A magnetic bearing rotor unbalance vibration compensation method based on quadrature demodulation

Abstract

The application discloses a magnetic bearing rotor unbalance vibration compensation method based on orthogonal demodulation, and belongs to the technical field of active vibration control of magnetic bearings. The application first calibrates a phase zero position, establishes a rotor displacement signal model, generates a same-frequency and same-phase orthogonal reference signal through a SOGI / EPLL single-phase phase-locked loop, extracts a direct current component through frequency mixing and first-order IIR adaptive low-pass filtering, and solves an unbalance amplitude and a spatial phase angle; a reverse feedforward signal is constructed and superimposed to a PID controller output; a minimum amplitude optimization method is used for offline calibration, online table lookup interpolation compensation link phase lag; a phase-locked loop tracks a rotating speed in real time, and adaptively updates filter coefficients, a reference frequency and a phase compensation amount. The application can accurately extract a phase and dynamically compensate a phase lag only by relying on an original displacement sensor, adaptively suppresses a same-frequency vibration under a wide rotating speed, is stable in control, high in precision, simple in algorithm, and easy to realize digitalization on a DSP and an FPGA.

Description

Technical Field

[0001] This invention relates to the field of active vibration control technology for magnetic levitation bearings, specifically to a method for compensating for unbalanced vibration of a magnetic bearing rotor based on orthogonal demodulation. Background Technology

[0002] This invention relates to the field of active vibration control technology for magnetic levitation bearings. Magnetic bearings rely on electromagnetic force to achieve rotor levitation support without mechanical contact, offering advantages such as no wear, no lubrication, high speed, and long lifespan. They are widely used in high-end equipment fields such as high-speed motors, centrifugal compressors, aerospace turbomachinery, and energy storage flywheels. During rotor operation, inconsistencies in material properties and machining / assembly deviations inevitably lead to mass imbalances, causing periodic vibrations at the same frequency as the rotor speed. These vibrations exacerbate stator-rotor coupling disturbances, reduce system levitation accuracy, induce overall machine noise and structural fatigue, and in severe cases, cause magnetic bearing system instability and high-speed equipment shutdown. Therefore, high-precision suppression of unbalanced vibrations at the same frequency of the magnetic bearing rotor is a core technical requirement in the field of magnetic bearing control.

[0003] Currently, the mainstream technologies for suppressing co-frequency vibration in magnetic bearings mainly fall into three categories: First, PID direct displacement feedback control in a fixed coordinate system, where the controller directly calculates and outputs control force based on the rotor radial displacement amplitude collected by the displacement sensor, only adjusting the vibration amplitude in a closed loop without distinguishing between the frequency components and phase characteristics of the vibration signal. Second, a feedforward compensation scheme that adds keyway slots or photoelectric sensors, where keyway slots and reflective strips are set on the rotor body, and a reference pulse is output by the sensor every revolution. This pulse is used to estimate the rotor angle and attempt to construct a feedforward compensation signal. Third, a fixed-parameter notch filter is connected in series in the control loop, setting the center frequency to the rotor speed frequency to attenuate the amplitude of the co-frequency vibration component. While these existing technologies can achieve a certain degree of vibration suppression under normal operating conditions, they still have many inherent technical defects in practical engineering applications, which have long constrained the improvement of high-precision, high-reliability, and all-condition vibration reduction control performance of magnetic bearings.

[0004] First, existing conventional PID control processes displacement time-domain signals only in a fixed rectangular coordinate system. It can only identify the magnitude of vibration amplitude and cannot accurately extract the instantaneous phase of rotor unbalanced vibration and the spatial azimuth angle of unbalanced mass. The controller cannot generate a compensating control force opposite to the unbalanced force in a directional manner and can only achieve passive amplitude suppression. It is difficult to counteract the same-frequency vibration force from the root, resulting in a low upper limit for vibration reduction accuracy.

[0005] Secondly, existing phase sensing and feedforward compensation schemes heavily rely on additional hardware such as keyway and photoelectric sensors. Keyway must be machined on the rotor structure or reflective detection components must be added, which not only increases machining costs, hardware costs and on-site installation and debugging complexity, but also makes photoelectric and contact phase sensors prone to failure and aging under harsh conditions such as high speed, ultra-high speed, high temperature radiation, oil mist and dust, and fully sealed cavities. Some small and sealed rotor structures even have no space to install additional phase detection sensors, which greatly limits the applicable scenarios.

[0006] Furthermore, the magnetic bearing control system consists of multiple cascaded components such as displacement sensors, signal conditioning circuits, power amplifiers, digital filters, and controllers. Each component inevitably introduces inherent phase lag with the operating frequency. However, existing traditional control methods generally do not identify and compensate for the phase lag of the system, resulting in a fixed phase deviation between the theoretically designed anti-phase compensation force and the actual electromagnetic output force. This makes it impossible to achieve ideal 180° anti-phase cancellation, significantly weakening the vibration suppression effect.

[0007] Meanwhile, in actual operation, the rotor speed will rise and fall within a wide range and frequently cross the critical speed. Furthermore, the circuit parameters and magnetic circuit parameters will slowly drift during long-term operation of the equipment, causing the system phase lag to change in real time with the speed and operating conditions. Existing controllers mostly use fixed control parameters and fixed phase shifts, and do not have the ability to adaptively adjust phase and self-correct parameters. Under variable speed and parameter drift conditions, compensating for phase mismatch can easily lead to a deterioration of vibration reduction effect and even cause the magnetic bearing rotor to become levitated and unstable. Summary of the Invention

[0008] Purpose of the invention: The purpose of this invention is to address the shortcomings of existing technologies by providing a method for compensating for unbalanced vibration of magnetic bearing rotors based on orthogonal demodulation. Without adding key slots or photoelectric sensors, this method accurately extracts the amplitude and spatial phase of unbalanced vibration, achieves online phase shift compensation for system phase lag, and has full-speed adaptive adjustment capability, thereby improving the accuracy of suppressing synchronous vibration and the operational stability of magnetic bearing rotors.

[0009] Technical solution: The present invention provides a method for compensating for unbalanced vibration of a magnetic bearing rotor based on orthogonal demodulation, comprising the following steps: After the system is powered on, phase zero-position calibration is performed, and the demodulated phase is electrically zero-positioned using a standard unbalance mass or an external key phase signal, so that the calculated spatial phase angle is consistent with the actual mechanical unbalance angle of the rotor.

[0010] S1. Establish a rotor displacement signal model in a rotating coordinate system; assume the rotor rotates at an angular velocity ω, and the displacement signal collected by the displacement sensor in the X direction in a fixed coordinate system is:

[0011] x(t) = Acos(ωt + θ)

[0012] Where A is the amplitude of rotor unbalanced vibration, and θ is the initial spatial phase angle of the unbalanced mass relative to the X-axis sensor;

[0013] S2. A SOGI or EPLL single-phase phase-locked loop is used to track the displacement signal and outputs quadrature reference signals with the same frequency, phase, and amplitude: a cosine reference signal cos(ωt) and a sine reference signal sin(ωt). The phase-locked loop locks the phase based on the tracking error between the displacement and the reference signal. When the vibration amplitude decreases, the compensation amount decreases synchronously, and there will be no loss of lock.

[0014] S3. Multiply and mix the acquired displacement signal with the two reference signals respectively;

[0015] S4. The mixing signal is filtered by a first-order IIR low-pass filter to remove the second harmonic component and extract the orthogonal DC components I and Q; the filter uses forward Euler discretization, and the recursive formula is:

[0016] y (k)= α*u (k)+(1-α)*y (k-1)

[0017] The control frequency is 15.625kHz, the control period is Ts=64μs, and the filter cutoff frequency is f. c The adaptive frequency is 0.1 times the rotor frequency, and the filter coefficient α = 2πfc*Ts;

[0018] The system updates the cutoff frequency and filter coefficient according to the real-time rotor frequency in each control cycle to achieve adaptive filtering;

[0019] S5. Calculate the unbalanced vibration amplitude A and spatial phase angle θ based on the DC component;

[0020] S6. Construct the feedforward compensation control force; invert the DC components I and Q in the rotating coordinate system to obtain the feedforward component I. ff Q ff ;

[0021] S7. By synthesizing the feedforward control signal in the fixed coordinate system through inverse coordinate transformation, the feedforward control signal and the rotor unbalanced vibration force are in 180° out-of-phase relationship.

[0022] S8. Offline establishment of speed-phase compensation data table: At multiple speed points, the compensation gain is set to a small value, with π / 4 as the initial phase. The phase is gradually adjusted to find the point of minimum vibration amplitude, which is the target phase angle θtarget at that speed. During operation, the corresponding phase compensation amount is obtained by looking up the table online based on the real-time speed and performing linear interpolation. The target phase satisfies: θtarget = θraw + Δφ, where Δφ is the total phase lag of the system composed of displacement sensor, signal conditioning circuit, low-pass filter, and power amplifier. The compensation control signal is resynthesized based on the target phase angle to offset the inherent phase lag of the control link.

[0023] S9. The corrected feedforward compensation signal is superimposed on the output signal of the basic PID controller to form the total control signal;

[0024] S10: The main control signal drives the magnetic bearing coil through the power amplifier to generate an electromagnetic force that is equal in magnitude and opposite in direction to the unbalanced centrifugal force of the rotor, thus suppressing the vibration at the same frequency.

[0025] S11: The phase-locked loop tracks the speed change in real time, dynamically updates the filter cutoff frequency and the orthogonal reference signal frequency, and matches the phase compensation amount by looking up the table online; the system judges whether the speed is stable. If it is not stable, it executes S2-S10 in a loop. If it is stable, it keeps the control logic running to achieve full-speed adaptive vibration suppression.

[0026] Furthermore, in step S3, the displacement signal is mixed and multiplied with the two orthogonal reference signals respectively, and the calculation expression is as follows:

[0027] x(t)*cos(ωt) = [cos(2ωt+θ)+cosθ]

[0028] x(t)*sin(ωt) = [sin (2ωt+θ)-sinθ]

[0029] After the second harmonic component is filtered out by low-pass filtering in step S4, the orthogonal DC component is demodulated:

[0030] I= cosθ, Q= sinθ;

[0031] The unbalanced vibration amplitude and spatial phase angle are solved by coordinate transformation in step S5:

[0032] A= θ = atan2(Q, I);

[0033] The phase angle θ is the spatial azimuth angle of the unbalanced mass heavy end of the rotor relative to the X-axis displacement sensor.

[0034] Furthermore, the feedforward component in step S6 satisfies:

[0035] I ff =-I,Q ff =-Q;

[0036] Step S7 involves inverse coordinate transformation to synthesize a feedforward control signal in a fixed coordinate system.

[0037] F ff (t)=I ff cos(ωt)-Q ff sin(ωt) = Acos(ωt + θ + π).

[0038] Furthermore, the target phase angle is obtained by the minimum amplitude optimization method in step S8, and phase lag compensation at all speeds is achieved by offline table building, online table lookup, and linear interpolation.

[0039] θ target =θ raw +Δφ,

[0040] The compensation control signal is resynthesized based on the target phase angle:

[0041] F comp (t)=Acos(ωt+θ target );

[0042] Phase lag compensation ensures that the electromagnetic force output by the magnetic bearing is strictly out of phase with the unbalanced centrifugal force of the rotor.

[0043] Furthermore, a phase-locked loop is used to identify the real-time rotor speed and instantaneous rotation angle, and synchronously generate orthogonal reference signals with dynamically adjustable frequency and phase, namely cos(ωt) and sin(ωt), to provide a synchronization reference for orthogonal demodulation.

[0044] Furthermore, the low-pass filter used in step S4 is adaptively adjusted in real time according to the rotor speed, which can effectively filter out the 2ω second harmonic component and retain the required DC component across the entire speed range.

[0045] A control system applying the above-mentioned magnetic bearing vibration compensation method includes a rotor, a magnetic bearing, a displacement sensor, a digital controller, and a power amplifier.

[0046] The digital controller uses a DSP or FPGA and has a built-in PID module, SOGI / EPLL phase-locked loop module, quadrature demodulation module, feedforward compensation module, phase-shift compensation module, and adaptive calculation module for filter coefficients.

[0047] The adaptive filter coefficient calculation module is used to dynamically calculate the coefficient α of the first-order IIR low-pass filter based on the real-time rotor frequency, so that the filter cutoff frequency is kept at 0.1 times the rotor frequency, and the coefficient is updated to the filter in real time.

[0048] The signal flow direction is:

[0049] The displacement sensor collects the rotor displacement signal and inputs it into the digital controller; the digital controller performs speed tracking, quadrature demodulation, phase calculation, lookup table compensation, feedforward and PID superposition calculation based on the displacement signal, and outputs a current command; the power amplifier executes the current command and drives the magnetic bearing coil to generate electromagnetic force;

[0050] The system is triggered at a timed interval of 15.625 kHz and performs closed-loop control in a loop to achieve adaptive suppression of rotor unbalance vibration.

[0051] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows:

[0052] (1) This invention only uses existing displacement sensor signals and extracts the unbalanced vibration amplitude and phase through software orthogonal demodulation algorithm. It does not require machining rotor keyway or adding photoelectric sensors, thus reducing hardware costs, machining costs and installation complexity. It can be adapted to harsh working conditions such as high speed, high temperature, oil stains, and full sealing where additional phase sensors cannot be installed.

[0053] (2) The present invention uses orthogonal demodulation to convert the time-varying sinusoidal vibration signal into a steady-state orthogonal DC component, accurately calculates the unbalanced mass spatial phase, and can construct a strict 180° anti-phase feedforward control force. The same frequency vibration suppression effect is better than the traditional PID and fixed notch filter scheme.

[0054] (3) The present invention can identify and compensate for the inherent phase lag introduced by the sensor, power amplifier and filter link online, correct the phase deviation of the compensation force, and ensure that the electromagnetic compensation force and the unbalanced force are always accurately out of phase under all working conditions, thereby reducing the vibration of the same frequency from the source; relying on the phase-locked loop to track the rotor speed change in real time, and adaptively update the reference signal frequency and phase compensation amount, it can adapt to the rotor low speed, high speed and cross the critical speed all working conditions.

[0055] (4) All the algorithms of orthogonal demodulation, low-pass filtering, coordinate transformation and phase-shift compensation in this invention can be implemented in DSP and FPGA embedded digital controllers. The operation logic is simple, the real-time requirements are low, and it is easy to integrate into the existing magnetic bearing control system. It has strong engineering portability and practicality. Attached Figure Description

[0056] Figure 1 This is a flowchart of Example 1;

[0057] Figure 2 This is a simulation diagram from the experimental example. Detailed Implementation

[0058] The technical solution of the present invention will be described in detail below, but the scope of protection of the present invention is not limited to the embodiments described.

[0059] Example 1

[0060] like Figure 1 As shown, this embodiment discloses a method for compensating for unbalanced vibration of a magnetic bearing rotor based on orthogonal demodulation, applied to the radial magnetic bearing control system of a high-speed magnetic levitation motor. The system includes a rotor, a radial magnetic bearing, X / Y displacement sensors, a digital controller, and a power amplifier. The digital controller uses a DSP or FPGA chip and integrates a PID control module, a single-phase lock-in loop module (SOGI or EPLL), an orthogonal demodulation module, a feedforward compensation module, and a phase-shift compensation module. This system does not require keyway slots on the rotor or additional photoelectric phase sensors; vibration compensation can be achieved solely by collecting the radial displacement signal of the rotor using the existing displacement sensors.

[0061] A method for compensating for unbalanced vibration of a magnetic bearing rotor based on orthogonal demodulation includes the following steps:

[0062] System initialization and phase zero-position calibration

[0063] After the system is powered on, phase zero-point calibration is performed first: a standard unbalance block of known mass is installed on the rotor, or an external key phase signal is connected as a mechanical angle reference to perform electrical zero-point calibration on the demodulated phase, so that the calculated spatial phase angle θ is consistent with the actual mechanical unbalance angle of the rotor, eliminating the fixed zero-point deviation caused by sensor installation and signal conditioning. S1. First, a rotor displacement signal model in a rotating coordinate system is established. The rotor rotates steadily at a set angular velocity ω. The rotor displacement signal is collected in real time by a displacement sensor in the X direction in a fixed coordinate system. The signal model is expressed as: x(t)=Acos(ωt+θ);

[0064] Where A is the rotor unbalanced vibration amplitude, and θ is the spatial mechanical phase angle of the unbalanced mass heavy end relative to the X-axis sensor, which is consistent with the actual unbalanced orientation after zero-position calibration.

[0065] Since the output is in phase with the spatial phase angle θ, the target phase angle θtarget is actually caused by the delay of the controller calculation, low-pass filter, power amplifier and sensor, etc. It can be obtained by frequency sweep. In actual operation, the compensation gain can be set to a small value first, the initial phase can be set to pi / 4 (empirical value), and the compensation phase angle can be gradually increased or decreased. The vibration can be observed to find the point that minimizes the amplitude, which is the target phase angle θtarget.

[0066] S2. The controller's built-in single-phase phase-locked loop (SOGI / EPLL) tracks the frequency and phase of the displacement signal in real time, outputting two orthogonal reference signals cos(ωt) and sin(ωt) with the same frequency, phase, and amplitude, providing a synchronization reference for orthogonal demodulation. The phase-locked loop achieves phase locking based on the tracking error between the displacement and the reference signals. When the vibration amplitude is suppressed and reduced, the compensation amount decreases synchronously, and the system maintains phase locking without losing lock, eventually tending towards a steady state.

[0067] S3. The rotor time-domain displacement signal acquired by the X-direction displacement sensor is multiplied by the two orthogonal reference signals to obtain two mixed signals. The expression for the operation is as follows:

[0068] x(t) *cos(ωt) = [cos(2ωt+θ)+cosθ]

[0069] x(t) *sin(ωt) = [sin (2ωt+θ)-sinθ]

[0070] S4. Feed the two mixed signals into a first-order IIR low-pass filter to filter out the 2ω second harmonic high-frequency components and demodulate the steady-state orthogonal DC components:

[0071] I= cosθ, Q= sinθ;

[0072] The low-pass filter is implemented as follows:

[0073] 1. Control frequency and period

[0074] In this embodiment, the control frequency of the digital controller is 15.625 kHz, corresponding to a control period T. s =64μs, and all digital filtering and control algorithms are executed synchronously according to this cycle.

[0075] 2. Filter Structure and Discrete Implementation

[0076] A first-order IIR low-pass filter is used, and the filter is implemented using forward Euler discretization. The discrete recursive formula is as follows:

[0077] y(k) = α•u(k) + (1-a) •y(k-1); where u(k) is the mixing signal input of the current control cycle; y(k) is the filter output (i.e., I or Q component) of the current control cycle; y(k-1) is the filter output of the previous control cycle; α is the filter coefficient, which directly determines the filter cutoff frequency.

[0078] 3. Adaptive cutoff frequency and coefficient update

[0079] Since the rotor angular velocity ω varies with the rotational speed, to avoid the problem that a fixed cutoff frequency can effectively filter out the effective DC component at low frequencies but cannot effectively filter out the 2ω component at high frequencies, the filter cutoff frequency f in this embodiment is... c The setting is: (This is a function of adjusting the rotor's real-time frequency adaptively.)

[0080] f c =0.1*f r

[0081] Among them, f r The current rotor frequency (unit: Hz).

[0082] The corresponding filter coefficients are calculated in real time from the current cutoff frequency:

[0083] a=2πf c T s It achieves effective filtering across the entire speed range without losing the DC component.

[0084] Within each control cycle, the system recalculates \(f_c\) and \(\alpha\) based on the current rotor frequency output by the phase-locked loop and updates them to the low-pass filter, achieving adaptive control of "speed change - cutoff frequency synchronous adjustment - filter coefficient real-time update".

[0085] S5. Based on the demodulated DC components I and Q, perform coordinate transformation to calculate the rotor unbalanced vibration amplitude A and spatial phase angle θ, thus completing the accurate extraction of vibration characteristics without additional hardware sensors; Unbalanced vibration amplitude A = Spatial phase angle θ = atan2(Q, I);

[0086] Where θ is the true spatial azimuth angle of the unbalanced mass after zero-position calibration, which can be directly used for feedforward control phase calculation.

[0087] S6. Invert the orthogonal DC components in the rotating coordinate system to obtain the feedforward component I. ff =-I,Q ff =-Q.

[0088] S7. Synthesize the feedforward control signal F in the fixed coordinate system through inverse coordinate transformation. ff (t) = Acos(ωt+θ+π), the feedforward signal itself is theoretically out of phase, the ultimate goal is to make the electromagnetic force actually acting on the rotor 180° out of phase with the unbalanced centrifugal force. S8, offline calibration of the control link total phase lag Δφ, and establishment of speed-phase compensation table:

[0089] At multiple speed points (e.g., 100Hz, 200Hz, 300Hz, 400Hz, 500Hz), the compensation gain is set to a small value, with π / 4 as the initial phase compensation angle. The phase is gradually increased / decreased, and the rotor vibration amplitude is observed. The phase that minimizes the amplitude is the optimal target phase angle θ at that speed. target .

[0090] θ corresponding to each rotation speed target The data is stored in a data table, and during runtime, the table is looked up online according to the real-time speed for matching. Linear interpolation is used between speeds to obtain intermediate speed compensation values.

[0091] The target phase satisfies:

[0092] θ target =θ raw +Δφ;

[0093] Based on θ target The compensation signal is resynthesized to offset the total phase lag caused by the sensor, filter, and power amplifier.

[0094] S9. The feedforward compensation signal after phase correction is superimposed on the output signal of the basic PID controller to form a closed-loop total control signal.

[0095] S10: The main control signal drives the magnetic bearing coil through the power amplifier to generate an electromagnetic force that is equal in magnitude and opposite in direction (180° out of phase) to the unbalanced centrifugal force, thereby suppressing the same-frequency vibration from the source.

[0096] Full-process signal flow and working logic

[0097] The displacement sensor collects rotor displacement → sends it to the digital controller → phase-locked loop generates a quadrature reference → quadrature demodulation extracts I / Q → phase calibration and lookup table compensation → feedforward + PID superimposed output current command → power amplifier executes → magnetic bearing generates electromagnetic force → enters the next control cycle, and executes cyclically.

[0098] S11. The phase-locked loop tracks the speed change in real time, dynamically updates the quadrature reference frequency and adaptive filter coefficients, and matches the phase compensation amount by looking up the table online. The system determines whether the speed is stable. If it is not stable, it executes S2–S10 in a loop. If it is stable, it keeps the control logic running to achieve full-speed adaptive suppression.

[0099] This embodiment achieves high-precision imbalance compensation without adding hardware by using adaptive filtering, offline table creation and online table lookup, phase zero-position calibration, and phase-locked loop stabilization. The algorithm is simple, has low resource consumption, and can operate stably under high-speed and variable-speed conditions.

[0100] Example 2

[0101] This embodiment is a control system equipped with the aforementioned magnetic bearing rotor unbalance vibration compensation method based on orthogonal demodulation. It is adapted to magnetic bearing-supported rotor equipment such as high-speed magnetic levitation motors, energy storage flywheels, and centrifugal compressors. The system mainly consists of a rotor, magnetic bearings, radial displacement sensors, digital controllers, and power amplifiers.

[0102] The digital controller employs a DSP / FPGA and integrates a PID module, a SOGI / EPLL phase-locked loop module, a quadrature demodulation module, a feedforward compensation module, a phase-shift compensation module, and an adaptive filter coefficient calculation module. Each module is triggered at a fixed period and operates in an orderly and coordinated manner with a fixed signal flow direction. No additional photoelectric phase sensors are required, nor is it necessary to machine keyway slots onto the rotor; vibration signal acquisition and adaptive compensation control can be achieved solely using the original radial displacement sensor provided with the equipment.

[0103] The displacement sensor detects the real-time displacement signal of the rotor and inputs the displacement signal into the digital controller. Based on the collected displacement signal, the digital controller sequentially performs speed tracking, quadrature demodulation, phase calculation, lookup table compensation, feedforward signal construction, and feedforward and PID superposition calculation to calculate the current command required for the magnetic bearing to generate the target electromagnetic force. The digital controller outputs the current command to the power amplifier, which executes the current command and drives the magnetic bearing coil to generate electromagnetic force, completing one closed-loop control cycle. The control process is triggered at a timed interval of 15.625 kHz. After execution, it waits for the next control cycle to arrive before repeating the above process, achieving real-time, periodic adaptive suppression of unbalanced vibration.

[0104] A radial displacement sensor is fixedly installed on the stator side of the magnetic bearing to collect the radial displacement vibration signals of the rotor in the X and Y directions in real time and send them to the digital controller. The phase-locked loop module identifies the rotor speed and instantaneous rotation angle in real time based on the displacement signal and generates an orthogonal reference signal with the same frequency and phase as the rotor. The orthogonal demodulation module mixes the displacement signal and performs a first-order IIR low-pass filter to extract the orthogonal DC component. The filter coefficient adaptive calculation module dynamically updates the filter cutoff frequency and filter coefficient according to the real-time rotor frequency to ensure stable filtering effect across the entire speed range.

[0105] The feedforward compensation module constructs a reverse feedforward signal based on the amplitude and phase obtained from demodulation. The phase-shift compensation module performs online lookup and interpolation based on the offline established speed-phase lag table to obtain the target phase angle at the current speed and complete the phase correction. The controller superimposes the phase-corrected feedforward compensation signal with the PID basic control signal to form the final current command and outputs it to the power amplifier. The power amplifier drives the magnetic bearing to generate an electromagnetic force opposite to the unbalanced centrifugal force, thereby achieving the suppression of same-frequency vibration.

[0106] During system operation, the phase-locked loop tracks the rotor speed change in real time, dynamically updates the frequency of the quadrature reference signal and the filter coefficients, and matches the phase lag compensation online. It cyclically executes the entire process of signal acquisition, demodulation, phase compensation, and control output, and can adapt to a wide range of operating conditions such as rotor speed increase, speed decrease, and crossing critical speeds, so as to achieve stable and adaptive suppression of rotor unbalanced vibration across the entire speed range.

[0107] Test case

[0108] To verify the control effect of the magnetic bearing rotor unbalance vibration compensation method based on orthogonal demodulation described in this invention, simulation experiments were conducted, and the experimental results are as follows: Figure 2 As shown in the figure, from top to bottom, the curves represent the changes of rotor displacement signal, magnetic bearing control current signal, and resultant force signal acting on the rotor over time.

[0109] The experiment was divided into three stages:

[0110] 1.0–0.3 s: Stage without compensation control applied

[0111] At this point, only basic notch filter control is used, and the controller does not output a synchronous frequency compensation current, so the rotor's unbalanced centrifugal force is not actively canceled. As can be seen from the displacement curve, the rotor's radial displacement vibration amplitude is relatively large, with a fluctuation range of approximately 1.95 × 10⁻⁻⁻⁶. 4 ~2.05×10⁻ 4 The resultant force curve shows that the combined disturbance force acting on the rotor fluctuates violently, with an amplitude range of approximately -1000 to 1000, indicating that the system is in a state of significant disturbance.

[0112] 2.0.3~1.0 s: Notch control only, without applying synchronous frequency compensation current.

[0113] The controller still did not output the same frequency compensation current. Although the displacement signal was slightly improved compared to the previous stage, the same frequency vibration component was still not actively suppressed. The displacement and resultant force still had obvious periodic fluctuations, and the system did not fundamentally eliminate the unbalanced disturbance force.

[0114] 3.1.0 s later: Apply the orthogonal demodulation feedforward compensation stage of this invention.

[0115] The controller begins to output a synchronous and reverse compensation current. As can be seen from the current curve, after 1.0 s, the magnetic bearing control current shows a significant synchronous compensation component; correspondingly, the rotor displacement signal converges rapidly, the vibration amplitude decreases significantly and tends to stabilize; the fluctuation of the resultant force signal also decreases rapidly and eventually remains at a low level.

[0116] The experimental results show that:

[0117] After compensation was applied, the amplitude of the rotor radial displacement vibration was significantly reduced compared to before compensation, and the same frequency vibration component was effectively suppressed. The compensation current output by the magnetic bearing formed an antiphase relationship with the unbalanced centrifugal force of the rotor, effectively offsetting the unbalanced disturbance force and significantly reducing the resultant force acting on the rotor. After the compensation control was added, the rotor displacement quickly converged and stabilized, verifying the suppression effect of the method of the present invention on the unbalanced vibration of the magnetic bearing rotor.

[0118] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A method for compensating for unbalanced vibration of a magnetic bearing rotor based on orthogonal demodulation, characterized in that, The process includes the following steps: After the system is powered on, phase zero-position calibration is performed. The demodulated phase is electrically zero-position calibrated using a standard unbalance mass or an external key phase signal, so that the calculated spatial phase angle is consistent with the actual mechanical unbalance angle of the rotor. S1. Establish a rotor displacement signal model in a rotating coordinate system; assume the rotor rotates at an angular velocity ω, and the displacement signal collected by the displacement sensor in the X direction in a fixed coordinate system is: x(t) = Acos(ωt + θ) Where A is the amplitude of rotor unbalanced vibration, and θ is the initial spatial phase angle of the unbalanced mass relative to the X-axis sensor; S2. A SOGI or EPLL single-phase phase-locked loop is used to track the displacement signal and outputs quadrature reference signals with the same frequency, phase, and amplitude: a cosine reference signal cos(ωt) and a sine reference signal sin(ωt). The phase-locked loop locks the phase based on the tracking error between the displacement and the reference signal. When the vibration amplitude decreases, the compensation amount decreases synchronously, and there will be no loss of lock. S3. Multiply and mix the acquired displacement signal with the two reference signals respectively; S4. The mixing signal is filtered by a first-order IIR low-pass filter to remove the second harmonic component and extract the orthogonal DC components I and Q; the filter uses forward Euler discretization, and the recursive formula is: y (k)= α*u (k)+(1-α)*y (k-1) The control frequency is 15.625kHz, the control period is Ts=64μs, and the filter cutoff frequency is f. c The adaptive frequency is 0.1 times the rotor frequency, and the filter coefficient α = 2πfc*Ts; The system updates the cutoff frequency and filter coefficient according to the real-time rotor frequency in each control cycle to achieve adaptive filtering; S5. Calculate the unbalanced vibration amplitude A and spatial phase angle θ based on the DC component; S6. Construct the feedforward compensation control force; invert the DC components I and Q in the rotating coordinate system to obtain the feedforward component I. ff Q ff ; S7. By synthesizing the feedforward control signal in the fixed coordinate system through inverse coordinate transformation, the feedforward control signal and the rotor unbalanced vibration force are in 180° out-of-phase relationship. S8. Offline establishment of speed-phase compensation data table: Set the compensation gain to a small value at multiple speed points, with π / 4 as the initial phase, and gradually adjust the phase to find the point of minimum vibration amplitude, which is the target phase angle θtarget at that speed; during operation, look up the table online based on the real-time speed and perform linear interpolation to obtain the corresponding phase compensation amount; the target phase satisfies: θtarget = θraw + Δφ, where Δφ is the total phase lag of the system composed of displacement sensor, signal conditioning circuit, low-pass filter, and power amplifier; resynthesize the compensation control signal based on the target phase angle to cancel the inherent phase lag of the control link; S9. The corrected feedforward compensation signal is superimposed on the output signal of the basic PID controller to form the total control signal; S10: The main control signal drives the magnetic bearing coil through the power amplifier to generate an electromagnetic force that is equal in magnitude and opposite in direction to the unbalanced centrifugal force of the rotor, thus suppressing the vibration at the same frequency. S11: The phase-locked loop tracks the speed change in real time, dynamically updates the filter cutoff frequency and the orthogonal reference signal frequency, and matches the phase compensation amount by looking up the table online; the system judges whether the speed is stable. If it is not stable, it executes S2-S10 in a loop. If it is stable, it keeps the control logic running to achieve full-speed adaptive vibration suppression.

2. The compensation method according to claim 1, characterized in that, In step S3, the displacement signal is mixed and multiplied with the two orthogonal reference signals respectively, and the calculation expression is as follows: x(t)*cos(ωt) = [cos(2ωt+θ)+cosθ] x(t)*sin(ωt) = [sin (2ωt+θ)-sinθ] After the second harmonic component is filtered out by low-pass filtering in step S4, the orthogonal DC component is demodulated: I= cosθ,Q= sinθ; The unbalanced vibration amplitude and spatial phase angle are solved by coordinate transformation in step S5: A= ,θ=atan2(Q,I) ; The phase angle θ is the spatial azimuth angle of the unbalanced mass heavy end of the rotor relative to the X-axis displacement sensor.

3. The compensation method according to claim 1, characterized in that, The feedforward component in step S6 satisfies: I ff =-I,Q ff =-Q; Step S7 involves inverse coordinate transformation to synthesize a feedforward control signal in a fixed coordinate system. F ff (t)=I ff cos(ωt)-Q ff sin(ωt)=Acos(ωt+θ+π).

4. The compensation method according to claim 1, characterized in that, In step S8, the target phase angle is obtained using the minimum amplitude optimization method, and phase lag compensation at all speeds is achieved through offline table creation, online table lookup, and linear interpolation. i target =θ raw +Df, The compensation control signal is resynthesized based on the target phase angle: F comp (t)=Acos(ωt+θ target ); Phase lag compensation ensures that the electromagnetic force output by the magnetic bearing is strictly out of phase with the unbalanced centrifugal force of the rotor.

5. The compensation method according to claim 1, characterized in that, A phase-locked loop is used to identify the real-time rotor speed and instantaneous rotation angle, and synchronously generate cos(ωt) and sin(ωt) quadrature reference signals with dynamically adjustable frequency and phase to provide a synchronization reference for quadrature demodulation.

6. The compensation method according to claim 1, characterized in that, The low-pass filter used in step S4 is adaptively adjusted in real time according to the rotor speed, which can effectively filter out the 2ω second harmonic component and retain the required DC component across the entire speed range.

7. A control system applying the magnetic bearing vibration compensation method according to any one of claims 1 to 6, characterized in that, Includes rotor, magnetic bearing, displacement sensor, digital controller, and power amplifier; The digital controller uses a DSP or FPGA and has a built-in PID module, SOGI / EPLL phase-locked loop module, quadrature demodulation module, feedforward compensation module, phase-shift compensation module, and adaptive calculation module for filter coefficients. The adaptive filter coefficient calculation module is used to dynamically calculate the coefficient α of the first-order IIR low-pass filter based on the real-time rotor frequency, so that the filter cutoff frequency is kept at 0.1 times the rotor frequency, and the coefficient is updated to the filter in real time.

Images