynamic characteristics. This strategy cuts off the transmission path of the excitation force to the frame, eliminates high-frequency resonance of the entire machine, and converts ineffective alternating power consumption into stable DC output, solving the prominent problem of high-frequency overheating in high-power magnetic levitation systems.

[0075] 5. Establish a nonlinear dynamic safety mechanism to enhance operational reliability under extreme conditions.

[0076] When the rotor crosses the critical speed or suffers a strong external impact, conventional algorithms are prone to falling into a continuous collision state due to phase abrupt changes or amplitude saturation. To address this issue, this invention employs two measures: first, switching the guiding source when a phase abrupt change is detected in the critical speed region to avoid chattering caused by mismatch; second, setting up an adjustable residual current distribution mechanism based on eccentricity triggering in the physical execution stage. When the rotor approaches the drop boundary, the system releases the ultimate electromagnetic pull force in a very short time, disrupting the energy balance that maintains high-frequency collisions and forcibly pulling the rotor back to the safe linear suspension region. This mechanism fundamentally ensures the operational safety of high-speed equipment throughout its entire lifecycle. Attached Figure Description

[0077] Figure 1 This is a flowchart illustrating a method for suppressing multi-frequency vibration in an electromagnetic bearing rotor system according to an embodiment of the present invention.

[0078] Figure 2 This is a schematic diagram of the process for generating reconstructed displacements in an embodiment of the present invention;

[0079] Figure 3 This is a schematic diagram of the dual-channel processing in an embodiment of the present invention;

[0080] Figure 4 This is a schematic diagram of the parameter optimization and current calculation process in an embodiment of the present invention;

[0081] Figure 5 This is a schematic diagram of the process for generating the integrated drive current in an embodiment of the present invention;

[0082] Figure 6 This is a schematic diagram of the process for generating a safe driving current in an embodiment of the present invention. Detailed Implementation

[0083] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0084] To address the problems existing in the prior art, this invention provides a method for suppressing multi-frequency vibration in an electromagnetic bearing rotor system, primarily aiming to overcome the following five technical limitations and achieve the corresponding objectives:

[0085] First, in view of the shortcomings of existing systems that ignore the underlying physical installation misalignment, which leads to serious distortion of the identification and compensation benchmark, the purpose of this invention is to completely eliminate the underlying spatial observation error by introducing machine learning for state reconstruction, and to provide a unique and reliable true absolute displacement benchmark for all subsequent control algorithms.

[0086] Secondly, addressing the issue that existing filters have limited frequency band coverage and are prone to reference mismatch and system chattering when crossing critical speeds due to the failure to cut off the closed-loop feedback topology, the purpose of this invention is to construct a dual-channel differentiated feature stripping architecture. While accurately extracting real vibrations at the same frequency, it forcibly cuts off the feedback loop of actual displacement errors for higher-order spurious jumps and reconstructs a pure reference source, thereby fundamentally isolating the interference of physical phase abrupt changes on the algorithm's internal stability.

[0087] Furthermore, addressing the shortcomings of existing control systems when facing complex multidimensional filtering, such as severe strong coupling between multidimensional filter parameters and the basic gain of the main control unit, and the lack of dynamic adaptability due to reliance on manual experience for tuning, the purpose of this invention is to introduce a model-free adaptive controller as the main control unit and innovatively construct a two-layer intelligent parameter tuning architecture of "offline global optimization + online dynamic correction". This architecture aims to achieve intelligent calculation of baseband levitation force by coordinating configuration to escape local optima in the early stage and real-time fuzzy fine-tuning during runtime, thus endowing the system with extremely strong robustness.

[0088] Furthermore, addressing the shortcomings of existing technologies that rely on idealized power amplifier inverse models, which are prone to failure, and whose underlying architecture inherently outputs alternating current to forcibly suppress disturbances, leading to severe resonance in the chassis, the core objective of this invention is to break away from the traditional zero-displacement control bias and propose a multi-dimensional vector anti-phase unloading mechanism. This mechanism aims to precisely clear the high-frequency alternating component in the final drive current by mirror reconstruction of the underlying data stream and vector cancellation operations within the addition node, thereby actively forcing the electromagnetic actuator to release the rigid constraint on the rotor's center of gravity.

[0089] Finally, in view of the lack of end-point safety protection mechanism in the existing technology to cope with sudden impacts, the purpose of this invention is to design a set of dynamic safety limiting and residual current distribution law to break the nonlinear bistable dead zone of the system under large deflection state with transient limit tensile force, so as to prevent rotor falling and destructive collision friction.

[0090] In summary, the ultimate goal of this invention is to completely block the transmission path of alternating force to the stator frame through the organic synergy of the aforementioned underlying sensing, multi-frequency extraction, intelligent calculation, vector cancellation, and safety limiting. This allows the flexible rotor to self-center around its own inertial axis in accordance with the laws of dynamics, achieving zero-current control. Consequently, this significantly reduces system power consumption and heat generation, ensuring the ultimate stability and safety of high-speed electromagnetic rotating machinery in the full speed range and under extreme operating conditions.

[0091] The method provided by this invention completely overturns the traditional control approach that attempts to forcibly suppress rotor disturbances using high-frequency alternating current. It constructs a five-step underlying data closed loop consisting of state reconstruction sensing, differentiated feature stripping, intelligent baseband calculation, vector anti-phase unloading, and dynamic safety limiting. Specifically, combined with... Figure 1 This may include the following steps:

[0092] Step 1: Obtain the reconfiguration displacement of the rotor when the actual electromagnetic bearing rotor system is running;

[0093] An inherent hardware contradiction exists in the physical structure of electromagnetic bearing systems: the displacement sensor probe and the electromagnet's force application point are limited by physical space and cannot be installed at the same absolute coordinate position on the shaft. This means that the rotor displacement "seen" by the sensor is not equal to the displacement at the electromagnet's "actual force application point" in terms of both amplitude and phase. Directly introducing a signal with this type of "spatial observation error" into the closed loop will cause a catastrophic reference deviation for subsequent high-frequency precision compensation. To completely eliminate this physical deviation at its source, this invention introduces a "offline physical training - online data correction" state reconstruction mechanism at the underlying data acquisition end. The specific operation of this mechanism is divided into two stages, as follows... Figure 2 As shown:

[0094] Step 1.1: Construct a rotor dynamics finite element model of the electromagnetic bearing rotor system. Input the excitation signals of various potential operating conditions into the rotor dynamics finite element model for simulation. Obtain the displacement data sequence of the preset sensor position as the input feature set and the displacement data sequence of the preset electromagnet force center position as the target label set. Based on the input feature set and the target label set, use the extreme gradient boosting regression algorithm to train the extreme gradient boosting model and obtain the trained extreme gradient boosting regression model.

[0095] This invention does not rely on expensive pure physics trial and error, but instead establishes a high-fidelity finite element model of the rotor dynamics of the magnetic levitation rotor system. This physical model accurately replicates the rotor's geometry, material properties, and the stiffness / damping characteristics of the electromagnetic bearings. Time-domain simulation and data sampling: In the rotor dynamics finite element model, excitation signals traversing various potential operating conditions (including different speed increases / decreases, unbalance distributions, and transient impact loads) are injected, and high-precision time-domain simulation is performed.

[0096] During the simulation, the system synchronously extracts the displacement data sequence of the "sensor corresponding position" in the finite element mesh as the input feature set. The actual displacement data sequence of the "force center position of the electromagnet" is extracted as the corresponding target label set. Subsequently, based on this massive dataset of multivariate nonlinear correspondences, the Extreme Gradient Boosting (XGBoost) regression algorithm was used to deeply train the Extreme Gradient Boosting model. Through continuous iterative optimization of the loss function, this machine learning model mastered the spatial deformation transmission law of the rotor from the sensor position to the electromagnet position under different vibration states, and was finally solidified into a model with extremely strong generalization ability.

[0097] Step 1.2: When the actual electromagnetic bearing rotor system is running, collect the original observed displacement of the rotor at the preset sensor position;

[0098] Specifically, during the actual operation of the physical system, the raw electrical signals measured by the hardware displacement sensor probe are acquired in real time at an extremely high sampling frequency, and the raw electrical signals are converted into raw observed displacements. (Unit: mm)

[0099] It should be noted that the displacement signal involved in this invention and its derivative signals (such as , All of these include displacement components in the X and Y axes, which are radially orthogonal to each other.

[0100] Step 1.3: Input the original observed displacement of the rotor into the trained extreme gradient boosting regression model to obtain the reconstructed displacement of the rotor. ;

[0101] This machine learning-based state reconstruction and correction mechanism effectively compensates for large-span spatial observation errors caused by non-coordinated sensor installations through high-dimensional spatial mapping at the algorithm level. This overcomes the inherent physical limitations of the underlying hardware spatial layout and reconstructs the true dynamic pose of the rotor at the actual force application point of the electromagnet with high precision. This provides a unique and highly reliable benchmark data source for subsequent core algorithms such as multi-frequency differential feature extraction and vector anti-phase unloading.

[0102] After obtaining the true absolute displacement signal that eliminates spatial observation errors Subsequently, the system faces the task of separating hybrid signals. In actual high-speed rotating machinery, the displacement waveform acquired by the sensor is a composite time-domain signal, which simultaneously includes first-order physical vibrations of the same frequency caused by the rotor's actual mass eccentricity, and second-order and higher-order geometric spurious vibrations induced by micro-machining scratches or out-of-roundness detected by the sensor on the surface. If frequency band differentiation is not performed, the controller will output a high-frequency alternating current to respond to the spurious displacements, causing the power amplifier to overheat severely. Therefore, the system will... The data are fed into a dual-channel processing unit in parallel to perform dimensionality reduction calculations and feature extraction based on the physical characteristics of different excitation sources.

[0103] Step 2: Construct a reduced-order generalized integrator with a dynamic lead-shifting phase matrix, and then process the reconstructed displacement of the rotor to obtain the discrete first-order true vibration characteristic vector of the same frequency.

[0104] Channel 1: Zero-delay extraction of first-order real vibrations at the same frequency based on the reduced-order generalized integrator (PSROGI);

[0105] Combination Figure 3 The system's first data processing channel is dedicated to extracting the rotor's first-order, same-frequency, true vibration component. Traditional full-order generalized integrators have an extremely high computational burden when processing dual-axis (X and Y axis) signals, and inevitably produce a time delay in signal extraction, resulting in a phase lag in the subsequently generated compensation force. To address this, this channel employs a phase-shifted reduced-order generalized integrator (PSROGI) with a dynamic lead-shifting phase matrix.

[0106] In terms of computational optimization, this channel employs a reduced-order generalized integrator. Leveraging the physical properties of the electromagnetic bearing's X and Y axis displacement signals being spatially orthogonal and 90 degrees out of phase in time, it constructs an internal cross-decoupling matrix to synthesize the mutually orthogonal radial X-axis and Y-axis displacement signals into a complex spatial vector that rotates synchronously with the rotor. This constructs a first-order complex coefficient generalized integrator, simplifying the original fourth-order state-space model to second-order, thus reducing computational complexity. This reduction mechanism requires only a single first-order complex coefficient integrator core to simultaneously complete the joint calculation of the dual-axis signals, significantly reducing the microprocessor's computational load.

[0107] At the phase compensation level, to address the physical phase lag caused by the sample-and-hold function and the inductance effect of the power amplifier coil in the digital system, this integrator introduces a dynamic lead-shift mechanism. The system reads the real-time rotational angular frequency of the rotor in real time. (Unit: rad / s) Calculate the system's inherent delay equivalent and dynamically and adaptively generate the lead phase angle. (Unit: rad). The system directly embeds the complex rotation transformation matrix containing this angle into the feedback loop of the integrator. This mechanism, through phase advance intervention, performs advance compensation for the signal phase at the solution level, thus offsetting the hardware delay of subsequent physical execution stages.

[0108] To illustrate the implementation logic of the aforementioned order reduction and phase shifting mechanisms, this channel constructs a generalized integrator with a dynamic lead phase shifting matrix. , is represented as:

[0109] ;

[0110] in, Adjust the gain of the integrator as the base; This is the complex rotation transformation matrix used to compensate for physical phase lag, where s is the complex frequency and j is the imaginary unit. ω is the real-time rotational angular frequency of the rotor;

[0111] The frequency domain control equations generated based on the reduced-order generalized integrator are expressed as follows:

[0112] ;

[0113] in, To reconstruct displacement The corresponding frequency domain signal; This is a first-order, same-frequency true vibration characteristic vector. The zero-delay characteristic of this vector ensures that it is absolutely synchronized with the rotor's true physical eccentric phase, laying a precise reference for subsequent same-frequency vector cancellation.

[0114] The theoretical model of channel one (PSROGI) is an analog transfer function established in the continuous complex frequency domain (s-domain). However, the core control algorithm of the electromagnetic bearing system runs in a microprocessor and can only be executed in the form of digital difference equations at discrete sampling times. Therefore, the bilinear transform method is used to discretize the frequency domain control equations to obtain the corresponding frequency domain control equations. Discrete transfer function of the domain, using The time-shift property of the transformation yields the discrete first-order true vibration characteristic vector with the same frequency. , is represented as:

[0115] ;

[0116] Where n is the current discrete sampling sequence number, representing the current control cycle count of the microprocessor. , and All are discretization coefficients. The reconstructed displacement in the nth discrete sampling sequence; It represents the discrete first-order true vibration feature vector of the same frequency in the (n-1)th discrete sampling sequence;

[0117] Step 3: Optimize the depth and width parameters of the adaptive cascaded notch filter and the control parameters of the model-free adaptive control (MFAC) algorithm, and then process the reconstructed displacement of the rotor to obtain the discrete Nth order high-frequency spurious jump characteristic vector, the master control feedback current and the DC bias current.

[0118] The next core task is for the main control unit to calculate the fundamental drive current that maintains stable rotor levitation. Traditional model-based control methods (such as optimal control or robust control) heavily rely on precise mathematical analytical models of the magnetically levitated rotor. However, under actual ultra-high-speed operating conditions, flexible rotor systems are often accompanied by strong nonlinear electromechanical coupling, complex gyroscopic effects, and unmodeled dynamics that are difficult to measure. Once the actual operating conditions deviate from the theoretical nominal model, the performance of traditional controllers deteriorates sharply. To fundamentally overcome this bottleneck of difficult underlying physical modeling, step 3 introduces a model-free adaptive control (MFAC) algorithm as the main control unit of the system.

[0119] The MFAC operating mechanism completely abandons the reliance on precise mathematical differential equations of the controlled object; its essence is a purely data-driven strategy. In a specific execution cycle, MFAC utilizes the control current command generated by the system in the previous cycle and the actual displacement feedback. The algorithm constructs an I / O data sequence. It introduces the concept of "pseudo-partial derivative (PPD)" to perform local dynamic linearization of the originally highly nonlinear dynamic system at each operating point. Through online adaptive estimation and high-frequency iterative updates of the PPD matrix, the MFAC can accurately sense the real-time evolution of the rotor's dynamic characteristics and thus calculate the main control feedback current used to provide stiffness. and the DC bias current that maintains the system's static levitation .

[0120] However, when integrating the MFAC main controller with the Adaptive Cascaded Notch Filter (ACNF) into a unified closed-loop system, a severe underlying engineering challenge emerges: there is an extremely serious multidimensional parameter strong coupling effect between the core structural parameters of the notch filter (such as the notch depth determining the filtering strength and the bandwidth determining the frequency capture range) and the basic control gain and penalty factor of the MFAC. Independent parameter tuning based on human experience often leads to unintended consequences, easily causing the system to fall into a local optimum nonlinear dead zone, resulting in vibration suppression performance failing to reach global optimum across the entire speed domain. To completely decouple this strongly coupled system, this invention innovatively constructs a two-layer intelligent parameter tuning architecture of "offline global optimization + online dynamic correction," combined with... Figure 4 As shown, the specific steps may include:

[0121] Step 3.1: In the offline stage, multiple particle vectors are set. The particle vectors include the depth and width parameters (including depth and width) of the adaptive cascaded notch filter and the control parameters of the model-free adaptive control (MFAC) algorithm. The improved particle swarm optimization (IPSO) algorithm is used to process all particle vectors to obtain the offline optimal particle vector.

[0122] Unlike conventional algorithms, the improved particle swarm optimization (IPSO) algorithm employs collaborative parameter optimization. The IPSO algorithm uses minimizing the integral absolute error throughout the system's operation as the objective function for evaluating fitness. Here, IPSO specifically introduces an adaptive inertia weight and a dynamic adjustment mechanism for the learning factor, enabling it to possess strong global exploration capabilities in the early stages of the search to escape local optima, while exhibiting high-precision local convergence capabilities in the later stages. Through offline iterative optimization, IPSO outputs a set of optimal "golden benchmark parameter solutions" that achieve dynamic balance between filtering and control across the entire velocity domain, endowing the system with extremely robust ground-state control performance.

[0123] Although IPSO provides an excellent steady-state parameter benchmark, the equivalent damping and stiffness of the rotor undergo drastic time-varying changes when actually accelerating, crossing critical speeds, or encountering sudden transient shocks. To compensate for the lag in dynamic response of offline fixed parameters when facing sudden nonlinear conditions, this architecture further enables an online parameter correction mechanism based on fuzzy logic during the high-speed operation phase (online phase).

[0124] Step 3.2: In the online phase, the instantaneous displacement error and error rate of change of the rotor are obtained. Based on the preset rotor dynamics expert experience fuzzy rule base, instantaneous displacement error, and error rate of change, a fuzzy logic algorithm is used to perform fuzzy inference and defuzzification operations within a microsecond-level control cycle to generate dynamic compensation increments. This high-frequency fine-tuning mechanism enables the underlying control parameters to adaptively and elastically expand and contract with the drastic changes in the transient stress state of the rotor. Based on the dynamic compensation increments and the offline optimal particle vector, an online optimal particle vector is generated. The online optimal particle vector includes the optimal depth and width parameters of the adaptive cascaded notch filter and the optimal control parameters of the MFAC.

[0125] Step 3.3: Configure the adaptive cascaded notch filter based on the optimal depth and width parameters, and reconstruct the displacement according to the configured adaptive cascaded notch filter. After processing, the discrete Nth-order high-frequency spurious pulsation feature vector is obtained. ;

[0126] Channel 2: High-order spurious bounce extraction and topology reconstruction based on cascaded notch filter (ACNF);

[0127] Combination Figure 3 The parallel second data processing channel is specifically responsible for removing high-order spurious noise. This is for specific multi-order high-frequency harmonics (assuming the order to be processed is...). This channel employs an adaptive cascaded notch filter (ACNF) architecture for step-by-step interception. The notch filter calculates the reference tracking angular frequency in real time. It automatically and dynamically locks the center angular frequency of each level to an integer multiple of the reference tracking angular frequency, thereby achieving adaptive tracking of the angular frequency.

[0128] According to the principles of rotor dynamics, the physical phase of the rotor at the instant it crosses the critical speed... It will happen in a very short time. To address sudden changes, this invention sets a reserved value before the critical speed. The difference between the critical speed and the reserved value is defined as the speed threshold. When the rotor speed is less than the speed threshold, the notch filter directly... As a reference signal source, it is fed from the source with disturbance via a phase-locked loop mechanism. The reference tracking angular frequency is calculated in real time. :

[0129] ;

[0130] When the rotor speed is greater than or equal to the critical speed, this abrupt change is simplified to an ideal step function. The total phase at this point can be written as the superposition of the fundamental rotation phase and the abrupt change phase. Substituting this phase into the formula for calculating the reference tracking angular frequency, we get:

[0131] ;

[0132] In the mathematical theory of signals and systems, the derivative of the step function is the Dirac Delta Function. The Dirac impulse function is a limiting concept: its amplitude is infinite at the instant of abrupt change (t=0), and zero at all other times. Therefore, the reference tracking angular frequency becomes:

[0133] ;

[0134] Physically, this means that at the instant of a phase abrupt change, the algorithm mistakenly believes that the rotor speed has reached "infinity." When the reference tracking angular frequency is then substituted into the transfer function, due to the presence of the impulse term, The term tends to infinity at the instant the rotor crosses the critical speed, which causes the poles of the system transfer function to shift drastically in an instant, thus triggering high-frequency chattering in the system.

[0135] To address this issue, this invention employs a reference signal source reconstruction strategy. When the channel detects that the rotor has entered the critical speed transition zone, it actively disconnects the closed-loop feedback tracking circuit for the actual displacement. The system directly extracts the absolute mechanical angle of the shaft measured by an independent photoelectric encoder. An ideal sine wave with constant amplitude and smooth phase is mathematically synthesized within the microprocessor and forcibly set as the angular frequency and phase tracking guide source for the notch filter. This reconstruction operation, by converting the closed-loop feedback channel, which is susceptible to physical abrupt changes, into a feedforward guide channel based on deterministic kinematic signals, fundamentally isolates the algorithm's internal stability from the impact of drastic external physical phase changes. At this point, the system's reference tracking angular frequency is:

[0136] ;

[0137] Because the rotor possesses a huge mechanical inertia J, according to the rotational law... Its angular acceleration Due to strict physical limitations, it is impossible to generate a mathematically meaningful impulse. Therefore, during the period exceeding the critical speed, even... The phase undergoes a step change of approximately π, and the calculated reference tracking angular frequency term still satisfies:

[0138] ;

[0139] At this point, the reference tracking angular frequency is substituted into the transfer function, when... When a 180° flip occurs, the denominator of the transfer function remains constant, and the pole positions of the filter only drift slowly with the smooth rotational speed. This completely shields the impact of physical phase abrupt changes on the internal stability of the algorithm, ensuring that the extracted feature vectors maintain a smooth envelope across the entire speed domain, thus achieving seamless switching when crossing critical speeds. Finally, in an extremely stable state, this channel strips and outputs the set of high-frequency spurious fluctuation feature vectors of each order, achieving precise filtering of high-frequency noise in the main control circuit.

[0140] Based on the above design concept and derivation process, in this step, the present invention first sets a speed threshold, collects the rotor speed in real time, and when the rotor speed is less than the speed threshold, calculates the reference tracking angular frequency based on the reconstructed displacement. Specifically, this is achieved through the following formula:

[0141] ;

[0142] in, To reconstruct displacement The physical phase;

[0143] When the rotor speed is greater than or equal to the speed threshold, obtain the absolute mechanical angle of the shaft. Then calculate the reference tracking angular frequency. Specifically, this is achieved through the following formula:

[0144] ;

[0145] It should be noted that, regarding the first-order in-frequency real vibration extracted from the first channel, although it undergoes phase reversal when crossing the critical speed, this invention does not reconstruct its input reference signal. The technical mechanism lies in the fact that PSROGI internally constructs a complex spatial rotation vector model based on the internal model principle, essentially a very narrow-band resonant cavity with adaptive phase-locked loop characteristics. When a physical phase reversal causes a surge in input error, PSROGI's feedback closed loop can sense this error change in real time and automatically correct the phase using its extremely high resonant gain, thus autonomously achieving precise locking and dynamic tracking of the reversed physical phase without external manual intervention.

[0146] Based on the optimal depth and width parameter configuration of the adaptive cascaded notch filter, the configured adaptive cascaded notch filter is obtained. For each high-frequency harmonic in the multi-order high-frequency harmonics contained in the reconstructed displacement, the angular frequency is tracked based on the reference. The continuous-domain transfer function corresponding to the configured adaptive cascaded notch filter is expressed as:

[0147] ;

[0148] in, For the first The continuous domain transfer function corresponding to the first-order high-frequency harmonics. To reconstruct the frequency domain signal corresponding to the displacement; This is the Nth order high-frequency spurious jump feature vector; For the set higher harmonic orders, k is the highest harmonic order; This refers to the dynamic gain coefficient.

[0149] The theoretical model of Channel 2 (ACNF) is also an analog transfer function established in the continuous complex frequency domain (s-domain). However, the core control algorithm of the electromagnetic bearing system runs in a microprocessor and can only be executed in the form of digital difference equations at discrete sampling times. Therefore, the bilinear transform method is used to discretize the continuous domain transfer function to obtain its corresponding... Discrete transfer function of the domain, using The time-shift property of the transformation yields the discrete Nth-order high-frequency spurious hopping characteristic vector. ;

[0150] ;

[0151] in, , , , , , These are the discretization coefficients. Let n be the reconstructed displacement in the nth discrete sampling sequence. This refers to the discrete Nth-order high-frequency spurious jump feature vector in the (n-1)th discrete sampling sequence;

[0152] Step 3.4: Configure the MFAC algorithm based on the optimal control parameters of MFAC, and reconstruct the displacement according to the configured MFAC algorithm. The process is performed to obtain the main control feedback current. and DC bias current ;

[0153] Through model-free solution of MFAC, global parameter optimization of IPSO, and online parameter compensation using fuzzy logic, the system effectively reduces its dependence on the precise analytical model of the magnetic levitation rotor and achieves dynamic decoupling and coordinated matching of notch filter parameters and main controller gain. The final calculated main control feedback current... With DC bias current It will be smoothly transmitted as a baseband control command to the subsequent step 4, and participate in the antiphase superposition and cancellation operation of multidimensional current vectors.

[0154] Step 4: Calculate the integrated drive current based on the discrete first-order same-frequency true vibration characteristic vector, the discrete Nth-order high-frequency false jumping characteristic vector, the main control feedback current, and the DC bias current;

[0155] This step breaks the core architecture of traditional zero-displacement control schemes, playing a pivotal role in the overall design. In traditional electromagnetic bearing control, once the main controller senses displacement fluctuations caused by mass eccentricity or sensor agitation, it instinctively outputs a high-frequency alternating current to generate a suppressive force. However, this zero-displacement control strategy not only fails to eliminate vibration but also transmits a strong high-frequency alternating excitation force to the stator frame through the electromagnetic actuator. The core task of this step is to actively shield this erroneous alternating response of the main controller through mirror reconstruction and vector superposition of the underlying data stream, such as... Figure 5 As shown.

[0156] (1) Multidimensional data aggregation and physical parameter retrieval;

[0157] Before the system's digital signal enters the digital-to-analog converter (D / A) and is sent to the power amplifier, a multi-dimensional current vector adder node is established at the algorithm's underlying layer. This node synchronously receives real-time data in the following three dimensions:

[0158] The first source is the basic main control feedback current calculated in real time. (Unit: A) and the DC bias current used to maintain the static levitation of the system. (Unit: A). Since MFAC receives the full signal including fluctuations, at this time... It inevitably contains alternating components that attempt to counteract the disturbance.

[0159] The second path consists of a first-order, same-frequency, real unbalanced displacement feature vector precisely extracted from the first channel, possessing zero-delay characteristics. (Unit: mm)

[0160] The third path consists of a set of high-frequency spurious jump displacement feature vectors extracted step by step from the second channel. (Unit: mm, where N = 2, 3, ... k).

[0161] (2) Equivalent space mapping and vector inversion reconstruction;

[0162] To achieve precise cancellation of displacement disturbances to control current, the algorithm must map the spatial displacement vector to an equivalent current vector. Based on the linearized electromagnetic force physical equations of electromagnetic bearings:

[0163] ;

[0164] In this invention, two inherent physical prior parameters are invoked: displacement-stiffness coefficient. (Characterizing the change in magnetic pull caused by rotor deviating from the center, unit: N / m) and current-attraction coefficient (Characterizing the change in attractive force caused by the change in coil current, unit: N / A). I ​​represents current, X represents displacement from the electromagnet, and F represents electromagnetic force.

[0165] Based on this, define the equivalent transformation gain matrix. , is represented as:

[0166] ;

[0167] in, This is the rotor's displacement-stiffness coefficient. The current-suction coefficient;

[0168] This gain (unit: A / m) represents the equivalent current amplitude required to offset a unit displacement disturbance. The system uses this gain to directly project the input displacement characteristics across each frequency band into an equivalent feedforward compensation current reference. Subsequently, the algorithm logic performs a strict mirror inversion operation (i.e., multiply by -1) on these references, thereby artificially generating an "anti-phase compensation current vector" that is absolutely equal in magnitude to the potential alternating response of the main controller but strictly 180 degrees out of phase.

[0169] (3) Vector cancellation composition equations and their execution utility;

[0170] Based on the equivalent transformation gain matrix Discrete first-order true vibration characteristic vector with the same frequency Discrete Nth order high-frequency spurious pulsation feature vector Main control feedback current and DC bias current Calculate the overall drive current Specifically, this is achieved through the following formula:

[0171] ;

[0172] Based on the aforementioned synthetic control equations, the system implements destructive intervention of multidimensional current vectors at the bottom-level data nodes: the main control current... The high-frequency alternating component contained within, which is in the same frequency as the disturbance, precisely cancels out the anti-phase compensation current generated by the feedforward channel in both amplitude and phase. The resulting integrated drive current... The alternating components at specific angular frequencies are filtered out, and the current is converted into a steady current containing only DC bias to maintain static levitation and suppress low-frequency drift.

[0173] When this smoothing command is applied to the power amplifier, the electromagnetic actuator actively stops outputting alternating electromagnetic force at the same frequency as the rotational speed, thereby releasing the rigid electromagnetic constraint on the rotor's geometric center. With this high-frequency electromagnetic constraint removed, the high-speed rotating flexible rotor, following its rotor dynamics, autonomously transitions from rotating around its geometric center to rotating around its own inertial axis, achieving zero-current control for self-centering operation. This underlying vector cancellation mechanism cuts off the transmission path of the rotor's unbalanced centrifugal force to the stator frame at its source, effectively suppressing abnormal heating of the power amplifier and high-frequency resonance of the frame caused by the high-frequency over-response of the control system.

[0174] Step 5: Calculate the rotor eccentricity based on the rotor's reconstructed displacement, then determine the safe drive current in conjunction with the comprehensive drive current, and transmit the safe drive current to the power amplifier to suppress the multi-frequency vibration of the electromagnetic bearing, prevent collisions, and ensure rotor safety.

[0175] After the vector cancellation operation in step 4, the system generates a stable overall drive current command. This gives the rotor the ability to rotate self-centeringly without sensor input. However, the physical essence of zero-current control is "weakened constraints." When the rotor encounters extreme transient mechanical shocks or extremely severe mass eccentricity, this smooth command is insufficient to provide sufficient transient restoring force. If the rotor's large offset approaches the physical air gap boundary of the backup protective bearing, the system will enter an extremely complex non-smooth dynamic region, which can easily lead to continuous collisions and severe friction between the rotor and the protective bearing. The purpose of step 5 is to serve as the final command review and energy scheduling node before the power amplifier executes the command. It aims to forcibly break the system's instability dead zone under large deflection conditions by nonlinearly releasing transient current before the rotor falls into the high-amplitude danger zone.

[0176] In traditional electromagnetic bearing control strategies, a hard-limiting strategy of "fixed residual current" is typically used to protect the power amplifier and coil from overload burnout, strictly limiting the upper limit of the main control current output. However, nonlinear dynamic analysis of the entire rotor shows that under extreme conditions of dry friction or perfectly elastic contact, the fixed residual current strategy causes the rotor to fall into a dangerous "bistable" region. Within this region, the rotor experiences severe jumping phenomena, generating high-frequency, high-energy continuous physical collisions with the magnetic poles. The limited pulling force output by the electromagnet is simply insufficient to overcome the enormous collision kinetic energy, ultimately leading to system overheating or even complete failure. This step completely abandons this fixed-limiting mechanism and instead introduces an "adjustable residual current strategy," combined with... Figure 6 Specifically, it includes the following steps:

[0177] Step 5.1: Obtain the physical clearance of the protective bearing, calculate the ratio of the reconstructed displacement to the physical clearance of the protective bearing, and obtain the eccentricity m ( );

[0178] Step 5.2: When the eccentricity is less than the preset threshold, the system is in the linear controllable region, and the comprehensive drive current is directly transmitted to the power amplifier as a safe drive current to suppress the multi-frequency vibration of the electromagnetic bearing; when the eccentricity is greater than or equal to the preset threshold, it means that the rotor is about to make mechanical contact, and step 5.3 is executed.

[0179] Step 5.3: Calculate the instantaneous motion phase angle Specifically, this is achieved through the following formula:

[0180] ;

[0181] in, and They are respectively Displacement components along the Y and X axes;

[0182] Based on the instantaneous motion phase angle The target coil that provides the reverse restoring force is determined, specifically based on the instantaneous phase angle. Determine the specific direction of the rotor's current deviation and locate the target anti-gravity side (or the side opposite to the impact) electromagnetic coil responsible for providing the reverse restoring force. For example, if the rotor's deviation direction is determined to be downward based on the instantaneous motion phase angle, then the target coil is the electromagnetic coil above.

[0183] Calculate the physical limiting current and DC bias current of the power amplifier. The difference is used to obtain the residual current capacity of the target coil. ;

[0184] Calculate the nonlinear gain function Specifically, this is achieved through the following formula:

[0185] ;

[0186] in, This is the steepness coefficient, which controls the "steepness" of the transition interval. The remaining current capacity is then added in full and instantaneously to the control command of the target coil to generate the final safe drive current. Specifically, this is based on the comprehensive drive current. Nonlinear gain function and residual current capacity Calculate the safe drive current of the target coil. Specifically, it is calculated using the following formula:

[0187] ;

[0188] Safety drive current The signal is transmitted to a power amplifier to suppress multi-frequency vibrations of the electromagnetic bearing.

[0189] Under the adjustable residual current strategy, the target electromagnetic coil generates a transient electromagnetic pull approaching the system's physical limits in the microseconds as the rotor approaches the boundary. This massive and highly concentrated nonlinear pull does work far exceeding the kinetic energy escaped by the rotor. From the dynamic phase diagram trajectory, this mechanism effectively suppresses the system's steady-state amplitude response and forcibly disrupts the energy balance conditions required to maintain a high-amplitude bistable state. Because the bistable region is instantaneously broken down, the rotor cannot generate continuous bouncing and friction at the boundary, but is forced back to the linear safe suspension domain at the system center by this ultimate pull. Through this mechanism of "nonlinear large eccentric triggering and transient ultimate pull recovery," the system effectively reduces the frequency of collision events under extremely harsh operating conditions, strictly limiting mechanical friction to an extremely short instant, thereby ensuring the absolute operational safety of the high-speed rotor throughout its entire life cycle.

[0190] In summary, the electromagnetic bearing vibration control method proposed in this invention, based on multi-frequency differential feature extraction and vector anti-phase unloading, completely breaks through the rigid control limitations of traditional magnetic levitation systems with zero displacement control, and constructs a full-chain, highly collaborative flexible control closed loop. This technical solution uses high-precision spatial reconstruction from machine learning as a reliable perception benchmark, achieves precise isolation of complex multi-frequency excitation sources through underlying topology reconstruction and parallel dual-channel technology, and relies on pure data-driven model-free adaptive control and a dual-layer intelligent parameter tuning architecture to establish solid and decoupled baseband control performance. On this basis, the core multi-dimensional vector anti-phase unloading mechanism actively releases the high-frequency alternating electromagnetic constraints to cope with disturbances at the physical execution end, enabling the flexible rotor to achieve zero-current control for self-centering operation in accordance with dynamic laws; while the nonlinear dynamic limiting mechanism based on adjustable residual current instantly triggers the ultimate tension when the rotor approaches the physical boundary, establishing a safety net against drops for the system.

[0191] The five core steps of this invention are interconnected and mutually supportive in the underlying data flow: forward precision sensing and feature cleaning ensure the stability of the control baseband, while steady-state zero-current control and transient extreme collision avoidance together constitute an extremely comprehensive physical execution strategy. This solution fundamentally eliminates spatial observation bias, solves the problem of strong coupling of multi-dimensional parameters, eradicates high-frequency alternating resonance heating, and effectively avoids nonlinear collision instability under extreme conditions, comprehensively improving the operational robustness and absolute safety of high-speed rotating machinery in the full speed range and under complex impact conditions.

[0192] In summary, the key points of this invention are:

[0193] 1. Spatial displacement state reconstruction driven by physical-data fusion

[0194] The misalignment of the displacement sensor and the electromagnet's force application point introduces observation bias. This technology deploys a pre-trained regression model at the sensing layer, completes offline feature modeling using a full rotor dynamics finite element model, and maps sensor observations to the actual displacement of the force application point online. This method eliminates control reference distortion caused by hardware installation from the ground up, ensuring spatial consistency between the control reference and the physical point of application.

[0195] 2. Parallel Multi-Frequency Feature Stripping and Topology Reconstruction Based on PSROGI and ACNF

[0196] This technology abandons the series filtering architecture and adopts a parallel processing structure of a reduced-order generalized integrator (PSROGI) and an adaptive cascaded notch filter (ACNF). PSROGI achieves zero-delay extraction of same-frequency vibrations through reduced-order operations and dynamic phase shifting, avoiding the phase lag problem of traditional filters. Addressing the defect of ACNF in inducing system chattering due to phase abrupt changes when the rotor crosses critical speeds, the system cuts off the actual displacement error feedback loop through topology reconstruction, instead using an ideal sine wave synthesized from an external speed signal as the guiding source. This completely isolates the interference of phase abrupt changes on algorithm stability and ensures the reliability of feature extraction across the entire speed domain.

[0197] 3. Model-free adaptive control and two-layer collaborative optimization architecture

[0198] The main control baseband calculation stage employs a data-driven model-free adaptive control (MFAC) algorithm, eliminating reliance on a precise mathematical model of the electromagnetic bearing. Addressing the strong coupling between MFAC and cascaded notch filter parameters, a two-layer parameter tuning architecture is established: "offline global optimization (improved particle swarm optimization algorithm) + online dynamic correction (fuzzy logic)." High-dimensional joint solving achieves deep decoupling between multi-order filters and control parameters, ensuring optimal phase margin and vibration suppression performance across the entire operating range.

[0199] 4. Zero-current control strategy based on vector anti-phase cancellation

[0200] This technology breaks through the traditional zero-displacement control approach and proposes a vector anti-phase superposition force relief scheme. Based on the equivalent mapping relationship between displacement-stiffness coefficient and current-suction coefficient, the extracted multi-frequency displacement features are converted into anti-phase compensation current, and vector cancellation is completed at the final current command synthesis node. This strategy actively shields the alternating pull output of the electromagnetic actuator, allowing the rotor to rotate around its own inertial axis without being subjected to alternating excitation force, thus eliminating the high-frequency heating problem of the power amplifier and the stator frame resonance problem at the root.

[0201] 5. Adjustable residual current protection mechanism to suppress nonlinear bistable rubbing

[0202] To address the bistable rubbing instability problem under conditions of large eccentricity or transient impact, this technology proposes an adjustable residual current distribution strategy based on eccentricity triggering. Unlike traditional fixed-limiting methods, this mechanism instantaneously releases the power amplifier's ultimate current capacity through a nonlinear gain function, generating an ultra-large transient restoring force to forcibly disrupt the energy balance of high-amplitude oscillations. This pulls the rotor from the nonlinear collision region back to the linear safe suspension region, significantly enhancing the system's survivability under extreme conditions.

[0203] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A method for suppressing multi-frequency vibration in an electromagnetic bearing rotor system, characterized in that, include: Step 1: Obtain the reconfiguration displacement of the rotor when the actual electromagnetic bearing rotor system is running; Step 2: Construct a reduced-order generalized integrator with a dynamic lead-shifting phase matrix, and then process the reconstructed displacement of the rotor to obtain the discrete first-order true vibration characteristic vector of the same frequency. Step 3: Optimize the depth and width parameters of the adaptive cascaded notch filter and the control parameters of the model-free adaptive control (MFAC) algorithm, and then process the reconstructed displacement of the rotor to obtain the discrete Nth order high-frequency spurious jump characteristic vector, the master control feedback current and the DC bias current. Step 4: Calculate the integrated drive current based on the discrete first-order same-frequency true vibration characteristic vector, the discrete Nth-order high-frequency false jumping characteristic vector, the main control feedback current, and the DC bias current; Step 5: Calculate the rotor eccentricity based on the rotor's reconfigured displacement, then determine the safe drive current in conjunction with the comprehensive drive current, and transmit the safe drive current to the power amplifier to suppress the multi-frequency vibration of the electromagnetic bearing.

2. The method for suppressing multi-frequency vibration of an electromagnetic bearing rotor system according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Construct a rotor dynamics finite element model of the electromagnetic bearing rotor system. Input the excitation signals of various potential operating conditions into the rotor dynamics finite element model for simulation. Obtain the displacement data sequence of the preset sensor position as the input feature set and the displacement data sequence of the preset electromagnet force center position as the target label set. Based on the input feature set and the target label set, use the extreme gradient boosting regression algorithm to train the extreme gradient boosting model and obtain the trained extreme gradient boosting regression model. Step 1.2: When the actual electromagnetic bearing rotor system is running, collect the original observed displacement of the rotor at the preset sensor position; Step 1.3: Input the original observed displacement of the rotor into the trained extreme gradient boosting regression model to obtain the reconstructed displacement of the rotor. .

3. The method for suppressing multi-frequency vibration of an electromagnetic bearing rotor system according to claim 1, characterized in that, Step 2 specifically includes: Constructing a reduced-order generalized integrator with a dynamic lead-shift phase matrix , is represented as: ； in, Adjust the gain of the integrator as the base; This is the complex rotation transformation matrix used to compensate for physical phase lag, where s is the complex frequency and j is the imaginary unit. ω is the real-time rotational angular frequency of the rotor; The frequency domain control equations generated based on the reduced-order generalized integrator are expressed as follows: ； in, To reconstruct displacement The corresponding frequency domain signal, It is the first-order characteristic vector of the real vibration at the same frequency; The frequency domain control equations are discretized using the bilinear transform method to obtain the corresponding frequency domain control equations. Discrete transfer function of the domain, using The time-shift property of the transformation yields the discrete first-order true vibration characteristic vector with the same frequency. , is represented as: ； Where n is the current discrete sampling sequence number, , and All are discretization coefficients. The reconstructed displacement in the nth discrete sampling sequence; It is the discrete first-order same-frequency true vibration feature vector in the (n-1)th discrete sampling sequence.

4. The method for suppressing multi-frequency vibration of an electromagnetic bearing rotor system according to claim 1, characterized in that, Step 3 specifically includes: Step 3.1: In the offline stage, multiple particle vectors are set. The particle vectors include the depth and width parameters of the adaptive cascaded notch filter and the control parameters of the model-free adaptive control (MFAC) algorithm. An improved particle swarm optimization algorithm is used to process all particle vectors to obtain the offline optimal particle vector. Step 3.2: In the online phase, obtain the instantaneous displacement error and error change rate of the rotor; based on the preset rotor dynamics expert experience fuzzy rule base, instantaneous displacement error and error change rate, use fuzzy logic algorithm to perform fuzzy reasoning and defuzzification operation to generate dynamic compensation increment; based on the dynamic compensation increment and offline optimal particle vector, generate online optimal particle vector. Step 3.3: Configure the adaptive cascaded notch filter based on the optimal depth and width parameters, and reconstruct the displacement according to the configured adaptive cascaded notch filter. After processing, the discrete Nth-order high-frequency spurious pulsation feature vector is obtained. ; Step 3.4: Configure the MFAC algorithm based on the optimal control parameters of MFAC, and reconstruct the displacement according to the configured MFAC algorithm. The process is performed to obtain the main control feedback current. and DC bias current .

5. The method for suppressing multi-frequency vibration of an electromagnetic bearing rotor system according to claim 4, characterized in that, Step 3.3 specifically includes: Set a speed threshold, collect the rotor speed in real time, and when the rotor speed is less than the speed threshold, calculate the reference tracking angular frequency based on the reconstructed displacement. Specifically, this is achieved through the following formula: ； in, To reconstruct displacement The physical phase; When the rotor speed is greater than or equal to the speed threshold, obtain the absolute mechanical angle of the shaft. Then calculate the reference tracking angular frequency. Specifically, this is achieved through the following formula: ； Based on the optimal depth and width parameter configuration of the adaptive cascaded notch filter, the configured adaptive cascaded notch filter is obtained. For each high-frequency harmonic in the multi-order high-frequency harmonics contained in the reconstructed displacement, the angular frequency is tracked based on the reference. The continuous-domain transfer function corresponding to the configured adaptive cascaded notch filter is expressed as: ； in, For the first The continuous domain transfer function corresponding to the first-order high-frequency harmonics. To reconstruct the frequency domain signal corresponding to the displacement; This is the Nth order high-frequency spurious jump feature vector; For the set higher harmonic orders, k is the highest harmonic order; This refers to the dynamic gain coefficient. The continuous domain transfer function is discretized using the bilinear transform method to obtain its corresponding... Discrete transfer function of the domain, using The time-shift property of the transformation yields the discrete Nth-order high-frequency spurious hopping characteristic vector. ; ； in, , , , , , These are the discretization coefficients. Let n be the reconstructed displacement in the nth discrete sampling sequence. It is the discrete Nth-order high-frequency spurious jump feature vector in the (n-1)th discrete sampling sequence.

6. The method for suppressing multi-frequency vibration of an electromagnetic bearing rotor system according to claim 1, characterized in that, Step 4 specifically includes: Define the equivalent transformation gain matrix , is represented as: ； in, This is the rotor's displacement-stiffness coefficient. The current-suction coefficient; Based on the equivalent transformation gain matrix Discrete first-order true vibration characteristic vector with the same frequency Discrete Nth order high-frequency spurious pulsation feature vector Main control feedback current and DC bias current Calculate the overall drive current Specifically, this is achieved through the following formula: 。 7. The method for suppressing multi-frequency vibration of an electromagnetic bearing rotor system according to claim 1, characterized in that, Step 5 specifically includes: Step 5.1: Obtain the physical clearance of the protective bearing, calculate the ratio of the reconstructed displacement to the physical clearance of the protective bearing, and obtain the eccentricity; Step 5.2: When the eccentricity is less than the preset threshold, the comprehensive drive current is transmitted to the power amplifier as a safe drive current to suppress the multi-frequency vibration of the electromagnetic bearing; when the eccentricity is greater than or equal to the preset threshold, proceed to step 5.

3. Step 5.3: Calculate the instantaneous motion phase angle Specifically, this is achieved through the following formula: ； in, and They are respectively Displacement components along the Y and X axes; Based on the instantaneous motion phase angle Identify the target coil that provides the reverse restoring force, and calculate the physical limiting current and DC bias current of the power amplifier. The difference is used to obtain the residual current capacity of the target coil. ; Calculate the nonlinear gain function Specifically, this is achieved through the following formula: ； in, This is the steepness coefficient. This is the trigger threshold; Based on the comprehensive drive current Nonlinear gain function and residual current capacity Calculate the safe drive current of the target coil. Specifically, it is calculated using the following formula: ； Safety drive current The signal is transmitted to a power amplifier to suppress multi-frequency vibrations of the electromagnetic bearing.

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