A time-delay feedback control method for a magnetic suspension bearing rotor system with time delay
Patent Information
- Application Number
- CN202611126244.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-28
- Publication Date
- 2026-10-23
AI Technical Summary
该策略的核心思路是通过设计特定补偿环节，以抵消或削弱时滞对系统的不利影响，但在系统对稳定性、控制精度要求更高的场景下，传统补偿策略不仅难以完全消除时滞干扰，复杂的补偿结构还可能增加系统设计难度与不确定性
（1）本发明提供的一种含时滞的磁悬浮轴承转子系统时滞反馈控制方法，通过信号发生器扫频激励获得控制电压输入至位移传感器输出之间的频响函数，并据此辨识磁悬浮轴承转子系统的二阶含时滞数学模型，使控制律设计建立在被控对象的实测动态特性基础上；与额外配置测试激励装置的方式相比，可利用磁悬浮轴承自身作为激励源，降低系统辨识成本。
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Figure CN122962952A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of magnetic levitation bearing rotor system control technology, and specifically to a time-delay feedback control method for a magnetic levitation bearing rotor system with time delay. Background Technology
[0002] As the application fields of magnetic levitation bearings continue to expand, applications requiring long-term operation in harsh environments have emerged, such as magnetic levitation subsea compressors, offshore wind turbines, and magnetic levitation pipeline compressors for long-distance natural gas pipelines. In these applications, to improve system reliability and environmental adaptability, the controller typically needs to be separated from the magnetic levitation bearing body and placed in a safer location, thus forming a distributed control structure. However, this distributed structure inevitably introduces signal transmission time delay, which becomes more prominent, especially in long-distance communication and network transmission conditions. In typical electromechanical coupling systems such as magnetic levitation bearing rotor systems, due to the generally high sampling frequency of the control system, even a small time delay can significantly affect the closed-loop stability, control accuracy, and dynamic response performance of the system. Currently, time delay compensation control strategies are commonly used both domestically and internationally to address the time delay problem in magnetic levitation bearing rotor systems. The core idea of this strategy is to design specific compensation elements to offset or weaken the adverse effects of time delay on the system. However, in scenarios where the system has higher requirements for stability and control accuracy, traditional compensation strategies not only struggle to completely eliminate time delay interference, but the complex compensation structure may also increase the difficulty and uncertainty of system design.
[0003] In view of this, this invention abandons the traditional approach of "counteracting time delay" and instead actively accepts the objectively existing time delay in the system, treating it as an important component of the feedback loop. By constructing a novel time-delay feedback control mechanism, this invention can achieve stable operation of the magnetic levitation bearing rotor system, providing an innovative technical path for solving the time-delay control problem of such systems. Summary of the Invention
[0004] The technical problem to be solved by this invention is to address the deficiencies of the prior art by proposing a time-delay feedback control method for a magnetic levitation bearing rotor system with time delay. This method utilizes a signal generator to sweep frequency excitation, constructs a second-order mathematical model of the magnetic levitation bearing rotor system with time delay, designs feedforward control and time-delay feedback control laws, clarifies the necessary and sufficient conditions for the critical stability of the system, and defines the range of control parameter values, thereby achieving stable operation of the magnetic levitation bearing rotor system and effectively solving the current technical problems. To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A time-delay feedback control method for a magnetic levitation bearing rotor system with time delay includes the following steps: Step S1: Use a signal generator to generate a sweep frequency signal to excite the magnetic levitation bearing rotor system. By identifying the parameters of the frequency response function between the control voltage input and the displacement sensor output, a second-order mathematical model with time delay of the magnetic levitation bearing rotor system is obtained. G p ( s ); Step S2: Based on the second-order mathematical model with time delay of the magnetic levitation bearing rotor system G p ( s By introducing the error signal between the actual output of the system and the reference input, and by designing a feedforward control loop to adjust the system balance point, the control objective is transformed from tracking the reference input to an error state adjustment problem that makes the error signal tend to zero. Step S3: Based on the identified second-order mathematical model of the magnetic levitation bearing rotor system with time delay G p ( s Considering the input time delay of the system, design a time-delay feedback control law; Step S4: Introduce the time-delay feedback control law, derive the characteristic equation of the closed-loop system, clarify the necessary and sufficient conditions for the critical stability of the system, and quantify the critical stability boundary in the control parameter domain based on the necessary and sufficient conditions for the critical stability of the system. Step S5: Perform implicit differentiation on the characteristic equation of the closed-loop system, and derive the partial differential expression of the real part of the characteristic root with respect to the control parameter by solving the problem; combine the system stability criterion that the real part of the characteristic root is less than zero, and further define the range of control parameter values that meet the asymptotic stability requirements of the system; select control parameters according to the range of control parameter values that meet the asymptotic stability requirements of the system, and apply the selected control parameters to the magnetic levitation bearing rotor system to make the rotor stably levitate.
[0005] Furthermore, the magnetic levitation bearing rotor system includes a controller, a power amplifier, a magnetic levitation bearing, a rotor, a displacement sensor, a frequency converter, and a motor; the displacement sensor detects the rotor displacement signal and inputs it into the controller, and the control voltage signal output by the controller is sent to the power amplifier, which converts it into a control current signal to drive the magnetic levitation bearing to work, thereby completing the control of the rotor.
[0006] Furthermore, in step S1, a sinusoidal control voltage signal with constant amplitude and increasing frequency is generated by a signal generator to perform frequency sweep excitation on the magnetic levitation bearing rotor system. The frequency response function between the control voltage input and the displacement sensor output is expressed as: in, G p ( s() represents a second-order mathematical model with time delay for a magnetic levitation bearing rotor system. b = k a k i k s / m For system gain, k xx =k x / m The stiffness per unit mass displacement is given by , where k a and k s These are the power amplifier gain and the displacement sensor gain, respectively. k i and k x These are current stiffness and displacement stiffness, respectively. m For rotor equivalent mass, τ Input time delay to the system; The second-order mathematical model with time delay can be expressed in state-space as follows: in, For displacement sensor output, u For control voltage input; They are respectively The first derivative.
[0007] Furthermore, in step S2, a reference input is set. r With displacement sensor output x The error signal between 1 and 1 is e 1. A feedforward term is constructed based on the error signal; the feedforward term is used to compensate for the influence of the reference input on the system equilibrium point, so that the subsequent time-delay feedback control law is adjusted according to the error state: in, r For reference input, e 1= r - x 1, For feedforward terms; They represent The first derivative of; where, e 2 represents the error. e The first derivative of 1; the feedforward term and the error state together constitute the adjustment amount of the feedforward control loop to the system equilibrium point; make e 1= z ,in z For reference inputr With displacement sensor output x The error state variable constructed from the difference of 1 is expressed by the differential equation of the closed-loop system as follows: in, for The second derivative of .
[0008] Furthermore, in step S3, the system control voltage input is selected as: in, For error feedback gain, The gain is the hysteresis error feedback term; the introduction of the error feedback term and the hysteresis error feedback term constitutes the design of the time-delay feedback control law; substituting the control voltage input expression of the closed-loop system into the differential equation of the system, the updated differential equation expression of the closed-loop system is obtained: Perform variable substitution, let , , The variable substitution is used to normalize the system gain, unit mass displacement stiffness, error feedback gain, and hysteresis error feedback gain to a unified closed-loop characteristic parameter, and to analyze the stability boundary within the control parameter domain; then the differential equation of the closed-loop system is expressed as: .
[0009] Furthermore, in step S4, after introducing the time-delay feedback control law, the characteristic equation of the closed-loop system is: in, , Let be the system angular frequency; when When the system is in a critically stable state, that is, the characteristic roots lie on the imaginary axis and their real parts are equal to zero, this is the necessary and sufficient condition for the system to be critically stable. Substituting into... The characteristic equation is expressed as: According to Euler's formula, and by separating the real and imaginary parts of the characteristic equation, we obtain the system of equations: Substitution The characteristic equation and the results of separating its real and imaginary parts together characterize the necessary and sufficient conditions for the critical stability of the system; the solution of the equation system in the control parameter domain The middle part is a set of curves: .
[0010] Furthermore, in step S5, the implicit differentiation processing of the characteristic equation of the closed-loop system includes: processing the characteristic roots... s Considered and implicit functions, i.e. The characteristic equation is paired with Implicit Differentiation: On the curve of the solution to the system of equations: make , express s The real part of the system, at this time the eigenvalues of the system are along the real part of the system. The direction of increase crosses negatively from the imaginary axis to the left half-plane of the imaginary axis, defining the parameter region that stabilizes the system: Control parameters are selected based on the parameter range that stabilizes the system, and the selected control parameters are applied to the magnetic levitation bearing rotor system to make the rotor levitate stably.
[0011] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects: (1) The present invention provides a time-delay feedback control method for a magnetic levitation bearing rotor system with time delay. The frequency response function between the control voltage input and the displacement sensor output is obtained by frequency sweep excitation through a signal generator, and the second-order mathematical model with time delay of the magnetic levitation bearing rotor system is identified accordingly, so that the control law design is based on the measured dynamic characteristics of the controlled object. Compared with the method of additionally configuring test excitation device, the magnetic levitation bearing itself can be used as the excitation source, reducing the system identification cost.
[0012] (2) The present invention provides a time-delay feedback control method for a magnetic levitation bearing rotor system with time delay. The system balance point is adjusted by the feedforward control loop, and the time-delay feedback control law is designed with error signal and lag error signal, so that the control target is transformed from directly tracking the reference input to error state adjustment. This reduces the number of control parameters to be tuned and facilitates the rapid determination of feasible parameter combinations in engineering debugging.
[0013] (3) The present invention provides a time-delay feedback control method for a magnetic levitation bearing rotor system with time delay. The critical stability boundary is derived based on the characteristic equation of the closed-loop system, and the asymptotic stability parameter region is defined by combining the stability criterion that the real part of the characteristic root is less than zero. Then, the control parameters are selected from this region and applied to the magnetic levitation bearing rotor system. Compared with the traditional time delay compensation method that attempts to offset the time delay, the present invention utilizes the objectively existing time delay as a component of the feedback loop, which can improve the feasibility of stable rotor suspension under time delay conditions. Attached Figure Description
[0014] Figure 1 The flowchart shows a time-delay feedback control method for a magnetic levitation bearing rotor system with time delay according to the present invention. Figure 2 This is a general framework diagram of the magnetic levitation bearing rotor system of the present invention; Figure 3 This is a diagram showing the stable region of the control parameters of the present invention; Figure 4 This is a block diagram illustrating the time-delay identification frequency sweep test principle of the present invention; Figure 5 These are the time-domain simulation results of this invention; Figure 6 This is a comparison chart of rotor displacement amplitude between the present invention and the traditional DDADRC control method. Detailed Implementation
[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0016] A time-delay feedback control method for a magnetic levitation bearing rotor system with time delay, such as... Figure 1 As shown, it includes the following steps: Step S1: Use a signal generator to generate a sweep frequency signal to excite the magnetic levitation bearing rotor system. By identifying the parameters of the frequency response function between the control voltage input and the displacement sensor output, a second-order mathematical model with time delay of the magnetic levitation bearing rotor system is obtained. G p ( s ); Step S2: Based on the second-order mathematical model with time delay of the magnetic levitation bearing rotor system G p ( s By introducing the error signal between the actual output of the system and the reference input, and by designing a feedforward control loop to adjust the system balance point, the control objective is transformed from tracking the reference input to an error state adjustment problem that makes the error signal tend to zero. Step S3: Based on the identified second-order mathematical model of the magnetic levitation bearing rotor system with time delay G p ( s Considering the input time delay of the system, design a time-delay feedback control law; Step S4: Introduce the time-delay feedback control law, derive the characteristic equation of the closed-loop system, clarify the necessary and sufficient conditions for the critical stability of the system, and quantify the critical stability boundary in the control parameter domain based on the necessary and sufficient conditions for the critical stability of the system. Step S5: Perform implicit differentiation on the characteristic equation of the closed-loop system, and derive the partial differential expression of the real part of the characteristic root with respect to the control parameter by solving the problem; combine the system stability criterion that the real part of the characteristic root is less than zero, and further define the range of control parameter values that meet the asymptotic stability requirements of the system; select control parameters according to the range of control parameter values that meet the asymptotic stability requirements of the system, and apply the selected control parameters to the magnetic levitation bearing rotor system to make the rotor stably levitate.
[0017] Furthermore, such as Figure 2 As shown, the magnetic levitation bearing rotor system includes a controller, a power amplifier, a magnetic levitation bearing, a rotor, a displacement sensor, a frequency converter, and a motor. The displacement sensor detects the rotor displacement signal and inputs it into the controller. The control voltage signal output by the controller is sent to the power amplifier and converted into a control current signal to drive the magnetic levitation bearing to work, thereby completing the control of the rotor.
[0018] Furthermore, in step S1, a sinusoidal control voltage signal with constant amplitude and increasing frequency is generated by a signal generator to perform frequency sweep excitation on the magnetic levitation bearing rotor system. The frequency response function between the control voltage input and the displacement sensor output is expressed as: in, G p ( s () represents a second-order mathematical model with time delay for a magnetic levitation bearing rotor system. b = k a k i k s / m For system gain, k xx =k x / m The stiffness per unit mass displacement is given by , where k a and k s These are the power amplifier gain and the displacement sensor gain, respectively. k i and k x These are current stiffness and displacement stiffness, respectively. m For rotor equivalent mass, τ Input time delay to the system; The second-order mathematical model with time delay can be expressed in state-space as follows: in, For displacement sensor output, u For control voltage input; They are respectively The first derivative.
[0019] Furthermore, in step S2, a reference input is set. r With displacement sensor output x The error signal between 1 and 1 is e 1. A feedforward term is constructed based on the error signal; the feedforward term is used to compensate for the influence of the reference input on the system equilibrium point, so that the subsequent time-delay feedback control law is adjusted according to the error state: in, r For reference input, e 1= r - x 1, For feedforward terms; They represent The first derivative of; where, e 2 represents the error. e The first derivative of 1; the feedforward term and the error state together constitute the adjustment amount of the feedforward control loop to the system equilibrium point; make e 1= z ,in z For reference input r With displacement sensor output x The error state variable constructed from the difference of 1 is expressed by the differential equation of the closed-loop system as follows: in, for The second derivative of .
[0020] Furthermore, in step S3, the system control voltage input is selected as: in, For error feedback gain, The gain is the hysteresis error feedback term; the introduction of the error feedback term and the hysteresis error feedback term constitutes the design of the time-delay feedback control law; substituting the control voltage input expression of the closed-loop system into the differential equation of the system, the updated differential equation expression of the closed-loop system is obtained: Perform variable substitution, let , , The variable substitution is used to normalize the system gain, unit mass displacement stiffness, error feedback gain, and hysteresis error feedback gain to a unified closed-loop characteristic parameter, and to analyze the stability boundary within the control parameter domain; then the differential equation of the closed-loop system is expressed as: .
[0021] Furthermore, in step S4, after introducing the time-delay feedback control law, the characteristic equation of the closed-loop system is: in, , Let be the system angular frequency; when When the system is in a critically stable state, that is, the characteristic roots lie on the imaginary axis and their real parts are equal to zero, this is the necessary and sufficient condition for the system to be critically stable. Substituting into... The characteristic equation is expressed as: According to Euler's formula, and by separating the real and imaginary parts of the characteristic equation, we obtain the system of equations: Substitution The characteristic equation and the results of separating its real and imaginary parts together characterize the necessary and sufficient conditions for the critical stability of the system; the solution of the equation system in the control parameter domain The middle part is a set of curves: .
[0022] Furthermore, in step S5, the implicit differentiation processing of the characteristic equation of the closed-loop system includes: processing the characteristic roots... s Considered and implicit functions, i.e. The characteristic equation is paired with Implicit Differentiation: On the curve of the solution to the system of equations: make , express s The real part of the system, at this time the eigenvalues of the system are along the real part of the system. The direction of increase crosses negatively from the imaginary axis to the left half-plane of the imaginary axis, defining the parameter region that stabilizes the system: Control parameters are selected based on the parameter range described above to stabilize the system, and these selected control parameters are applied to the magnetic levitation bearing rotor system to ensure stable rotor levitation. For example... Figure 3 The figure shows the parameter range that makes the system stable, obtained from the above formula.
[0023] like Figure 4 The diagram shown illustrates the system's principle for identifying the frequency sweep test. A frequency sweep excitation signal is applied. S Afterwards, record S arrive S 1. Frequency response function curve. Then, the control voltage signal input of the magnetic levitation bearing rotor system was quantified using a frequency sweep test. U ( s ) to displacement sensor signal output X s ( s The experimental frequency response function curves of the part were obtained, and the transfer function of the magnetic levitation bearing rotor system was obtained by fitting the curves using a second-order time-delay model.
[0024] Combined with time delay identification and verification procedures, Figure 4 In R ( s This indicates the rotor reference position signal. G c ( s ) represents the controller transfer function. G a ( s ) represents the transfer function of the power amplifier. G s ( s ) represents the transfer function of the displacement sensor. G ( s ) represents the equivalent transfer function of the magnetic levitation bearing rotor mechanical subsystem, A / D represents the analog-to-digital converter, and D / A represents the digital-to-analog converter. Figure 4 In τ 1. τ 2. τ 3 is used to characterize the local equivalent time delay introduced by different links in the frequency sweep identification link, where τ 1 corresponds to the time delay introduced by the power amplifier within the real system. τ 2 corresponds to the inherent time delay caused by electromagnetic actuation lag and rotor response. τ 3. Measurement time delay corresponding to displacement detection, acquisition, and output signal processing stages. The dispersed time delays can be uniformly converted into an equivalent input time delay from the control voltage input to the displacement sensor output channel. τ In this embodiment, the equivalent input delay is approximately 200 μs, and it is substituted into a second-order delay-containing model. G p ( s This is used for subsequent stability analysis.
[0025] like Figure 5 The figure shows the time-domain simulation results of a time-delay feedback control method for a magnetic levitation bearing rotor system with time delay. Based on the identification results of the system's frequency response function, the system's input time delay is approximately... τ =200μs, and based on the stable region, the transfer function for controlling the input can be selected as follows: The main parameters used in the simulation and comparison in this embodiment are taken from the system frequency response identification results, as shown in Table 1.
[0026] Table 1. Main parameters used in simulation and comparison are taken from the system frequency response identification results.
[0027] Simulation results show that, under the condition that the system input time delay is about τ=200μs, the rotor displacement response can tend to stabilize after selecting the control input according to the stable parameter region. A time delay feedback control method for a magnetic levitation bearing rotor system with time delay can achieve stable rotor levitation. Compared with the traditional compensation approach of simply canceling the time delay, this method incorporates the time delay into the design of the feedback control law, so that the selection of control parameters and the closed-loop stability criterion form a clear correspondence.
[0028] like Figure 6 As shown, the rotor displacement amplitude of the method of this invention is compared with that of the traditional DDADRC control method under the same frequency sweep disturbance excitation conditions. The two control methods are compared under the same input time delay, the same disturbance excitation, and the same displacement measurement channel. DDADRC serves as the benchmark method for passive time delay compensation. This invention improves the vibration dissipation capability in the key frequency band by actively introducing a time delay term in the feedback loop, transforming the input time delay into the system's equivalent virtual damping. Using the peak value of the rotor displacement amplitude envelope as the comparison index, the results show that the method of this invention reduces the maximum vibration amplitude by 58.3% compared to DDADRC near the modal peak of approximately 60 Hz. Although there are local amplitude differences in the low-frequency band below 19.8 Hz, the absolute displacement amplitude under the control of this invention is still less than 6 μm, demonstrating its stronger vibration suppression capability and stable suspension effect in the key resonant frequency band.
[0029] Those skilled in the art should understand that, unless otherwise specified, the meanings of the technical and scientific terms used herein are consistent with the general understanding of the relevant technical field. Furthermore, terms defined in general dictionaries should be understood in the context of the technical background in this field and should not be interpreted in an overly idealized or formalistic manner divorced from practical application scenarios.
[0030] The above embodiments have described in detail the main concept, technical solution, and technical effects of the present invention. It should be noted that the above content is merely illustrative and not intended to limit the scope of protection of the present invention. Any equivalent modifications, substitutions, or optimizations based on the present invention without departing from its core principles are within the scope of the present invention.
Claims
1. A time-delay feedback control method for a magnetic levitation bearing rotor system with time delay, characterized in that, Includes the following steps: Step S1: Use a signal generator to generate a sweep frequency signal to excite the magnetic levitation bearing rotor system. By identifying the parameters of the frequency response function between the control voltage input and the displacement sensor output, a second-order mathematical model with time delay of the magnetic levitation bearing rotor system is obtained. G p ( s ); Step S2: Based on the second-order mathematical model with time delay of the magnetic levitation bearing rotor system G p ( s By introducing the error signal between the actual output of the system and the reference input, and by designing a feedforward control loop to adjust the system balance point, the control objective is transformed from tracking the reference input to an error state adjustment problem that makes the error signal tend to zero. Step S3: Based on the identified second-order mathematical model of the magnetic levitation bearing rotor system with time delay G p ( s Considering the input time delay of the system, design a time-delay feedback control law; Step S4: Introduce the time-delay feedback control law, derive the characteristic equation of the closed-loop system, clarify the necessary and sufficient conditions for the critical stability of the system, and quantify the critical stability boundary in the control parameter domain based on the necessary and sufficient conditions for the critical stability of the system. Step S5: Perform implicit differentiation on the characteristic equation of the closed-loop system, and derive the partial differential expression of the real part of the characteristic root with respect to the control parameter by solving the problem; combine the system stability criterion that the real part of the characteristic root is less than zero, and further define the range of control parameter values that meet the asymptotic stability requirements of the system; select control parameters according to the range of control parameter values that meet the asymptotic stability requirements of the system, and apply the selected control parameters to the magnetic levitation bearing rotor system to make the rotor stably levitate.
2. The time-delay feedback control method for a magnetic levitation bearing rotor system with time delay according to claim 1, characterized in that, The magnetic levitation bearing rotor system includes a controller, a power amplifier, a magnetic levitation bearing, a rotor, a displacement sensor, a frequency converter, and a motor. The displacement sensor detects the rotor displacement signal and inputs it into the controller. The controller outputs a control voltage signal, which is then sent to the power amplifier and converted into a control current signal to drive the magnetic levitation bearing to work, thus completing the control of the rotor.
3. The time-delay feedback control method for a magnetic levitation bearing rotor system with time delay according to claim 2, characterized in that, In step S1, a sinusoidal control voltage signal with constant amplitude and increasing frequency is generated by a signal generator to perform frequency sweep excitation on the magnetic levitation bearing rotor system. The frequency response function between the control voltage input and the displacement sensor output is expressed as: in, G p ( s () represents a second-order mathematical model with time delay for a magnetic levitation bearing rotor system. b = k a k i k s / m For system gain, k xx =k x / m The stiffness per unit mass displacement is given by , where k a and k s These are the power amplifier gain and the displacement sensor gain, respectively. k i and k x These are current stiffness and displacement stiffness, respectively. m For rotor equivalent mass, τ Input time delay to the system; The second-order mathematical model with time delay can be expressed in state-space as follows: in, For displacement sensor output, u For control voltage input; They are respectively The first derivative.
4. The time-delay feedback control method for a magnetic levitation bearing rotor system with time delay according to claim 3, characterized in that, In step S2, a reference input is set. r With displacement sensor output x The error signal between 1 and 1 is e 1. A feedforward term is constructed based on the error signal; the feedforward term is used to compensate for the influence of the reference input on the system equilibrium point, so that the subsequent time-delay feedback control law is adjusted according to the error state: in, r For reference input, e 1= r - x 1, For feedforward terms; They represent The first derivative of; where, e 2 represents the error. e The first derivative of 1; the feedforward term and the error state together constitute the adjustment amount of the feedforward control loop to the system equilibrium point; make e 1= z ,in z For reference input r With displacement sensor output x The error state variable constructed from the difference of 1 is expressed by the differential equation of the closed-loop system as follows: in, for The second derivative of .
5. The time-delay feedback control method for a magnetic levitation bearing rotor system with time delay according to claim 4, characterized in that, In step S3, the system control voltage input is selected as follows: in, For error feedback gain, The gain is the hysteresis error feedback term; the introduction of the error feedback term and the hysteresis error feedback term constitutes the design of the time-delay feedback control law; substituting the control voltage input expression of the closed-loop system into the differential equation of the system, the updated differential equation expression of the closed-loop system is obtained: Perform variable substitution, let , , The variable substitution is used to normalize the system gain, unit mass displacement stiffness, error feedback gain, and hysteresis error feedback gain to a unified closed-loop characteristic parameter, and to analyze the stability boundary within the control parameter domain; then the differential equation of the closed-loop system is expressed as: 。 6. The time-delay feedback control method for a magnetic levitation bearing rotor system with time delay according to claim 5, characterized in that, In step S4, after introducing the time-delay feedback control law, the characteristic equation of the closed-loop system is: in, , Let be the system angular frequency; when When the system is in a critically stable state, that is, the characteristic roots lie on the imaginary axis and their real parts are equal to zero, this is the necessary and sufficient condition for the system to be critically stable. Substituting into... The characteristic equation is expressed as: According to Euler's formula, and by separating the real and imaginary parts of the characteristic equation, we obtain the system of equations: Substitution The characteristic equation and the results of separating its real and imaginary parts together characterize the necessary and sufficient conditions for the critical stability of the system; the solution of the equation system in the control parameter domain The middle part is a set of curves: 。 7. The time-delay feedback control method for a magnetic levitation bearing rotor system with time delay according to claim 6, characterized in that, In step S5, the implicit differentiation processing of the characteristic equation of the closed-loop system includes: processing the characteristic roots... s Considered and implicit functions, i.e. The characteristic equation is paired with Implicit Differentiation: On the curve of the solution to the system of equations: make , express s The real part of the system, at this time the eigenvalues of the system are along the real part of the system. The direction of increase crosses negatively from the imaginary axis to the left half-plane of the imaginary axis, defining the parameter region that stabilizes the system: Control parameters are selected based on the parameter range that stabilizes the system, and the selected control parameters are applied to the magnetic levitation bearing rotor system to make the rotor levitate stably.