Finite time composite vibration suppression control method and system for same-frequency vibration of magnetic bearing-rotor system

Abstract

The invention discloses a finite time composite vibration suppression control method and system for same-frequency vibration of a magnetic bearing-rotor system. The finite time composite vibration suppression control method comprises the steps that a synchronous vibration component in rotor displacement is extracted through a same-frequency narrow-band tracking filter; performing phase lead correction by using an all-pass phase shifter, generating a feed-forward compensation force by combining an equivalent gain and electromagnetic linear model based on a feedback link, and offsetting a displacement stiffness force which causes vibration transmission from a physical source; a finite time same-frequency narrow-band extended state observer is constructed, and rapid and accurate finite time estimation is carried out on total disturbance including model mismatch; and designing a finite time nonsingular terminal sliding mode controller, fusing the feedforward compensation force and the disturbance estimation value, and generating a control law with a finite time convergence characteristic. According to the method, through cooperation of feed-forward compensation, finite time observation and finite time control, rapid convergence and high-robustness stabilization of same-frequency vibration and effective suppression of control buffeting under a dynamic working condition are realized.

Description

Technical Field

[0001] This invention belongs to the field of active vibration control technology for magnetic levitation rotors, and in particular relates to a finite-time composite vibration suppression control method and system for magnetic bearing-rotor systems with the same frequency vibration. It is especially suitable for high-speed magnetic levitation motors, flywheel energy storage systems and other equipment under dynamic working conditions such as speed change and passing through rigid critical speed, to quickly suppress the same frequency vibration excited by mass imbalance and suppress its transmission to the foundation. Background Technology

[0002] Magnetic bearing-rotor systems have become a key technology for achieving high-speed and high-efficiency rotating machinery due to their advantages of being contactless and having controllable support characteristics. However, the inherent mass imbalance of the rotor generates synchronous centrifugal force during rotation, exciting vibrations at the same frequency as the rotational speed. This vibration not only restricts performance improvement but also affects the overall stability by being transmitted to the machine base through the displacement stiffness force of the magnetic bearing (a coupled disturbance force generated by negative stiffness characteristics and in phase with the displacement).

[0003] Existing methods for suppressing vibration at the same frequency can be mainly divided into three categories: First, automatic balancing techniques (such as notch filters, generalized notch filters, or phase-shifting notch filters). These methods primarily suppress vibration by eliminating or compensating for the same-frequency components in the rotor displacement signal. Although they can significantly suppress the response, traditional notch filters often cannot offset displacement stiffness forces, and phase lag may affect the overall stability of the system. Second, unbalanced force feedforward compensation techniques. These techniques utilize algorithms such as adaptive feedforward or repetitive control to suppress vibration by identifying and actively injecting reverse forces online. They can eliminate same-frequency interference caused by unbalanced forces, but they typically suffer from slow dynamic response and sensitivity to model parameters. Third, robust control combined with disturbance observation (such as sliding mode control combined with an extended state observer). This method estimates disturbances through an observer or suppresses vibration using sliding mode control. Although it has good robustness, traditional designs are mostly asymptotically convergent, with limited response speed, and the observer is not optimized for same-frequency disturbances, making the control law prone to chattering at high frequencies.

[0004] In summary, existing technologies struggle to simultaneously achieve rapid (finite-time) suppression and effective isolation of vibration transmission during dynamic processes, while also ensuring strong robustness and low chattering. Therefore, there is an urgent need for an advanced control method with rigorous theoretical safeguards. Summary of the Invention

[0005] To address the above technical problems, this invention provides a finite-time composite vibration suppression control method and system for synchronous vibration of a magnetic bearing-rotor system.

[0006] The technical solution adopted by this invention to solve its technical problem is: A finite-time composite vibration suppression control method for synchronous vibration of a magnetic bearing-rotor system, the method comprising the following steps: S1. Obtain the displacement signal of the magnetic bearing-rotor, and extract the vibration component that is synchronized with the rotor speed from the displacement signal through a narrow-band tracking filter of the same frequency. S2. The extracted same-frequency vibration components are phase-advanced through a full-pass phase shifter, and the phase-corrected signal is multiplied by the feedforward compensation gain determined based on the equivalent gain of the feedback loop and the electromagnetic force linearization model to generate a feedforward compensation force to offset the displacement stiffness force. S3. Construct a finite-time same-frequency narrowband extended state observer (FT-SNBESO). Input the displacement signal, which has been preprocessed by the same-frequency narrowband tracking filter and the all-pass phase shifter, into the observer. This is used to estimate the total disturbance caused by model mismatch, parameter changes and external disturbances in real time within a finite time, and output the disturbance estimate. S4. Design a finite-time non-singular terminal sliding mode controller FT-NSTSMC. The controller receives the system tracking error, the fused feedforward compensation force and the total disturbance estimated by FT-SNBESO, and generates a control law with finite-time convergence characteristics through internal fusion and finite-time control law calculation. S5. The control law is converted into a control current, which forms the final control input acting on the magnetic bearing-rotor to suppress vibration.

[0007] Preferably, the transfer function of the same-frequency narrowband tracking filter in S1 for: in, For filter gain coefficients, This is the filter damping coefficient. The frequency is the same as the rotational speed. s For the Laplace operator.

[0008] Preferably, the all-pass phase shifter in S2 is for achieving advance. Transfer function of an angle-based all-pass phase shifter for: in, , The phase shifter parameters are obtained by calculating using the following formula: in, The damping coefficient of the full-pass phase shifter at the same frequency. The frequency is the same as the rotational speed. The compensation angle is calculated based on the system lag time. , As an intermediate variable, This is the characteristic angular frequency of the full-pass phase shifter at the same frequency; The generated feedforward compensation force is specifically as follows: in, The feedforward compensation gain is derived based on the equivalent gain of the feedback loop and the linearization model of electromagnetic force. , which is the equivalent control gain of the sliding mode controller. This is the electromagnetic force displacement stiffness coefficient. This is the current stiffness coefficient. , These are the displacement signals for the two radial channels, respectively. The equivalent control gain of the sliding mode controller. For sensor gain.

[0009] Preferably, the finite-time same-frequency narrowband extended state observer FT-SNBESO in S3 is constructed as follows: definition , Let be the attenuation coefficient, then the state equation of FT-SNBESO is: in, , , These are the estimated values ​​for system displacement, velocity, and total disturbance, respectively. , , For observer gain parameters, , , , For power-order parameters, The nominal value of the system input gain. To control the input, For displacement estimation error, displacement The error signal after preprocessing by a full-pass phase shifter and a narrow-band tracking filter at the same frequency.

[0010] make ,consider sat In the nonlinear region of the function, the error dynamic equation of FT-SNBESO is: in, , , Let represent the derivatives of the displacement estimation error, velocity estimation error, and disturbance estimation error, respectively. , These are the speed and disturbance estimation errors, respectively. The derivative of the total disturbance; The displacement signal, after passing through a notch filter, phase compensation, and filtering, is input to the FT-SNBESO. The notch filter is uniformly configured as follows: in, This refers to the notch filter gain parameter.

[0011] Preferably, the finite-time non-singular terminal sliding mode controller FT-NSTSMC employs a non-singular power-integral composite sliding surface: in, For the sliding surface variable, The gain coefficient of the sliding surface. The integral term of the error. for The amplitude limit, , For terminal exponentiation parameters, It is a micro-offset constant. It is a saturation function. These are the boundary layer parameters.

[0012] Preferably, the control law , For equivalent control, For switching control; where, equivalent control for: in, For rotor mass, The current stiffness coefficient of electromagnetic force. This is the displacement stiffness coefficient of the electromagnetic force. For boundary layer parameters, To fix the boundary layer thickness; Switching control for: in, To switch gain parameters, For power-order parameters, Let be the norm of the system state error. The boundary layer thickness is adaptively varied with the error norm.

[0013] Preferably, switching control A variable boundary layer saturation function and a variable gain switching law are used to suppress high-frequency chattering of the control signal; The variable boundary layer saturation function is defined as follows: in, >0 represents the time-varying or state-dependent boundary layer thickness, which is the system state error norm. The function is designed to vary with the error norm. The decrease is adaptive and decreases accordingly; Variable gain switching law enables switching gain It is a function that adaptively adjusts with the system state error, i.e. , And satisfy: in, k 10 >0, k 20 A value greater than 0 represents the base gain, used to ensure minimum robustness. k 11 , k 12 >0, k 21 , k 22 >0, f (|| e ||) and g (|| e ||) is || e The monotonically non-decreasing function of || allows the switching gain to adaptively increase as the error increases.

[0014] A finite-time composite vibration suppression control system for synchronous vibration of a magnetic bearing-rotor system includes: The displacement stiffness force feedforward compensation module is used to acquire the displacement signal of the magnetic bearing-rotor. It extracts the vibration component that is synchronous with the rotor speed from the displacement signal through a narrow-band tracking filter of the same frequency. The extracted vibration component of the same frequency is phase-advanced through a full-pass phase shifter. The phase-corrected signal is multiplied by the compensation gain determined based on the equivalent gain of the feedback loop and the electromagnetic force linearization model to generate the feedforward compensation force to offset the displacement stiffness force. The Finite-Time Narrowband Extended State Observer Module is used to construct the Finite-Time Narrowband Extended State Observer (FT-SNBESO). The displacement signal, which has been preprocessed by the narrowband tracking filter and the all-pass phase shifter, is input into the observer to estimate the total disturbance caused by model mismatch, parameter changes and external disturbances in real time within a finite time, and outputs the disturbance estimate. The Finite-Time Non-Singular Terminal Sliding Mode Controller (FT-NSTSMC) module is used to design the FT-NSTSMC. The controller receives the system tracking error, the fused feedforward compensation force, and the total disturbance estimated by FT-SNBESO. Through internal fusion and finite-time control law calculation, it generates a control law with finite-time convergence characteristics. The vibration suppression module is used to convert the control law into a control current, which forms the final control input acting on the magnetic bearing-rotor to suppress vibration.

[0015] A magnetically levitated rotating machine integrates a finite-time composite vibration suppression control system for the synchronous vibration of a magnetic bearing-rotor system.

[0016] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of a finite-time composite vibration suppression control method for synchronous vibration of a magnetic bearing-rotor system.

[0017] Compared with existing technologies, the core innovation of this invention lies in proposing a hierarchical finite-time composite disturbance rejection control architecture, the innovation of which is reflected in: (1) Model feedforward and real-time compensation coordination mechanism for high dynamic processes: The feedforward compensation based on the displacement stiffness physical model is deeply integrated with the real-time disturbance estimation based on the finite-time same frequency narrowband extended state observer (FT-SNBESO). While utilizing model information, the dependence on model accuracy is reduced, ensuring the effectiveness of source cancellation in dynamic processes.

[0018] (2) Finite-time fast convergence co-frequency disturbance observer (FT-SNBESO): It deeply integrates co-frequency narrowband tracking, total disturbance estimation and finite-time convergence law, and can quickly and accurately estimate the total disturbance, including the feedforward model error, within a preset finite time.

[0019] (3) Finite-time sliding mode controller with high dynamic response and low chattering (FT-NSTSMC): It adopts non-singular terminal sliding surface, variable boundary layer saturation function and variable gain switching law, which effectively suppresses chattering of control signal while ensuring finite-time convergence. Attached Figure Description

[0020] Figure 1 This is a flowchart of a composite vibration suppression control method for a magnetic bearing-rotor system with finite-time convergence in one embodiment of the present invention; Figure 2 This is a schematic diagram of a magnetic bearing-rotor system structure in one embodiment of the present invention; Figure 3 This is a flowchart illustrating the FC (Fluid Force Feedforward Compensation) process for displacement stiffness force in one embodiment of the present invention. Figure 4 This is a structural diagram of the finite-time same-frequency narrowband extended state observer FT-SNBESO in one embodiment of the present invention; Figure 5 This is a flowchart of the finite-time non-singular terminal sliding mode controller FT-NSTSMC in one embodiment of the present invention; Figure 6 A feedback loop is included in one embodiment of the present invention. G ec Block diagram of a finite-time composite control system; Figure 7 This is a comparison diagram of the step disturbance response of the conventional method and the present invention in one embodiment of the present invention; Figure 8 This is a comparison diagram of the shaft center trajectory at a constant speed of 8000 rpm in one embodiment of the present invention; Figure 9 The image shows a comparison of shaft center trajectories for 0-10000 rpm speed variation in one embodiment of the present invention, wherein (a) is a shaft center trajectory diagram for full speed variation and (b) is a shaft center trajectory diagram for high speed variation. Detailed Implementation

[0021] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0022] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a composite vibration suppression control method for magnetic bearing-rotor systems with finite-time convergence. This method, through innovative hierarchical design, ensures that the system can quickly and accurately suppress vibration and force transmission during dynamic processes, and exhibits strong robustness to model uncertainties.

[0023] To achieve the above objectives, the technical solution proposed in this invention is a finite-time composite vibration suppression control method for the same-frequency vibration of a magnetic bearing-rotor system. Its core lies in the collaborative design of a displacement stiffness force feedforward compensation module based on a same-frequency narrowband tracking filter and an all-pass phase shifter, a finite-time same-frequency narrowband extended state observer (FT-SNBESO), and a finite-time non-singular terminal sliding mode controller (FT-NSTSMC). Finite-time stability of each module and the closed-loop system is achieved through a finite-time convergent attractor. The process is summarized as follows: Figure 1 As shown, a finite-time composite vibration suppression control method for synchronous vibration of a magnetic bearing-rotor system includes the following steps: S1. Obtain the displacement signal of the magnetic bearing-rotor, and extract the vibration component that is synchronized with the rotor speed from the displacement signal through a narrow-band tracking filter of the same frequency. S2. The extracted same-frequency vibration component is phase-adjusted using a full-pass phase shifter, and the phase-corrected signal is multiplied by a feedback-based signal. G ec Equivalent gain and compensation gain determined by the electromagnetic force linearization model This generates a feedforward compensation force to counteract the displacement stiffness force. S3. Construct a finite-time same-frequency narrowband extended state observer (FT-SNBESO). Input the displacement signal, which has been preprocessed by the same-frequency narrowband tracking filter and the all-pass phase shifter, into the observer. This is used to estimate the total disturbance caused by model mismatch, parameter changes and external disturbances in real time within a finite time, and output the disturbance estimate. S4. Design a finite-time non-singular terminal sliding mode controller FT-NSTSMC. The controller receives the system tracking error, the fused feedforward compensation force and the total disturbance estimated by FT-SNBESO, and generates a control law with finite-time convergence characteristics through internal fusion and finite-time control law calculation. S5. The control law is converted into a control current, which forms the final control input acting on the magnetic bearing-rotor to suppress vibration.

[0024] Next, we will analyze the overall method step by step.

[0025] Step 1: Dynamic modeling of the magnetic bearing-rotor system considering unbalanced disturbances This invention considers as follows Figure 2 The five-degree-of-freedom magnetic bearing-rotor system is shown. For its radial translational degrees of freedom, which require active vibration suppression, its dynamic equations can comprehensively consider the mass imbalance excitation force. Fu Factors such as the electromagnetic force Fe of the magnetic bearing and internal and external disturbances. The electromagnetic force is linearized near the operating point (equilibrium position) and can be expressed as... Fe ≈ k i i k h x ,in k i For current stiffness, k h For displacement negative stiffness, i To control the current, x Let be the rotor displacement. Therefore, for a single translational degree of freedom, the system can be described by a second-order equation of the following form: (1) in, For displacement, i Electromagnetic current ， To control the current, For system gain, Unbalanced force, displacement with negative stiffness Lumped disturbances, including unmodeled dynamics and external disturbances. In this embodiment, a 11kW magnetic levitation rotor test bench is used to further illustrate the invention. Key parameters, such as rotor mass, are obtained through experimental measurement and identification. First-order rigid translational critical frequency Current stiffness Negative stiffness due to displacement Control gain .

[0026] Step 2: Feedforward Compensation (FC) Design Based on Narrowband Tracking and Phase Correction at the Same Frequency This step constructs a feedforward channel specifically designed to counteract the negative stiffness caused by displacement. Caused co-frequency disturbance force This is the key to achieving vibration transmission isolation in this invention.

[0027] First, the displacement signal of the magnetic bearing-rotor is acquired. Then, the vibration component synchronized with the rotor speed is extracted from the displacement signal using a narrowband tracking filter. The extracted synchronous vibration component is then phase-adjusted using a full-pass phase shifter. Finally, the phase-corrected signal is multiplied by a feedback-based... G ec Equivalent gain and compensation gain determined by the electromagnetic force linearization model This generates a feedforward compensation force to counteract the displacement stiffness force. For example... Figure 3 As shown, its implementation includes three core components: 1. Same-frequency signal extraction: Same-frequency narrowband tracking filter Used to measure rotor displacement signal In the process, it extracts the value related to the current rotation speed with high precision and selectivity. Perfectly synchronized vibration components Its transfer function is designed as follows: (2) in, For filter gain coefficients, This is the filter damping coefficient. This is the frequency at which the rotational speed is synchronized. The filter operates at this frequency. The gain is 1 and the phase is 0, while it has a strong attenuation effect on other frequency components, thus purely extracting the same frequency displacement signal.

[0028] 2. Phase lead correction: Due to phase lag introduced by the sensor, signal conditioning circuit, and filter itself. Use directly Compensation results in the generated counteracting force not being precisely aligned with the actual displacement stiffness force in the time domain. Therefore, a full-pass phase shifter is designed. right Perform phase lead correction: (3) in, , The phase shifter parameters are obtained by calculating using the following formula: (4) The filter has a constant gain of 1 across the entire frequency domain, except at a specific frequency. A phase lead is generated at this point. By setting It can accurately compensate for system lag and ensure that the feedforward force and the disturbance force are out of phase.

[0029] 3. Feedforward compensation force It is generated by the following formula: (5) in, For feedback-based G ec The feedforward compensation gain derived from the linearization model of gain and electromagnetic force , which is the equivalent control gain of the sliding mode controller. This is the electromagnetic force displacement stiffness coefficient. This feedforward force is directly injected into the control loop. A key feature of this invention is that it allows... If there are modeling errors or time-varying errors, these errors will be estimated and compensated in real time by the subsequent observer module along with other uncertainties in the system, thereby significantly reducing the dependence on the absolute accuracy of the feedforward model at the system level.

[0030] In the digital controller, the speed signal is read in real time to update... ω And calculate the feedforward compensation force online. f ks .

[0031] Step 3: Finite-Time Narrowband Extended State Observer (FT-SNBESO) and Convergence Design To the total disturbance To perform fast, accurate, and finite-time estimation, FT-SNBESO is designed. Its structure is as follows: Figure 4 As shown, the innovation lies in integrating the same-frequency narrowband tracking filter and the all-pass phase shifter as preprocessing steps into the observer input, and combining them with the core of the extended state observer that has a finite-time convergence law.

[0032] 1. Finite-time, same-frequency narrowband observer structure: make , , The observer equation is: (6) in, Using a power function, the estimation error convergence speed of a broadband ESO is achieved. for The estimated value; displacement After the error signal is preprocessed by the same-frequency full-pass phase shifter and the same-frequency narrowband tracking filter, this design enables the observer to focus mainly on the same-frequency disturbance band, improve the estimation accuracy of same-frequency disturbances (including feedforward compensation residual errors), and suppress broadband noise interference. 2. Finite-time convergence design under the same frequency perturbation: Define estimation error Combining the system dynamics (1) and the observer dynamics (6), the error dynamic system can be obtained: (7) Its finite-time convergence is achieved by designing a finite-time attractor power function. This is achieved by constructing Lyapunov functions. And make its derivative satisfy (in , This can be achieved through [the following].

[0033] That is, for the system (Equation (1)) if it satisfies The maximum perturbation is bounded, and the derivative of the perturbation is bounded, through design parameters. >0, >0, >0, power function and powers , , Gain coefficient at the same frequency and same frequency narrowband tracking filter Bandwidth and gain exist >0 and 0< A value less than 1 allows FT-SNBESO to converge to the neighborhood in finite time. or The convergence formula is as follows: (8) in, , >0, >0, >0, , , , The sign of the smallest eigenvalue. , This represents the convergence time coefficient. , LgFor a certain positive number, This is the scaling factor for the convergent neighborhood.

[0034] 3. Parameter tuning method: Power parameter: Based on the principle of homogeneity, set the homogeneity degree. ,but , , ,in Gain parameter: Critically damped configuration method is used. The desired observer bandwidth is set. (Usually taken as 2 to 3 times the frequency of the system's first-order rigid mode), then , , Increase It can accelerate convergence, but a trade-off must be struck between estimation speed and noise suppression. Boundary layer: This is used to smooth power functions and suppress observer chattering caused by high-frequency measurement noise, and is usually taken as a small value.

[0035] The power term is changed to a linear term, and the FT-SNBESO is transformed into LESO. The parameters of ESO are set using the critical damping and equal bandwidth method. Based on this, the value of FT-SNBESO is set according to the disturbance convergence time and jitter peak value, with a range of (0.6~1). This set of parameters ensures that the estimation error system satisfies the finite-time convergence inequality (8) in the invention.

[0036] Step 4: Finite-Time Non-Singular Terminal Sliding Mode Controller (FT-NSTSMC) and Convergence Design The FT-NSTSMC is designed to integrate feedforward compensation force. Compared with the disturbance estimate This achieves finite-time convergence of tracking errors and employs a unique structure to suppress and control chattering. Its detailed workflow is as follows: Figure 5 As shown.

[0037] 1. FT-NSTSMC controller structure: By employing a non-singular power integral composite sliding surface with finite time and a power-approaching law, the convergence speed and chattering suppression performance are improved.

[0038] Define tracking error (Desired displacement) Design of non-singular power integral type composite sliding surface: (9) in A power function is used to improve the terminal convergence speed, achieving finite-time convergence from the sliding surface to the equilibrium point. Integral amplitude limiting is applied to prevent saturation. micro offset Avoid singularity Boundary layer parameters , , , This is the correlation gain coefficient.

[0039] The control law consists of two parts: equivalent control and switching control. Among them, equivalent control Integrating the feedforward compensation force and disturbance estimate, the switching control law is as follows: Using a variable boundary layer With variable gain , Its finite-time convergence is demonstrated by constructing a Lyapunov function. The sliding mode surface parameters and control law parameters are designed such that their derivatives satisfy the following condition after the disturbance estimation converges: (in , To ensure its realization.

[0040] Regarding the single-degree-of-freedom suspension control in formula (1) of the invention, let Let from equation (9) Solve the following equation (1) in conjunction with the invention content: , and hour The following formulas are shown respectively: (10) The switching function is improved to a saturation function, and the first-order and fractional-order powers are combined to suppress boundary layer chattering. To switch the gain, a micro-offset is also added. To prevent the occurrence of singular values.

[0041] (11) Since the derivative of the equivalent control is zero, therefore: (12) Combining equations (10) and (11), we get : (13) in .

[0042] ① By replacing the ideal sign function or conventional saturation function with a variable boundary layer saturation function, the control signal can be dynamically smoothed according to the system state while ensuring finite-time convergence characteristics, thus suppressing the high-frequency chattering problem inherent in traditional sliding mode control.

[0043] (14) >0 represents the time-varying or state-dependent boundary layer thickness, which is the system state error. e The norm of ||e|| is a function of .

[0044] ② Design a variable gain switching law so that the strength of the switching control can be adaptively adjusted according to the system state error. This provides strong robustness in the initial transient phase to quickly suppress vibrations, while reducing the gain near the steady state to further smooth the control (compared to traditional sliding mode switching gain). This is usually a fixed constant and must be set large enough during the design phase to cover the worst disturbances. This can introduce unnecessary strong switching in steady state and exacerbate chattering.

[0045] (15) in, The base gain is used to ensure minimum robustness. , yes Monotone non-decreasing functions (such as) , 2 This allows the switching gain to adaptively increase as the error increases. Primarily addresses errors caused by same-frequency disturbances; k 20 >0 is the base gain, used to ensure minimum robustness. 21 ,k 22 >0, yes Monotone non-decreasing functions (such as) , 2 This allows the switching gain to adaptively increase as the error increases. It mainly targets the error caused by same-frequency disturbances.

[0046] Parameter design guidelines: The power terms are converted to linear terms, such as the FT-NSTSMC transformation to PD. The root locus scan method is then used to determine the distribution range of the main parameters. Based on this, the critical damping and equal bandwidth methods are used to set the parameters of each controller. The effective control coefficients in FT-NSTSMC are the same as the PD coefficients in LADRC feedback control. , Based on this, adjustments can be made according to dynamics, stability, and steady-state chattering. The range of values ​​for . This set of parameters ensures that the sliding surface dynamically satisfies the finite-time convergence inequality (13) in the invention, and that the switching control is smooth.

[0047] 2. FT-NSTSMC Finite-Time Convergence Design: Consider Lyapunov functions Differentiate it and substitute it into the control law (11) and system dynamics (1). Since FT-SNBESO guarantees the disturbance estimation error In a limited time It then converges to a small neighborhood near zero (i.e. Therefore, when At that time, there are positive numbers. and , so that: For any initial state V(x 0 )=V 0. The Lyapunov function converges to the origin in finite time, with the convergence time being: (13) Based on the finite-time convergent attractor (power function), the sliding surface variables In another limited time It converges to zero. Furthermore, according to the structure of the sliding surface equation (9), once... Tracking error and its derivative In another limited time It converges to its neighborhood. and All satisfy equation (13).

[0048] Among them, variable boundary layer With variable gain , The design ensures strong robustness by guaranteeing convergence within a finite time while maintaining the smoothness of the control signal, fundamentally suppressing the inherent high-frequency chattering problem of traditional sliding mode control.

[0049] 3. Parameter tuning method: Sliding surface parameters: , The pole placement method in classical control can be used to determine the value after linearizing equation (9). satisfy This is to balance the effect of nonlinear terms on the convergence speed and their impact on smoothness.

[0050] Switching gain: Base gain Must meet Because FT-SNBESO provides high-precision perturbation estimation, The value is very small, therefore It can be set to a gain much smaller than that required by traditional sliding mode control, which is key to reducing chattering at its source. This is used to further improve robustness under transient large errors.

[0051] Boundary layer parameters: Set according to the system's steady-state accuracy requirements. Used to adjust the smoothness of control during transient processes.

[0052] Step 5: Finite-time stability of the overall closed-loop system Since both the error dynamic system (6) of FT-SNBESO and the sliding surface dynamic system (8) of FT-NSTSMC are designed based on finite-time attractor power functions, the entire closed-loop control system composed of the two is finite-time stable. The tracking error of the system... The error in the disturbance estimation will be within a finite time. The method is uniformly bounded internally and eventually converges to a pre-designable bounded small neighborhood near the origin. This achieves the fast and robust dynamic performance of the proposed method.

[0053] Finally, simulation and system experiments were conducted to verify the proposed finite-time composite vibration suppression control algorithm. This algorithm was then integrated into a digital signal processor (DSP) to form a complete control system. Figure 6 As shown. On a magnetic levitation rotor test bench, through constant speed steady-state experiments, wide-range variable speed experiments, and excitation mutation experiments, the superior performance of the method of this invention (FT-NSTSMC / FT-SNBESO / FC) compared with traditional methods (such as LADRC) was fully verified.

[0054] (1) Transient convergence verification: step disturbance response To verify the finite-time convergence characteristics of the system during transient processes, a step disturbance test was conducted. The results show that the method of this invention can reduce system displacement fluctuation by 26.3% and shorten the convergence time by 25.6% when dealing with step disturbances. This result (corresponding to...) Figure 7 This directly verifies that the proposed control method has the theoretical characteristic of fast convergence and can significantly accelerate the system's recovery speed under disturbance.

[0055] (2) Steady-state accuracy verification: shaft center trajectory at a constant speed of 8000 rpm The vibration suppression accuracy of the present invention was evaluated under steady-state conditions at a constant speed of 8000 rpm. Simulation results (corresponding to...) Figure 8 The results show that the proposed method significantly reduces the peak-to-peak value of rotor displacement from 4.8 μm in the comparative method to 1 μm, with a suppression rate of approximately 75%. This indicates that the method of the present invention has excellent ability to suppress same-frequency vibration and maintain operational stability during steady-state operation, achieving high-precision steady-state control.

[0056] (3) Dynamic robustness verification: shaft center trajectory with variable speed from 0-10000 rpm To verify performance under complex dynamic conditions, a wide-range variable speed (0-10000 rpm) test was conducted. Simulation results (corresponding to...) Figure 9 The results show that, under the dual dynamic processes of excitation switching and speed variation, the method of the present invention reduces the peak displacement by 24% in the translational rigid mode, and reduces the displacement amplitude by approximately 26% and 76% in the low-speed and high-speed regions, respectively. This fully demonstrates that the method can still maintain rapid response and strong vibration suppression capability under dynamic changing working conditions.

[0057] The above embodiments demonstrate that the method proposed in this invention can effectively solve the problem of same-frequency vibration in high-speed magnetic bearing-rotor systems during dynamic processes. Based on feedforward compensation with same-frequency narrowband tracking and phase correction, and observation and control design with strict finite-time convergence guarantee, it achieves superior comprehensive performance of fast suppression, effective vibration suppression, strong robustness and low chattering.

[0058] In one embodiment, a finite-time composite vibration suppression control system for synchronous vibration of a magnetic bearing-rotor system is also provided, comprising: The displacement stiffness force feedforward compensation module is used to acquire the displacement signal of the magnetic bearing-rotor. It extracts the vibration component synchronized with the rotor speed from the displacement signal using a narrowband tracking filter of the same frequency. The extracted same-frequency vibration component undergoes phase lead correction via a full-pass phase shifter, and the phase-corrected signal is multiplied by a feedback-based... G ec Equivalent gain and compensation gain determined by the electromagnetic force linearization model This generates a feedforward compensation force to counteract the displacement stiffness force. The Finite-Time Narrowband Extended State Observer Module is used to construct the Finite-Time Narrowband Extended State Observer (FT-SNBESO). The displacement signal, which has been preprocessed by the narrowband tracking filter and the all-pass phase shifter, is input into the observer to estimate the total disturbance caused by model mismatch, parameter changes and external disturbances in real time within a finite time, and outputs the disturbance estimate. The Finite-Time Non-Singular Terminal Sliding Mode Controller (FT-NSTSMC) module is used to design the FT-NSTSMC. The controller receives the system tracking error, the fused feedforward compensation force, and the total disturbance estimated by FT-SNBESO. Through internal fusion and finite-time control law calculation, it generates a control law with finite-time convergence characteristics. The vibration suppression module is used to convert the control law into a control current, which forms the final control input acting on the magnetic bearing-rotor to suppress vibration.

[0059] In one embodiment, a magnetically levitated rotating machine is also provided, which integrates a finite-time composite vibration suppression control system for the synchronous vibration of a magnetic bearing-rotor system.

[0060] Specific limitations regarding the finite-time composite vibration suppression control system for synchronous vibration of a magnetic bearing-rotor system and the magnetic levitation rotating machinery can be found in the above-described limitations regarding the finite-time composite vibration suppression control method for synchronous vibration of a magnetic bearing-rotor system, and will not be repeated here. The various modules in the aforementioned finite-time composite vibration suppression control system for synchronous vibration of a magnetic bearing-rotor system and the magnetic levitation rotating machinery can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0061] In one embodiment, a computer device is also provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of a finite-time composite vibration suppression control method for synchronous vibration of a magnetic bearing-rotor system.

[0062] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0063] The foregoing has provided a detailed description of the finite-time composite vibration suppression control method and system for synchronous vibration of a magnetic bearing-rotor system provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention, and the descriptions of the embodiments above are merely for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from the principles of this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A finite-time composite vibration suppression control method for synchronous vibration of a magnetic bearing-rotor system, characterized in that, The method includes the following steps: S1. Obtain the displacement signal of the magnetic bearing-rotor, and extract the vibration component that is synchronized with the rotor speed from the displacement signal through a narrow-band tracking filter of the same frequency. S2. The extracted same-frequency vibration components are phase-advanced through a full-pass phase shifter, and the phase-corrected signal is multiplied by the compensation gain determined based on the equivalent gain of the feedback loop and the electromagnetic force linearization model to generate a feedforward compensation force to offset the displacement stiffness force. S3. Construct a finite-time same-frequency narrowband extended state observer (FT-SNBESO). Input the displacement signal, which has been preprocessed by the same-frequency narrowband tracking filter and the all-pass phase shifter, into the observer. This is used to estimate the total disturbance caused by model mismatch, parameter changes and external disturbances in real time within a finite time, and output the disturbance estimate. S4. Design a finite-time non-singular terminal sliding mode controller FT-NSTSMC. The controller receives the system tracking error, the fused feedforward compensation force and the total disturbance estimated by FT-SNBESO, and generates a control law with finite-time convergence characteristics through internal fusion and finite-time control law calculation. S5. The control law is converted into a control current, which forms the final control input acting on the magnetic bearing-rotor to suppress vibration.

2. The method according to claim 1, characterized in that, The transfer function of the same-frequency narrowband tracking filter in S1 for: in, For filter gain coefficients, This is the filter damping coefficient. The angular frequency is the same as the rotational speed. s For the Laplace operator.

3. The method according to claim 2, characterized in that, The all-pass phase shifter in S2 is used to achieve advance. Transfer function of an angle-based all-pass phase shifter for: in, , The phase shifter parameters are obtained by calculating using the following formula: in, The damping coefficient of the full-pass phase shifter at the same frequency. The frequency is the same as the rotational speed. The compensation angle is calculated based on the system lag time. , As an intermediate variable, This is the characteristic angular frequency of the full-pass phase shifter at the same frequency; The generated feedforward compensation force is specifically as follows: in, The feedforward compensation gain is derived based on the equivalent gain of the feedback loop and the linearization model of electromagnetic force. , which is the equivalent control gain of the sliding mode controller. This is the electromagnetic force displacement stiffness coefficient. This is the current stiffness coefficient. , These are the displacement signals for the two radial channels, respectively. For sensor gain.

4. The method according to claim 3, characterized in that, The finite-time same-frequency narrowband extended state observer FT-SNBESO in S3 is constructed as follows: definition , Let be the attenuation coefficient, then the state equation of FT-SNBESO is: in, , , These are the estimated values ​​for system displacement, velocity, and total disturbance, respectively. , , For observer gain parameters, , , , For power-order parameters, The nominal value of the system input gain. To control the input, For displacement estimation error, displacement The error signal after preprocessing by a full-pass phase shifter and a narrow-band tracking filter at the same frequency; make ,consider sat In the nonlinear region of the function, the error dynamic equation of FT-SNBESO is: in, , , Let represent the derivatives of the displacement estimation error, velocity estimation error, and disturbance estimation error, respectively. , These are the speed and disturbance estimation errors, respectively. The derivative of the total disturbance; The displacement signal, after passing through a notch filter, phase compensation, and filtering, is input to the FT-SNBESO. The notch filter is uniformly configured as follows: in, This refers to the notch filter gain parameter.

5. The method according to claim 4, characterized in that, The finite-time nonsingular terminal sliding mode controller FT-NSTSMC employs a nonsingular power integral composite sliding surface: in, For the sliding surface variable, The gain coefficient of the sliding surface. The integral term of the error. for The amplitude limit, , For terminal exponentiation parameters, It is a micro-offset constant. It is a saturation function. These are the boundary layer parameters.

6. The method according to claim 5, characterized in that, Control Law , For equivalent control, For switching control; where, equivalent control for: in, For rotor mass, The current stiffness coefficient of electromagnetic force. This is the displacement stiffness coefficient of the electromagnetic force. For boundary layer parameters, To fix the boundary layer thickness; Switching control for: in, To switch gain parameters, For power-order parameters, Let be the norm of the system state error. The boundary layer thickness is adaptively varied with the error norm.

7. The method according to claim 6, characterized in that, Switching control A variable boundary layer saturation function and a variable gain switching law are used to suppress high-frequency chattering of the control signal; The variable boundary layer saturation function is defined as follows: in, >0 represents the time-varying or state-dependent boundary layer thickness, which is the system state error norm. The function is designed to vary with the error norm. The decrease is adaptive and decreases accordingly; Variable gain switching law enables switching gain It is a function that adaptively adjusts with the system state error, i.e. , And satisfy: in, k 10 >0, k 20 A value greater than 0 represents the base gain, used to ensure minimum robustness. k 11 , k 12 >0, k 21 , k 22 >0, f (|| e ||) and g (|| e ||) is || e The monotonically non-decreasing function of || allows the switching gain to adaptively increase as the error increases.

8. A finite-time composite vibration suppression control system for synchronous vibration of a magnetic bearing-rotor system, characterized in that, include: The displacement stiffness force feedforward compensation module is used to acquire the displacement signal of the magnetic bearing-rotor and extract the vibration component that is synchronized with the rotor speed from the displacement signal through a same-frequency narrowband tracking filter. The extracted same-frequency vibration components are phase-advanced through a full-pass phase shifter, and the phase-corrected signal is multiplied by a compensation gain determined based on the equivalent gain of the feedback loop and the electromagnetic force linearization model to generate a feedforward compensation force to counteract the displacement stiffness force. The Finite-Time Narrowband Extended State Observer Module is used to construct the Finite-Time Narrowband Extended State Observer (FT-SNBESO). The displacement signal, which has been preprocessed by the narrowband tracking filter and the all-pass phase shifter, is input into the observer to estimate the total disturbance caused by model mismatch, parameter changes and external disturbances in real time within a finite time, and outputs the disturbance estimate. The Finite-Time Non-Singular Terminal Sliding Mode Controller (FT-NSTSMC) module is used to design the FT-NSTSMC. The controller receives the system tracking error, the fused feedforward compensation force, and the total disturbance estimated by FT-SNBESO. Through internal fusion and finite-time control law calculation, it generates a control law with finite-time convergence characteristics. The vibration suppression module is used to convert the control law into a control current, which forms the final control input acting on the magnetic bearing-rotor to suppress vibration.

9. A magnetically levitated rotating machine, characterized in that, It integrates the control system as described in claim 8.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

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