A radial magnetic bearing displacement vibration suppression method based on phase shift order reduction generalized integrator

Abstract

The application discloses a radial magnetic bearing displacement vibration suppression method based on a phase shift reduced-order generalized integrator, and comprises the following steps: firstly, a magnetic bearing system model containing rotor mass imbalance is established; then, a synchronous displacement vibration suppression algorithm based on a phase shift reduced-order generalized integrator is designed, the orthogonal relationship of X / Y radial displacement error signals of the magnetic bearing is utilized, and the simultaneous extraction and compensation of double-channel synchronous components are realized; finally, the system stability is analyzed, and the phase shift angle parameters are designed in sections; the phase shift angle is introduced to adjust the phase without changing the amplitude characteristics at the synchronous frequency, so that the system stability is expanded. The application adopts the reduced-order generalized integrator structure, has less state quantity and lower calculation amount, and is suitable for high-speed real-time implementation of DSP / FPGA; the phase shift angle is introduced for phase advance adjustment, so that the stable working range of the algorithm can be effectively expanded; the orthogonal characteristics of the displacement signals are utilized to realize the unified implementation of X / Y double-channel synchronous compensation, and the structure is more simple.

Description

Technical Field

[0001] This invention belongs to the field of active magnetic bearing (AMB) control technology, and relates to a control method for suppressing synchronous displacement vibration caused by rotor mass imbalance, specifically a radial magnetic bearing displacement vibration suppression method based on a phase-shifted reduced-order generalized integrator. Background Technology

[0002] Active magnetic bearing systems offer advantages such as contactless support, low loss, high precision, and active control, making them widely used in high-speed rotating machinery. However, in practical applications, factors such as rotor machining errors, assembly errors, and material inhomogeneity can cause the rotor's geometric center and center of mass to misalign, resulting in mass imbalance. This imbalance can occur as the rotor rotates at various speeds. When rotating downwards, synchronous centrifugal disturbance force is generated, causing the rotor to vibrate significantly (at the same frequency as the rotation speed), thereby reducing the suspension accuracy and affecting the stability and reliability of the equipment.

[0003] To address imbalance compensation suppression, existing technologies typically employ the following methods:

[0004] 1) Iterative optimization / search methods: These methods search for the compensation current through iterative learning, recursive optimization, variable step size, and variable angle search. The advantage of this type of method is its low dependence on the model, but it often suffers from the following drawbacks: ① It is difficult to balance convergence speed and steady-state accuracy; ② It requires complex search logic; ③ It lacks adaptability to variable speed operating conditions.

[0005] 2) Notch / synchronization filtering methods (such as polarity-switched notch filters, phase-shift generalized integrators (PSGIs), etc.): These methods can suppress synchronization components within a certain steady-state speed range. Common problems with polarity switching include: polarity switching may introduce oscillations or stability risks; the suppression effect is limited near the critical speed of a rigid body; parameter adjustment depends on experience, and stability margin is not easy to guarantee. Furthermore, PSGIs have a large number of state variables, which consumes computational resources and affects real-time performance when implemented on a digital signal processor (DSP) or field-programmable gate array (FPGA).

[0006] Therefore, existing imbalance compensation techniques generally suffer from problems such as complex algorithm structure, large computational load, and limited stability coverage, which are particularly prominent in magnetic bearing systems that require high-speed real-time control. Summary of the Invention

[0007] This invention provides a radial magnetic bearing displacement vibration suppression method based on a phase-shifted reduced-order generalized integrator, aiming to solve the following problems existing in magnetic bearing imbalance compensation methods: 1) The synchronous component extraction and compensation algorithm has a large computational load, making it difficult to implement efficiently on resource-constrained DSPs / FPGAs; 2) Stability is difficult to guarantee over a wide speed range, with the risk of instability in certain speed intervals; 3) X / Y dual-channel compensation usually requires two sets of filtering / estimation structures, resulting in complex structures. This invention can be applied to vibration control and precision suspension control scenarios of magnetic levitation rotor systems such as high-speed motors, flywheel energy storage, air compressors, and aerospace rotating equipment.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] A method for suppressing radial magnetic bearing displacement vibration based on a phase-shifted reduced-order generalized integrator includes the following steps:

[0010] Step 1: Establish a model of the magnetic bearing system that includes rotor imbalance:

[0011]

[0012] In the formula, the left side of the equal sign represents the magnetic bearing force on the magnetic bearing rotor, and the right side of the equal sign represents the magnetic bearing vibration force generated by the magnetic levitation rotor under the action of rotor mass imbalance. The mass of the rotor; and These represent the translational displacements of the rotor in the X and Y axes, respectively. and These are the unbalanced forces on the rotor in the X and Y axes, respectively. This is the transfer function of the magnetic bearing displacement controller; This is the transfer function of the power amplifier; This is the gain coefficient of the displacement sensor; and These are current stiffness and displacement stiffness, respectively. For the Laplace operator;

[0013] Step 2: Based on the magnetic bearing system model in Step 1, design a phase-shifted reduced-order generalized integrator to suppress rotor synchronous displacement vibration. The specific steps are as follows:

[0014] In the magnetic bearing displacement controllers for the X and Y channels of the magnetic bearing, a phase-shifted reduced-order generalized integrator is introduced in parallel. Specifically, the displacement error signals of the X and Y channels of the magnetic bearing are used as control inputs, denoted as follows: , The displacement error signal is input to the phase-shifted reduced-order generalized integrator to obtain the corresponding compensation output signal. , Compensation output signal , With magnetic bearing displacement controller The outputs of the two amplifiers are superimposed and used together as a power amplifier. The input is used to generate a control current for driving the magnetic bearing coil, thereby producing an electromagnetic force to counteract the disturbance of rotor mass imbalance.

[0015] The transfer function of the phase-shifted reduced-order generalized integrator Represented as:

[0016]

[0017] In the formula, For the Laplace operator, The imaginary unit is used; key parameters of a phase-shifted reduced-order generalized integrator include: gain coefficient. Center frequency Phase shift angle Where: gain coefficient The center frequency determines the bandwidth and response speed of the phase-shifted reduced-order generalized integrator. Corresponding to rotor speed; phase shift angle Used to adjust the phase characteristics of the compensation channel at the synchronization frequency to meet system stability requirements;

[0018] Step 3, Phase shift angle segment selection:

[0019] By switching the phase shift angle at different speeds Ensure system stability:

[0020] Step 3-1: Perform an offline frequency scan on the system from Step 1 to obtain the system transfer function. The phase frequency characteristics, where: the rotor dynamics model is defined. System transfer function Represented as:

[0021]

[0022] Step 3-2: Determine based on stability conditions. Feasible range:

[0023]

[0024] Step 3-3: Based on stability conditions, select different speed ranges. ,make This establishes the system's stability across the entire speed domain.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] 1) Significant effect of synchronous vibration suppression: It can effectively suppress the synchronous component in the displacement signal at different speeds, significantly reducing the amplitude of rotor displacement vibration and improving suspension accuracy.

[0027] 2) Low computational load and strong real-time performance: Due to the adoption of a reduced-order structure, the required state variables are reduced, making it suitable for real-time controllers at 20kHz and higher PWM frequencies.

[0028] 3) Stability can be guaranteed over a wide speed range: through phase shift angle The introduction and segmentation selection of [the technology] enable the system to remain stable over a wider frequency range, making it suitable for both constant speed and acceleration conditions.

[0029] 4) Simple structure and easy to implement in engineering: The compensator is connected in parallel with the existing position controller without changing the original system hardware structure, which is convenient for upgrading and deployment on the existing magnetic bearing control platform. Attached Figure Description

[0030] Figure 1 The flowchart shows the implementation of a radial magnetic bearing displacement vibration suppression method based on a phase-shifted reduced-order generalized integrator.

[0031] Figure 2 This is a block diagram of the magnetic bearing X-channel control system;

[0032] Figure 3 This is a general block diagram of the phase-shifted reduced-order generalized integrator used in this invention to achieve synchronous displacement vibration suppression (and the PID controller). Parallel injection);

[0033] Figure 4 A schematic diagram of a phase-shifted, order-reduced generalized integrator.

[0034] Figure 5 The diagram shows the X / Y channel displacement waveforms before and after compensation under constant speed conditions: (a) 30Hz speed, (b) 60Hz speed, (c) 90Hz speed. Detailed Implementation

[0035] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0036] This invention provides a radial magnetic bearing displacement vibration suppression method based on a phase-shifted reduced-order generalized integrator. First, a magnetic bearing system model incorporating rotor mass imbalance is established. Then, a synchronous displacement vibration suppression algorithm based on the phase-shifted reduced-order generalized integrator is designed. Utilizing the orthogonality of the X / Y radial displacement error signals of the magnetic bearing, simultaneous extraction and compensation of the dual-channel synchronous components are achieved, reducing computational load. Finally, the system stability is analyzed, and the phase shift angle parameter is designed piecewise. This is achieved by introducing the phase shift angle... By adjusting the phase without changing the amplitude characteristics at the synchronization frequency, the stability of the system can be extended. For example... Figure 1 As shown, the specific implementation steps are as follows:

[0037] Step 1: Establish a model of the magnetic bearing system that includes rotor mass imbalance:

[0038] The system model of the magnetic bearing X channel is as follows: Figure 2 As shown, where: For magnetic bearing position controllers, a proportional-integral-derivative (PID) controller is typically used to generate control current commands based on displacement error signals; It is a power amplifier used to convert control current commands into actual magnetic bearing coil current; ( Figure 2 The portion within the box represents the rotor dynamics model, used to describe the radial motion of the rotor under the influence of coil current, and can be expressed as follows: The dynamic equation of the X-axis rotor can then be expressed as:

[0039]

[0040] In the formula, The mass of the rotor; This represents the translational displacement of the rotor along the X-axis. This represents the unbalanced force on the rotor in the X-axis direction. This is the transfer function of the magnetic bearing displacement controller; This is the transfer function of the power amplifier; This is the gain coefficient of the displacement sensor; and These are current stiffness and displacement stiffness, respectively. For the Laplace operator.

[0041] The system models of the Y-channel and X-channel magnetic bearings are basically identical, therefore the dynamic equation of the Y-axis rotor can be expressed as:

[0042]

[0043] In the formula, This represents the translational displacement of the rotor in the Y-axis direction. This represents the unbalanced force on the rotor in the Y-axis direction.

[0044] Step 2: Construction and parallel injection of the phase-shifted reduced-order generalized integrator:

[0045] Imbalance in the mass of a magnetic bearing rotor generates periodic disturbance forces synchronized with its rotational speed during rotor rotation, resulting in synchronous vibration of the rotor's radial displacement. To suppress this synchronous vibration, this invention integrates a phase-shifted, reduced-order generalized integrator with magnetic bearing displacement controllers in the X and Y channels. Parallel connection, such as Figure 3 As shown. Figure 3 Mid-displacement error input: , Due to the orthogonal nature of the displacement sensor installation, the displacement error input is: , Satisfies orthogonality. Output of the phase-shifted, reduced-order generalized integrator: , Phase-shifted reduced-order generalized integrator output and magnetic bearing displacement controller Output , The superimposed components then enter the power amplifier. .

[0046] Figure 4 The block diagram of the phase-shifted reduced-order generalized integrator is given, which utilizes the displacement error input in the radial X / Y channels. , The orthogonality relationship allows the phase-shifted, order-reduced generalized integrator to simultaneously extract the synchronous components of both channels, avoiding the need to construct two separate filters and thus reducing computational complexity. The synchronous electromagnetic force generated after the compensation current enters the magnetic bearing is opposite in direction to the unbalanced disturbance force, thereby achieving synchronous vibration suppression.

[0047] Specifically, the transfer function of the phase-shifted reduced-order generalized integrator It can be represented as:

[0048]

[0049] The key parameters of the phase-shifted reduced-order generalized integrator include: ① gain coefficient ① Determines the compensator bandwidth and convergence speed; ② Center frequency : Synchronized with the rotational speed, which can be provided by the rotational speed estimation or frequency tracking module; ③ Phase shift angle Used to adjust the system in The phase characteristics at the point ensure system stability.

[0050] The transfer function between the rotor position and the unbalanced disturbance force in the X / Y channels can be expressed as:

[0051]

[0052] When the rotor speed equals the center frequency hour:

[0053]

[0054] Therefore, the present invention can completely suppress displacement fluctuations caused by unbalanced disturbances, thereby achieving unbalanced compensation.

[0055] 3. Selection of phase shift angle segments

[0056] Since the introduction of a compensator may change the closed-loop pole distribution of the system, this invention proposes to switch the phase shift angle at different speeds. Ensure system stability:

[0057] ① Perform offline frequency sweep on the original system without a compensator to obtain the equivalent transfer function. Phase frequency characteristics (where for Figure 2 Controller output To displacement error (closed-loop transfer function)

[0058] ② Determine based on stability conditions The feasible range;

[0059] according to Figure 2 , Figure 3 and Figure 4 The system block diagram given in the figure includes the closed-loop characteristic equation of the magnetic bearing system containing the phase-shifted reduced-order generalized integrator. and equivalent transfer function It can be represented as:

[0060]

[0061] when When =0, This indicates that the starting point of the root locus is located on the imaginary axis, and that the root locus will follow... The slope of the root locus changes accordingly. To ensure system stability, all poles must lie in the left half of the complex plane. Therefore, the arctangent of the slope at the starting point must be limited to the range of π / 2 to 3π / 2, i.e.:

[0062]

[0063] Therefore, the stability condition can be expressed as:

[0064]

[0065] ③ Due to different speeds The values ​​are different, therefore different values ​​need to be selected for different speed ranges based on stability conditions. (Segmented switching) enables This establishes the system's stability across the entire speed domain.

[0066] Figure 5 (a)-(c) are schematic diagrams of the X / Y channel displacement waveforms of the rotor provided by the present invention before and after the phase shift order reduction generalized integral under constant speed conditions. The vertical axis represents the rotor displacement of the X / Y channel, and the horizontal axis represents time. Before the algorithm is applied, the rotor has large displacement fluctuations. After the algorithm is applied, it can be seen that the displacement vibration is significantly weakened.

[0067] Compared with traditional methods, the differences of this invention are: ① It adopts a reduced-order generalized integrator structure, which has fewer state variables and lower computational load, making it suitable for high-speed real-time implementation in DSP / FPGA; ② It introduces a phase shift angle. Phase advance adjustment can effectively extend the stable working range of the algorithm; ③ Utilizing the orthogonal characteristics of displacement signals, a unified realization of X / Y dual-channel synchronous compensation can be achieved, resulting in a simpler structure.

Claims

1. A method for suppressing radial magnetic bearing displacement vibration based on a phase-shifted reduced-order generalized integrator, characterized in that... The method includes the following steps: Step 1: Establish a model of the magnetic bearing system that includes rotor imbalance: In the formula, the left side of the equal sign represents the magnetic bearing force on the magnetic bearing rotor, and the right side of the equal sign represents the magnetic bearing vibration force generated by the magnetic levitation rotor under the action of rotor mass imbalance. The mass of the rotor; and These represent the translational displacements of the rotor in the X and Y axes, respectively. and These are the unbalanced forces on the rotor in the X and Y axes, respectively. This is the transfer function of the magnetic bearing displacement controller; This is the transfer function of the power amplifier; This is the gain coefficient of the displacement sensor; and These are current stiffness and displacement stiffness, respectively. For the Laplace operator; Step 2: Based on the magnetic bearing system model in Step 1, design a phase-shifted reduced-order generalized integrator to suppress rotor synchronous displacement vibration. The specific steps are as follows: In the magnetic bearing displacement controllers for the X and Y channels of the magnetic bearing, a phase-shifted reduced-order generalized integrator is introduced in parallel. Specifically, the displacement error signals of the X and Y channels of the magnetic bearing are used as control inputs, denoted as follows: , The displacement error signal is input to the phase-shifted reduced-order generalized integrator to obtain the corresponding compensation output signal. , Compensation output signal , With magnetic bearing displacement controller The outputs of the two amplifiers are superimposed and used together as a power amplifier. The input is used to generate a control current for driving the magnetic bearing coil, thereby producing an electromagnetic force to counteract the disturbance of rotor mass imbalance. Step 3, Phase shift angle segment selection: Step 3-1: Perform an offline frequency scan on the system from Step 1 to obtain the system transfer function. Phase frequency characteristics; Step 3-2: Determine based on stability conditions. Feasible range: Step 3-3: Based on stability conditions, select different speed ranges. ,make This establishes the system's stability across the entire speed domain.

2. The radial magnetic bearing displacement vibration suppression method based on a phase-shifted reduced-order generalized integrator according to claim 1, characterized in that... The transfer function of the phase-shifted reduced-order generalized integrator Represented as: In the formula, It is the imaginary unit.

3. The radial magnetic bearing displacement vibration suppression method based on a phase-shifted reduced-order generalized integrator according to claim 1, characterized in that... The key parameters of the phase-shifted reduced-order generalized integrator include: gain coefficient. Center frequency Phase shift angle Where: gain coefficient The center frequency determines the bandwidth and response speed of the phase-shifted reduced-order generalized integrator. Corresponding to rotor speed; phase shift angle Used to adjust the phase characteristics of the compensation channel at the synchronization frequency to meet system stability requirements.

4. The radial magnetic bearing displacement vibration suppression method based on a phase-shifted reduced-order generalized integrator according to claim 1, characterized in that... The system transfer function Represented as: In the formula, This is a rotor dynamics model.

5. The radial magnetic bearing displacement vibration suppression method based on a phase-shifted reduced-order generalized integrator according to claim 4, characterized in that... The .

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