Method for optimizing magnetically suspended impeller nutation mode damping based on speed adaptive phase shifter

Abstract

The application discloses a kind of based on speed adaptive phase shifter's magnetic suspension impeller nutation mode optimal damping optimization method, comprising the following steps: the dynamic model of asymmetric magnetic suspension rigid rotor system is established;Based on damping optimization theory, the optimal control phase at the frequency near nutation mode is quantitatively solved;The wave-trap parameters of general wave-trap and improved double-T wave-trap are accurately designed, and the same frequency vibration and modal vibration are accurately suppressed;The actual lag phase in the internal of magnetic bearing closed-loop control system is obtained, combined with optimal control phase, and the optimal compensation phase is calculated;Qualitative analysis of the influence of the parameters of phase shifter on its amplitude-phase frequency characteristic;Based on optimal compensation phase, introduce phase shifter;Add speed-based phase shifter parameter adaptive adjustment algorithm.The application has the advantages of simple principle and high reliability, and can effectively suppress the elastic vibration mode in a wide range of full speed based on ensuring that the nutation mode has optimal damping.

Description

Technical Field

[0001] This invention belongs to the field of magnetic levitation bearing control technology, and in particular relates to an optimal damping optimization method for the nutation mode of a magnetic levitation impeller based on a speed adaptive phase shifter. Background Technology

[0002] Magnetic levitation bearings, as a novel contactless support component, offer advantages over traditional mechanical bearings, including oil-free operation, frictionless operation, active vibration control, high permissible speed, minimal vibration, long lifespan, and low energy consumption. They have achieved significant advantages in high-speed, high-power-density rotating machinery and have been successfully applied in aerospace (e.g., magnetic levitation flywheels, magnetic levitation control torque gyroscopes) and power systems (e.g., high-speed turbomachinery such as turbopumps, compressors, and blowers). Traditional mechanical bearing molecular pumps, due to their high vibration and noise levels and oil diffusion contamination, struggle to meet the requirements of ultra-clean, ultra-high vacuum, and quiet environments. Magnetic levitation molecular pumps, as a highly clean, high-performance, and ultra-energy-efficient vacuum acquisition device, have become a key component in high-end scientific instruments and equipment designed to achieve ultra-high vacuum environments.

[0003] The main performance characteristics of magnetically levitated molecular pumps are high pumping speed and high compression ratio. However, the upper limit of rotational speed largely determines the limits of these two characteristics. Therefore, breaking through the upper limit of rotational speed is of great practical significance for improving the performance of magnetically levitated molecular pumps and the future development of my country's vacuum industry. Due to the characteristics of magnetically levitated molecular pumps, such as high rated speed, strong gyroscopic effect, and thin-bladed structure, and the highly complex dynamic characteristics of their turbine rotors, including not only rigid eddy mode (such as nutation and precession modes) caused by gyroscopic effect, but also elastic vibration modes (such as bending mode and blade mode), the instability of nutation mode at high speed becomes the main factor limiting further increases in the rotational speed of the magnetically levitated rotor. The direct cause of nutation mode instability is the excessive phase lag in the high-frequency range of the control system. The higher the nutation frequency, the greater the phase lag, and the worse the system stability. Because the magnetic bearing closed-loop control system has phase delay (such as in power amplifiers and filters) and integral components, both rigid eddy mode and elastic vibration mode become unstable at high speeds due to low damping. Unstable modes are very easily excited by vibrations of the same frequency or harmonics, causing modal oscillations. Modal oscillations will cause the magnetic levitation rotor to vibrate violently and significantly, causing it to fall and collide with the protective bearing, which can lead to rotor instability in severe cases. When instability occurs, the violent and large-amplitude vibration of the rotor will directly affect the working performance and service life of the magnetic levitation molecular pump, causing irreversible damage to the entire system and resulting in serious economic losses.

[0004] Currently, most methods for suppressing non-stationary states caused by the elastic vibration modes of magnetically levitated molecular pumps primarily employ notch filters. However, for turbine rotors with asymmetric structures and relatively large moment of inertia ratios, the backward eddy frequency of the rotor's first-order bending mode and the nutation mode frequency intersect at high speeds. Therefore, the phase lag angle introduced by the notch filter easily causes instability in the nutation mode. Thus, there is an urgent need to achieve effective suppression of elastic vibration modes across a wide range of speeds without compromising the stability of the nutation modes. Summary of the Invention

[0005] To effectively suppress elastic vibration modes across a wide range of speeds while ensuring optimal damping of the nutation mode, this invention provides an optimal damping optimization method for the nutation mode of a magnetic levitation impeller based on a speed-adaptive phase shifter. The method utilizes the speed-adaptive phase shifter to implement speed-based adaptive compensation for the phase lag angle of the magnetic bearing closed-loop control system.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The optimal damping optimization method for the nutation mode of a magnetic levitation impeller based on a speed-adaptive phase shifter includes the following steps:

[0008] Step A: Establish a dynamic model of the asymmetric magnetically levitated rigid rotor system based on the magnetically levitated molecular pump;

[0009] Step B: Calculate the optimal control phase θ at the frequency near the nutation mode based on damping optimization theory.

[0010] Step C: Precisely design a general-purpose notch filter, improve the notch parameters of the double-T notch filter, and accurately suppress both co-frequency vibration and modal vibration respectively;

[0011] Step D: The phase lag angle of the notch filter is obtained directly through Bode plot, the phase lag angle of the power amplifier is obtained by frequency sweep detection, the actual lag phase inside the magnetic bearing closed-loop control system is recorded as θ′, and the optimal compensation phase θ0 is calculated by combining the optimal control phase θ.

[0012] Step E: Qualitatively analyze the influence of various parameters of the phase shifter on its amplitude and phase frequency characteristics;

[0013] Step F: Based on the calculation results of the optimal compensation phase θ0, quantitatively calculate each parameter of the phase shifter and introduce it into the phase shifter;

[0014] Step G: Add an adaptive adjustment algorithm for phase shifter parameters based on rotational speed.

[0015] Furthermore, in step B, the process of obtaining the optimal control phase θ includes:

[0016] The controller model is G c (s), the power amplifier model is G a (s), the rotor model is G r (s), the sensor model is G s (s);

[0017] The unbalanced disturbance torque is D(s) = m d rs 2 =ds 2 m d is the unbalanced mass; r is the distance vector from the unbalanced mass to the rotor axis of rotation; d is the unbalanced mass moment; s is the independent variable in the transfer function, called the complex frequency;

[0018] The frequency response from the unbalanced mass moment d to the nutation amplitude C(s), i.e., the unbalanced response, is as follows:

[0019]

[0020] In order to analyze the frequency characteristics of the transfer function in the frequency domain, let s = jw, where j is the imaginary unit and w is the imaginary part;

[0021] The frequency response from nutation amplitude C(s) to electromagnetic force F(s) is as follows:

[0022]

[0023] Where A(w) is the magnitude of the transfer function. The phase magnitude of the transfer function;

[0024] Assume that near the nutation mode frequency, A(w) is independent of w and takes the value of a constant A, i.e., the controller gain coefficient. It is independent of w and takes the value of That is, the phase angle coefficient of the controller, then the above formula becomes:

[0025]

[0026] make The frequencies of magnitude w1 and w are obtained. 2，3 The nutation mode frequency is the forward whirling frequency of the rotor's rigid whirling mode, therefore, G′ cd The peak frequency of (jw) is G′ cd The peak value of (jw) is The frequency at the peak value. The magnitude of the peak value;

[0027] The principle for determining the controller gain coefficient is: when the rotor's nutation amplitude is at its maximum allowable value, i.e., when the rotor's vibration is half of the saturation gap, the magnetic bearing provides the maximum control force F. max The controller gain coefficient is defined as follows: φ s1 φ s2 φ is the nutation amplitude at the sensor location. p x represents the nutation amplitude at the B-end protective bearing. p To protect the radial unilateral protective clearance of the bearing;

[0028] With a constant controller gain coefficient, let Solving This is the control phase when the rotor nutation amplitude is minimized, which is also the optimal control phase at the frequency near the nutation mode, denoted as .

[0029] Furthermore, the process of designing a general-purpose notch filter in step C includes:

[0030] The same-frequency notch filter is designed as a general-purpose notch filter, connected in series with the controller, and its transfer function is:

[0031]

[0032] The notch filter parameters are designed according to the following formula:

[0033]

[0034] Where Ω is the rotor speed, i.e., the center frequency of the general-purpose notch filter, and its notch frequency changes synchronously with the rotor speed; l depth Δf is the notch depth in dB; Δf is the notch width in Hz; B w ε is the notch bandwidth; ε is the bandwidth factor; Q1 is the first quality factor;

[0035] The second-order notch filter with a fixed center frequency is designed as an improved double-T notch filter, connected in series with the controller, and its transfer function is...

[0036] The notch filter parameters are designed according to the following formula:

[0037]

[0038] Among them, w f To improve the center frequency of the double-T notch filter, ζ is the depth parameter and k is the width parameter; depth Δf is the notch depth in dB; Δf is the notch width in Hz; B w Q1 is the notch bandwidth; Q2 is the second quality factor.

[0039] Furthermore, the process of obtaining the actual lag phase θ′ in step D includes:

[0040] The power amplifier model is frequency swept, and a sinusoidal excitation signal is added at the reference displacement of the program. The input test point is the controller output, and the output test point is the sampled value of the current signal.

[0041] Based on the Bode plot of the notch filter and the sweep frequency plot of the power amplifier, the actual hysteresis phase θ′ inside the magnetic bearing closed-loop control system is obtained.

[0042] Furthermore, the process of obtaining the optimal compensation phase θ0 in step D includes:

[0043] Obtain the controller model G c The phase lead angle provided by (s) is combined with the obtained optimal control phase θ and actual lag phase θ′ to calculate the optimal compensation phase θ0 that the phase shifter needs to provide at the frequency near the nutation mode.

[0044] Furthermore, the design process of the phase shifter in step F includes:

[0045] First, a zero-pole phase shifter is used:

[0046]

[0047] Among them, K f is the scaling factor; w1 and w1* are a pair of conjugate zeros; w2 and w2* are a pair of conjugate poles; i is the imaginary unit;

[0048] Then, let Transforming a zero-pole phase shifter into a general-type phase shifter:

[0049]

[0050] Let a1 = a2 = a, the center frequency (compensation frequency) be c, the compensation interval be (b1 = cb, b2 = c + b), and the width of the compensation interval be b2 - b1 = 2b. Solving these values, we obtain the parameters for the general form of the phase shifter:

[0051]

[0052] The physical parameters of a typical phase shifter are calculated and solved as follows:

[0053] (1) Compensation interval: (cb, c+b)

[0054] (2) Center frequency and compensated frequency: c

[0055] (3) Phase lead angle:

[0056] c is determined based on the center frequency and the compensation frequency, b is determined based on the compensation interval, and a is determined based on the phase lead angle.

[0057] Based on the above analysis, constraints on the phase shifter parameters are designed, and an adaptive adjustment algorithm for the phase shifter parameters based on rotational speed is added to achieve adaptive phase compensation based on rotational speed.

[0058] The technical effects of this invention are as follows:

[0059] (1) Regarding notch filters: Unlike the rough design of notch filter parameters based on engineering experience, this invention performs precise design of notch filter parameters based on parameter definitions, realizing qualitative analysis and quantitative calculation of notch filter parameters. It effectively solves the problem of notch filter parameters being difficult to tune, facilitates trade-offs between notch filter parameters to take into account the dynamic and static responses of the system, and achieves a balance in notch filter performance.

[0060] (2) Regarding phase shifters: Characteristic analysis and parameter design were performed on both zero-pole type and general type phase shifters. A phase shifter with a specific structure was introduced, and an adaptive adjustment algorithm for phase shifter parameters based on rotational speed was added. The parameter design of the phase shifter meets the actual requirements of the magnetic bearing closed-loop control system for the compensation range and phase lead angle at frequencies near the nutation mode. It can accurately perform phase compensation for specific frequency bands without adversely affecting other frequency bands.

[0061] (3) Overall design: This invention effectively suppresses elastic vibration modes across a wide range of speeds without affecting the stability of the nutation modes. To address the phase lag in the magnetic bearing closed-loop control system, adaptive phase compensation based on rotational speed is implemented, ensuring optimal phase margin at frequencies near the nutation modes and achieving optimal damping control of the nutation modes. Attached Figure Description

[0062] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0063] Figure 1 This is a flowchart of the optimal damping method for the nutation mode of a magnetic levitation impeller based on a speed adaptive phase shifter in an embodiment of the present invention.

[0064] Figure 2 This is a block diagram of the magnetic bearing control system in an embodiment of the present invention;

[0065] Figure 3a , Figure 3b This is a schematic diagram illustrating the working principle of the notch filter in an embodiment of the present invention; wherein, Figure 3a This is a schematic diagram of the working principle of a general-purpose notch filter. Figure 3b To improve the working principle diagram of the double-T notch filter;

[0066] Figure 4a , Figure 4b This is a Bode plot showing the amplitude-phase frequency response of the notch filter in an embodiment of the present invention; wherein, Figure 4a The amplitude-frequency and phase-frequency characteristic curves of a traditional notch filter are shown. Figure 4b To improve the amplitude-frequency and phase-frequency response curves of the double-T notch filter;

[0067] Figure 5 This is a schematic diagram of the power amplifier frequency sweep principle in an embodiment of the present invention;

[0068] Figure 6a , Figure 6b The Bode plot shows the amplitude-phase frequency response of the phase shifter; where, Figure 6a Given Kf = 1, a1 + a2 = 10, b1 = 16, b2 = 24, and simultaneously varying a1 and a2, the amplitude-frequency and phase-frequency characteristic curves of the phase shifter are as follows: Figure 6b The amplitude-frequency and phase-frequency characteristic curves of the phase shifter when Kf = 1, a1 = a2 = 2, b1 + b2 = 40 or b1 + b2 = 64, and b1 and b2 are changed simultaneously. Detailed Implementation

[0069] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0070] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0071] Example 1

[0072] like Figure 1 As shown, this embodiment provides a method for optimizing the optimal damping of the nutation mode of a magnetic levitation impeller based on a speed-adaptive phase shifter, including the following steps:

[0073] Step 1: Perform dynamic modeling of the magnetically levitated rigid rotor system for the asymmetric structure of the magnetically levitated molecular pump.

[0074] Step 2: From the perspective of optimal phase compensation, analyze the feasibility and effectiveness of nutation mode vibration suppression. Based on damping optimization theory, quantitatively calculate the optimal control phase θ at the frequency near the nutation mode.

[0075] Step 3: Introduce a general-purpose notch filter and an improved double-T notch filter to suppress co-frequency vibration and modal vibration respectively. Perform qualitative analysis and quantitative calculation of the notch filter parameters to reduce the phase lag angle introduced by the notch filter.

[0076] Step 4: Obtain the phase lag angle introduced by the notch filter directly through the Bode plot of the notch filter, obtain the phase lag angle introduced by the power amplifier through frequency sweep detection, obtain the actual lag phase θ′ inside the magnetic bearing closed-loop control system, and calculate the optimal compensation phase θ0 by combining the optimal control phase θ.

[0077] Step 5: Analyze the influence of the phase shifter parameters on its amplitude and phase frequency characteristics.

[0078] Step 6: Based on the calculation results of the optimal compensation phase θ0, design a phase shifter with a specific structure.

[0079] Step 7: Add a rotational speed-based adaptive adjustment algorithm for phase shifter parameters. First, achieve optimal phase compensation for the nutation mode at a fixed rotational speed. Then, ensure optimal phase margin of the nutation mode at different rotational speeds, and finally achieve optimal damping control of the nutation mode over a wide range of rotational speeds.

[0080] like Figure 2 The diagram shown is a block diagram of the magnetic bearing control system in this embodiment. The maximum electromagnetic torque provided by the magnetic bearing (the product of the maximum bearing capacity and the rotor displacement at the bearing) must be greater than the unbalanced disturbance for the rotor to accelerate smoothly. How the magnetic bearing provides the corresponding electromagnetic torque to the rotor is the main task of the control system. For example... Figure 2 As shown, the controller first calculates the corresponding control quantity based on the rotor displacement detected by the sensor. Then, a certain control current is supplied to the coil through a power amplifier, and finally, the magnetic bearing converts it into the required electromagnetic force. Therefore, the parameters of the controller and the power amplifier play a crucial role in the generation of electromagnetic force.

[0081] The controller model (i.e., the transfer function) is Gc(s), and the power amplifier model is G... a (s), the rotor model (the transfer function from the magnetic bearing coil current to the rotor nutation amplitude) is G r (s), the sensor model is G s (s).

[0082] The unbalanced disturbance torque is:

[0083] D(s)=m d rs 2 =ds 2

[0084] Where, m dis the unbalanced mass; r is the distance vector from the unbalanced mass to the rotor axis of rotation; d is the unbalanced mass moment. s is the independent variable in the transfer function, called the complex frequency.

[0085] The transfer function from the unbalanced disturbance torque D(s) to the nutation amplitude C(s) is:

[0086]

[0087] The transfer function from the unbalanced mass moment d to the nutation amplitude C(s) is:

[0088]

[0089] The frequency response (i.e., unbalanced response) from the unbalanced mass moment d to the nutation amplitude C(s) is as follows:

[0090]

[0091] In order to analyze the frequency characteristics of the transfer function in the frequency domain, let s = jw, where j is the imaginary unit and w is the imaginary part;

[0092] The transfer function from the nutation amplitude C(s) to the electromagnetic force F(s) is:

[0093]

[0094] The frequency response from nutation amplitude C(s) to electromagnetic force F(s) is as follows:

[0095]

[0096] Where A(w) is the magnitude of the transfer function. The phase magnitude of the transfer function.

[0097] The nutation mode frequency is the product of the rotor speed and the ratio of rotor moment of inertia. Therefore, for a constant speed, the range of variation of the nutation mode frequency is relatively narrow. That is, the frequency characteristic from the nutation amplitude C(s) to the electromagnetic force F(s) changes very little near the nutation mode frequency. Let's assume that near the nutation mode frequency, A(w) is independent of w and takes a constant value A, i.e., the controller gain coefficient. It is independent of w and takes the value of That is, the phase angle coefficient of the controller, then the above formula can be simplified to:

[0098]

[0099] In summary, we can obtain G′ cd (jw). Order The frequencies can be obtained as w1 and ω. 2，3The nutation mode frequency is the forward whirling frequency of the rotor's rigid whirling mode, therefore G′ cd The peak frequency of (jw) is G′ cd The peak value of (jw) is in, The frequency at the peak value. This represents the magnitude of the peak value.

[0100] The principle for determining the controller gain coefficient is: when the rotor's nutation amplitude is at its maximum allowable value (the rotor's vibration is half of the saturation gap), the magnetic bearing can provide the maximum control force F. max At this point, the power amplifier is just approaching saturation but not yet saturated. The controller gain coefficient at this point is defined as:

[0101]

[0102] φ s1 φ s2 φ is the nutation amplitude at the sensor location. p x represents the nutation amplitude at the B-end protective bearing. p To protect the radial unilateral protective clearance of the bearing.

[0103] With a constant controller gain coefficient, let Solving This is the control phase when the rotor nutation amplitude is minimized, which is also the optimal control phase at the frequency near the nutation mode, denoted as .

[0104] Figure 3a , Figure 3b This is a schematic diagram illustrating the working principle of the notch filter in this embodiment. Figure 3a This is a schematic diagram of the working principle of a general-purpose notch filter. Figure 3b The working principle diagram for improving the double-T notch filter.

[0105] The same-frequency notch filter is designed as a general-purpose notch filter, connected in series with the controller, and its transfer function is:

[0106]

[0107] The notch filter parameters are designed according to the following formula:

[0108]

[0109] Where Ω is the rotor speed, i.e., the center frequency of the general-purpose notch filter, and its notch frequency changes synchronously with the rotor speed; l depth Δf is the notch depth in dB; Δf is the notch width in Hz; B wLet ε be the notch bandwidth; ε be the bandwidth factor; and Q1 be the first quality factor. A larger Q1 results in more precise notch filtering while minimizing phase lag in the system. Note that the notch depth of a general-purpose notch filter is always infinite.

[0110] The second-order notch filter with a fixed center frequency is designed as an improved double-T notch filter, connected in series with the controller, and its transfer function is:

[0111]

[0112] The notch filter parameters are designed according to the following formula:

[0113]

[0114] Among them, w f To improve the center frequency of the double-T notch filter, ζ is the depth parameter, and k is the width parameter. Where, l depth Δf is the notch depth in dB; Δf is the notch width in Hz; B w ζ represents the notch bandwidth; Q2 is the second quality factor. When k is constant, decreasing ζ increases the notch depth and slightly widens the notch width; when ζ is constant, decreasing k keeps the notch depth constant but narrows the notch width. By adjusting ζ and k respectively, the ideal notch effect can be achieved. A larger Q2 results in more precise notch filtering and less phase lag, but the notch depth also decreases slightly, and the convergence speed slows down.

[0115] Figure 4a , Figure 4b This is a comparison diagram of the amplitude, phase, and frequency characteristics of the notch filter in this embodiment. Figure 4a Traditional notch filter The amplitude-frequency and phase-frequency characteristic curves, where w n The center frequency of a conventional notch filter is given, and k1 and k2 are two notch filter parameters. Figure 4b To improve the double-T notch filter The amplitude-frequency and phase-frequency characteristic curves are shown. Analysis of the Bode plot reveals that for traditional notch filters, increasing the notch depth leads to faster convergence and a significantly wider notch width, resulting in faster response but poorer point resistance. Conversely, decreasing the notch width improves filtering specificity but slows response, and a significantly shallower notch depth further slows convergence. Traditional notch filters cannot independently adjust notch width and depth; however, the improved double-T notch filter achieves decoupling between these two parameters.

[0116] Figure 5This is a schematic diagram of the power amplifier model frequency sweep principle in this embodiment of the invention. The power amplifier model is frequency swept, with a sinusoidal excitation signal added at the reference displacement in the program. The input test point is the controller output, and the output test point is the sampled value of the current signal. Based on the Bode plot of the notch filter and the frequency sweep diagram of the power amplifier, the actual hysteresis phase θ′ inside the magnetic bearing closed-loop control system can be obtained. First, the controller calculates the corresponding control voltage based on the rotor displacement detected by the sensor. Then, a certain control current is provided to the coil winding through the power amplifier, and finally, the electromagnet converts this into the required electromagnetic force acting on the rotor system.

[0117] Figure 6a , Figure 6b This is the Bode plot of the amplitude-phase frequency response of the phase shifter. All types of phase shifters are fundamentally the same in principle, utilizing their phase-leading and gain-attenuating frequency bands to compensate for the system's phase. For ease of characteristic analysis, a zero-pole type phase shifter is used, whose transfer function is derived from a pair of conjugate zeros (w1, w2). i *), a pair of conjugate poles (w2, w2*), and the scaling factor K f constitute:

[0118]

[0119] Currently, the parameter design of phase shifters mainly relies on engineering experience, lacking consideration of a1, b1, a2, b2, and K. f Qualitative analysis and quantitative calculation.

[0120] The physical parameters of the phase shifter are defined as follows:

[0121] (1) Compensation interval: the frequency range between b1 and b2;

[0122] (2) Center frequency: The frequency at the midpoint of the compensation interval;

[0123] (3) Compensation frequency: The frequency corresponding to the maximum phase lead angle within the compensation interval;

[0124] (4) Phase lead angle: the phase corresponding to the peak value of the phase frequency response curve.

[0125] Figure 6a Given Kf = 1, a1 + a2 = 10, b1 = 16, b2 = 24, and simultaneously varying a1 and a2, the amplitude-frequency and phase-frequency characteristic curves of the phase shifter are as follows: The smaller a1 is, the deeper the trough on the left side of the amplitude-frequency characteristic curve (i.e., the more significant the gain attenuation), the lower the peak on the right side (i.e., the smaller the high-frequency gain), and the steeper the slope on the left side of the phase-frequency characteristic curve (i.e., the larger the phase lag angle introduced to the left side of the compensation interval). The smaller a2 is, the shallower the trough on the left side of the amplitude-frequency characteristic curve, the higher the peak on the right side, and the steeper the slope on the right side of the phase-frequency characteristic curve.

[0126] The larger the difference between a1 and a2, the larger the maximum phase lead angle that can be provided within the compensation interval. When the difference between a1 and a2 is equal, a1 < a2 provides a larger maximum phase lead angle than a1 > a2. When a1 < a2, the phase lag angle introduced on the left side of the compensation interval is smaller than the phase lag angle introduced on the right side of the compensation interval when a1 > a2. The gain attenuation and high-frequency gain are more ideal when a1 < a2 than when a1 > a2.

[0127] In summary, the smaller a1 is, the larger the maximum phase lead angle that the phase frequency response curve can provide within the compensation interval, but the phase lag angle introduced to the left side of the compensation interval will also increase. In other words, there is a contradiction between the maximum phase lead angle that the phase shifter can provide and the potential phase lag angle: considering only the potential phase lag angle, the closer a1 and a2 are, the better; when a1 = a2, the entire phase frequency response curve is above 0°. Considering only the maximum phase lead angle that can be provided, the larger the difference between a1 and a2, the better. If the difference between a1 and a2 is equal, then a1 < a2 is better than a1 > a2.

[0128] Figure 6b The amplitude-frequency and phase-frequency characteristic curves of the phase shifter are given when Kf = 1, a1 = a2 = 2, b1 + b2 = 40 or b1 + b2 = 64, and b1 and b2 are varied simultaneously. When b1 + b2 = b1' + b2', the center frequency is the same. When b2 - b1 = b2' - b1', the width of the compensation interval is the same, but the position of the compensation interval is not necessarily the same.

[0129] Based on the above analysis, we can conclude that: a1 and a2 determine the maximum phase lead angle that can be provided within the compensation interval, that is, the magnitude of the phase lead angle at the compensation frequency; b1 and b2 determine the magnitude of the center frequency, the width and position of the compensation interval.

[0130] Because the phase frequency response curve has poor symmetry when a1 and a2 differ significantly, a large phase lag is introduced on one side of the compensation interval, which contradicts the original intention of the phase shifter to suppress vibration by providing phase lead. Therefore, this invention sets a1 = a2 = a and c - b1 = b2 - c. At this point, the center frequency and the compensation frequency coincide, and the phase frequency response curve is above 0°. In practical applications of the phase shifter, K is determined based on the designed a1, b1, a2, and b2. f Its gain in the low-frequency range is generally less than 0dB. If it is directly connected in series with the magnetic bearing closed-loop control system, it will reduce the low-frequency gain of the system and affect the low-frequency stability of the system. Therefore, this invention makes K f >1, making the low-frequency gain of the phase shifter equal to 0dB.

[0131] To facilitate parameter design, let

[0132] Zero-pole phase shifter converted to general form:

[0133]

[0134] Let it satisfy the above constraints, a1=a2=a, the center frequency (i.e., the compensation frequency) is c, the compensation interval is (b1=cb, b2=c+b), and the compensation interval width is b2-b1=2b. Solving these conditions, we obtain the parameters of the general form phase shifter as follows:

[0135]

[0136] The phase shifter designed according to the above requirements has a center frequency and a compensation frequency that coincide, a phase frequency characteristic curve above 0°, and a symmetrical amplitude and phase frequency characteristic curve. It has a small impact on the stability of the magnetic bearing closed-loop control system and is easy to tune the phase shifter parameters.

[0137] The physical parameters of a typical phase shifter are calculated and solved as follows:

[0138] (1) Compensation interval: (cb, c+b)

[0139] (2) Center frequency and compensated frequency: c

[0140] (3) Phase lead angle:

[0141] First, determine c based on the center frequency and the compensation frequency; second, determine b based on the compensation interval; and finally, determine a based on the phase lead angle.

[0142] Based on the above analysis, by designing constraints on the phase shifter parameters and adding an adaptive phase shifter parameter adjustment algorithm based on rotational speed, adaptive phase compensation based on rotational speed can be achieved.

[0143] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for optimizing the optimal damping of the nutation mode of a magnetic levitation impeller based on a speed-adaptive phase shifter, characterized in that, Includes the following steps: Step A: Establish a dynamic model of the asymmetric magnetically levitated rigid rotor system based on the magnetically levitated molecular pump; Step B: Quantitatively calculate the optimal control phase at frequencies near the nutation mode based on damping optimization theory. ; Step C: Precisely design a general-purpose notch filter, improve the notch parameters of the double-T notch filter, and accurately suppress both co-frequency vibration and modal vibration respectively; The process of designing and improving the double-T notch filter is as follows: The second-order notch filter with a fixed center frequency is designed as an improved double-T notch filter, connected in series with the controller, and its transfer function is... ; The notch filter parameters are designed according to the following formula: ； in, To improve the center frequency of the double-T notch filter, For depth parameters, For width parameters; Notch depth, in units of ; Notch width, in units of ; Notch bandwidth; It is the second quality factor; Step D: Directly obtain the phase lag angle of the notch filter through the Bode plot, obtain the phase lag angle of the power amplifier through frequency sweep detection, and record the actual lag phase inside the magnetic bearing closed-loop control system as . Combined with optimal control phase The optimal compensation phase is calculated. ; Step E: Qualitatively analyze the influence of various parameters of the phase shifter on its amplitude and phase frequency characteristics; Step F, based on the optimal compensation phase The calculation results are used to quantitatively calculate the various parameters of the phase shifter and introduce them into the phase shifter; Step G: Add an adaptive adjustment algorithm for phase shifter parameters based on rotational speed.

2. The optimal damping optimization method for the nutation mode of a magnetic levitation impeller based on a speed adaptive phase shifter according to claim 1, characterized in that, In step B, the optimal control phase is obtained. The process includes: The controller model is The power amplifier model is The rotor model is The sensor model is ; Unbalanced disturbance torque is , It is an unbalanced mass; It is the distance vector from the unbalanced mass to the rotor's axis of rotation; It is an unbalanced mass moment; The independent variable in the transfer function is called the complex frequency; From unbalanced mass moment To nutation amplitude The frequency characteristics, i.e., the unbalanced response, are: ； In order to analyze the frequency characteristics of the transfer function in the frequency domain, let ,in, The imaginary unit, The imaginary part; from the nutation amplitude To electromagnetic force The frequency characteristics are: ； in, The magnitude of the transfer function. The phase magnitude of the transfer function; Assuming that near the nutation mode frequency, and It is irrelevant and takes the value of a constant. That is, the controller gain coefficient. and Irrelevant, and takes the value That is, the phase angle coefficient of the controller, then the above formula becomes: ； make To obtain the frequency magnitude The nutation mode frequency is the forward whirling frequency of the rotor's rigid whirling mode, therefore, The peak frequency is , The peak value is ; The frequency at the peak value. The magnitude of the peak value; The principle for determining the controller gain coefficient is: when the rotor's nutation amplitude is at its maximum allowable value, i.e., when the rotor's vibration is half of the saturation gap, the magnetic bearing provides the maximum control force. The controller gain coefficient is defined as follows: , , The nutation amplitude at the sensor location. for Nutting amplitude at the end protection bearing To protect the radial unilateral protective clearance of the bearing; With a constant controller gain coefficient, let Solving for This is the control phase when the rotor nutation amplitude is minimized, which is also the optimal control phase at the frequency near the nutation mode, denoted as . .

3. The optimal damping optimization method for the nutation mode of a magnetic levitation impeller based on a speed adaptive phase shifter according to claim 2, characterized in that, The process of designing a general-purpose notch filter in step C includes: The same-frequency notch filter is designed as a general-purpose notch filter, connected in series with the controller, and its transfer function is... ; The notch filter parameters are designed according to the following formula: ； in, The rotor speed is the center frequency of the general-purpose notch filter, and its notch frequency changes synchronously with the rotor speed. Notch depth, in units of ; Notch width, in units of ; Notch bandwidth; It is the bandwidth factor; It is the first quality factor.

4. The optimal damping optimization method for the nutation mode of a magnetic levitation impeller based on a speed adaptive phase shifter according to claim 3, characterized in that, In step D, the actual lag phase is obtained. The process includes: The power amplifier model is frequency swept, and a sinusoidal excitation signal is added at the reference displacement of the program. The input test point is the controller output, and the output test point is the sampled value of the current signal. Based on the Bode plot of the notch filter and the frequency sweep plot of the power amplifier, the actual hysteresis phase inside the magnetic bearing closed-loop control system is obtained. .

5. The optimal damping optimization method for the nutation mode of a magnetic levitation impeller based on a speed adaptive phase shifter according to claim 4, characterized in that, In step D, the optimal compensation phase is obtained. The process includes: Obtain the controller model The provided phase lead angle, combined with the obtained optimal control phase Actual lag phase The optimal compensation phase that the phase shifter needs to provide at frequencies near the nutation mode is calculated. .

6. The optimal damping optimization method for the nutation mode of a magnetic levitation impeller based on a speed adaptive phase shifter according to claim 5, characterized in that, The design process of the phase shifter in step F includes: First, a zero-pole phase shifter is used: ； in, It is a scaling factor; , They are a pair of conjugate zeros; , These are a pair of conjugate poles; i is the imaginary unit; Then, let , , , , The zero-pole phase shifter is transformed into a general-type phase shifter: ； Pick The center frequency, also known as the compensation frequency, is The compensation range is The width of the compensation interval is The parameters of the general form phase shifter are obtained as follows: ； The physical parameters of a typical phase shifter are calculated and solved as follows: (1) Compensation range: ; (2) Center frequency and compensated frequency: ; (3) Phase lead angle: ; Determined based on center frequency and compensation frequency Determined based on the compensation range Determined based on the phase lead angle ; Based on the above analysis, constraints on the phase shifter parameters are designed, and an adaptive adjustment algorithm for the phase shifter parameters based on rotational speed is added to achieve adaptive phase compensation based on rotational speed.

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