A magnetic bearing same-frequency vibration force suppression method based on complex LMS algorithm

Abstract

The application discloses a magnetic bearing same-frequency vibration force suppression method based on a complex LMS algorithm, comprising the following steps: firstly, a dynamic model of a magnetic suspension bearing-rotor system containing rotor mass imbalance is constructed; a radial displacement sensor is used to obtain a first signal; a first complex LMS algorithm and a second complex LMS algorithm with steady-state error compensation are constructed; the first signal is input into the first complex LMS algorithm; a steady-state output is obtained by superimposing an original channel and a compensation channel; weight values are updated based on the calculation error of the steady-state output and the first signal; actual current is obtained; expected current is calculated based on the steady-state output; and a difference between the expected current and the actual current is input into the second complex LMS algorithm to obtain a compensation output. The application can avoid residual current stiffness force caused by inconsistent rotor radial displacement amplitudes, and can compensate displacement stiffness force while suppressing same-frequency current, so that complete suppression of same-frequency vibration force is realized.

Description

Technical Field

[0001] This invention belongs to the field of active magnetic bearing control technology, and in particular relates to a method for suppressing the same-frequency vibration force of magnetic bearings based on the complex LMS algorithm. Background Technology

[0002] Magnetic bearings, with their advantages of being contactless, requiring no lubrication, and being actively controllable, are widely used in high-speed rotating machinery such as magnetic levitation motors, magnetic levitation molecular pumps, and magnetic levitation control torque gyroscopes. Due to inhomogeneous rotor materials and machining errors, the rotor generates synchronous vibration forces during high-speed rotation. While offline dynamic balancing can reduce these synchronous vibration forces, it requires multiple trial weighings at different speeds, a cumbersome and inefficient process, and residual mass imbalances still exist in the rotor. Leveraging the active controllability of magnetic bearings, applying control algorithms to actively suppress rotor vibration is a crucial approach to improving system performance.

[0003] Commonly used single-channel control algorithms include adaptive notch filters, repetitive controllers, resonant controllers, and the LMS algorithm, while dual-channel control algorithms mainly employ methods such as synchronous rotating coordinate transformation. Generally, dual-channel control strategies have lower computational complexity and faster convergence speeds. However, a problem with dual-channel controllers is that these algorithms assume consistent rotor radial displacement amplitudes with a 90° phase difference. In reality, due to factors such as displacement sensor installation errors, differences in sensor board gain between the X and Y channels, and differences in power amplifiers between the X and Y channels, the rotor radial X and Y channel displacement amplitudes are usually inconsistent. Under asymmetrical rotor displacement, the assumptions of traditional dual-channel control algorithms do not hold. In practice, traditional dual-channel control algorithms suffer from steady-state errors after control current decay, and residual current stiffness forces still exist, failing to guarantee the accuracy of vibration suppression.

[0004] Compared with patents CN111708278B and CN114114919B, the innovation of this invention lies in the following: it adopts a dual-channel controller, considers the influence of the radial displacement amplitude asymmetry of the magnetic levitation rotor on the dual-channel controller, analyzes the existing current error, and adds an error compensation channel to track and compensate for the error current caused by displacement asymmetry in real time, thus achieving higher current notch filtering accuracy; compared with patent CN112432634A, this invention is based on discrete domain design, which is easier to program on DSP or other hardware resources, and this invention contains only one parameter to be adjusted, which is convenient for parameter tuning and suitable for engineering application scenarios. Summary of the Invention

[0005] The purpose of this invention is to provide a method for suppressing the same-frequency vibration force of magnetic bearings based on the complex LMS algorithm, so as to solve the problems existing in the prior art.

[0006] To achieve the above objectives, this invention provides a method for suppressing the same-frequency vibration force of magnetic bearings based on the complex LMS algorithm, comprising:

[0007] Based on Newton's second law, a dynamic model of a magnetic levitation bearing-rotor system with rotor mass imbalance disturbance force is constructed, wherein the dynamic model of the magnetic levitation bearing-rotor system with rotor mass imbalance disturbance force includes imbalance disturbance force and magnetic levitation electromagnetic force.

[0008] The first signal is obtained based on the rotor radial displacement sensor;

[0009] A complex LMS algorithm with steady-state error compensation is constructed, wherein the complex LMS algorithm with steady-state error compensation includes a first complex LMS algorithm and a second complex LMS algorithm, both of which include an original channel and a compensation channel; the first signal is input into the first complex LMS algorithm to obtain a steady-state output, and the weights are updated based on the steady-state output and the calculation error of the first signal until convergence;

[0010] The actual current is obtained, and the desired current is calculated based on the steady-state output. The difference between the desired current and the actual current is input into the second complex number LMS algorithm to obtain the compensation output, thereby achieving high-precision compensation of negative displacement stiffness force.

[0011] Optionally, the unbalanced disturbance force is expressed as:

[0012]

[0013] Among them, F x F y ε is the projection of the unbalanced disturbance force onto the x and y axes, m is the rotor mass, ω is the rotational speed, ε is the distance between the rotor's center of mass and centroid, and β is the initial phase angle of the rotor's center of mass position.

[0014] Optionally, the calculation process of the magnetic levitation electromagnetic force includes:

[0015] The electromagnetic force on the plane of the magnetic bearing can be considered as a linear model:

[0016]

[0017] Where K i It is the current stiffness force matrix, K h It is the displacement stiffness force matrix, f ax f bx f ay f by Let i represent the electromagnetic forces in the x and y directions on the plane of the magnetic bearings at ends A and B. ax i bx iay i by The control currents for the coils of the magnetic bearings at ends A and B are in the x and y directions, respectively. sa x sb y sa y sb The rotor displacement sensors at ends A and B detect rotor displacement in the x and y directions.

[0018] The rotor displacement sensor detects the centroid coordinates of the rotor, and the coordinate transformation relationship between the centroid coordinates and the mass center coordinates is expressed as follows:

[0019] x = x s +εcos(β+Ωt)

[0020] y = y s +εsin(β+Ωt)

[0021] Based on force balance, the coordinate transformation relationship expression is input into the linear model to obtain the electromagnetic force expression for magnetic levitation:

[0022]

[0023] Optionally, based on the coordinate information, the process of obtaining the first signal using a rotor radial displacement sensor includes:

[0024] Based on the rotor radial displacement sensor, displacement signals on the x-channel and y-channel are collected respectively, and the displacement signals on the x-channel and y-channel are used as the real part and imaginary part of the complex number respectively to obtain the first signal.

[0025] Optionally, the process of inputting the first signal into the first complex LMS algorithm to completely filter out the unbalanced signal in the first signal includes:

[0026] The first signal is input into the first complex LMS algorithm, and the second signal is obtained by matrix transformation of the original channel and the compensation channel in the first complex LMS algorithm.

[0027] The weights are obtained based on the second signal, wherein the weights include the original channel weights and the compensated channel weights;

[0028] The weights are transformed by matrix to obtain the filtered outputs of positive and negative order components. The filtered outputs include the filtered outputs of the positive order components of the original channel and the filtered outputs of the negative order components of the compensation channel. Both the filtered outputs of the positive order components of the original channel and the filtered outputs of the negative order components of the compensation channel include real and imaginary parts.

[0029] The real part of the original channel's filtered output is superimposed with the real part of the compensation channel's filtered output to obtain the real part of the final filtered output. The imaginary part of the original channel's filtered output is superimposed with the imaginary part of the compensation channel's filtered output to obtain the imaginary part of the final filtered output. Based on the real and imaginary parts of the final filtered output, the steady-state output is obtained.

[0030] Based on the error between the first signal and the steady-state output, the weights are updated, and the process is iterated until the unbalanced signal is completely filtered out.

[0031] Optionally, the first complex LMS algorithm process includes:

[0032]

[0033] Among them, X n For the input signal, take the unit circle X. n =x R (n)+jx I (n), x R (n)=cos(nΩT), x I (n)=sin(nΩT), x' R (n) = cos(nΩT+θ) and x' I (n) = sin(nΩT + θ) is the reference signal after adding the phase compensation angle θ, d n As the first signal, d n =d R (n)+jd I (n), e n To estimate the error, e n =e R (n)+je I (n), W n W′ represents the weight. n The value represents the weight of the compensation channel, μ represents the step size factor, T represents the transpose operation, the subscripts R and I represent the real and imaginary parts of the complex number, respectively, and j represents the imaginary unit.

[0034] Optionally, the weights are updated based on the Z-transform, and the updated weights include the weight updates for the original channels and the weight updates for the compensated channels.

[0035] Optionally, the second complex LMS algorithm process includes:

[0036]

[0037] Where i(z) is the Z-transform of the coil output control current, y(z) is the steady-state output of the first complex LMS algorithm, and e(z) is the Z-transform of the error between the first signal and the steady-state output. f (z) is the Z-transform of the difference between the desired current and the actual current, cf (z) is the steady-state output of the second complex LMS algorithm, K h It is the displacement stiffness coefficient, K i It is the current stiffness coefficient, K s It is the displacement sensor gain, k ad G is the AD conversion factor. c (z) is the transfer function of the controller, G p (z) is the transfer function of the power amplifier, G clms (z) and G′ clms (z) are the transfer functions of the first complex LMS algorithm and the second complex LMS algorithm, respectively.

[0038] The technical effects of this invention are as follows:

[0039] 1) Traditional dual-channel vibration suppression algorithms for magnetic levitation rotor systems are all based on the premise that the rotor radial displacement amplitude is consistent, without considering the impact of non-ideal and asymmetric displacement signals on the dual-channel controller. This invention considers the phenomenon of inconsistent radial displacement amplitudes of the rotor under actual operating conditions when designing the controller. An error compensation channel is added to eliminate the error current caused by asymmetry, achieving high-precision suppression of the same-frequency current stiffness force under abnormal operating conditions. Furthermore, a phase compensation angle is added to achieve stability across the entire speed range.

[0040] 2) This invention uses two complex LMS controllers to perform high-precision current notch filtering and negative displacement stiffness compensation under unbalanced operating conditions. The second complex LMS controller is connected in parallel with the power amplifier stage, which can offset the adverse effects of the power amplifier's amplitude attenuation at high frequencies on the compensation current. The algorithm is designed based on the discrete domain, which is convenient for writing code in DSP. The dual-channel controller has the advantages of low computational load and fast convergence speed. The entire controller contains only one parameter to be adjusted, which is easy to tune. Attached Figure Description

[0041] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0042] Figure 1 This is a schematic diagram of the rotor mass imbalance principle in an embodiment of the present invention, wherein (a) is a schematic diagram of the mass imbalance space, and (b) is a schematic diagram of the mass imbalance cross section;

[0043] Figure 2 This is a structural diagram of the complex LMS algorithm in an embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram of the complex LMS algorithm structure with error compensation in an embodiment of the present invention;

[0045] Figure 4 This is a control block diagram of a magnetic bearing control system that utilizes a complex LMS algorithm with error for high-precision current notch filtering and a complex LMS algorithm for compensating for negative displacement stiffness force in an embodiment of the present invention.

[0046] Figure 5 As described in the embodiments of the present invention Figure 4 The equivalent single-channel control block diagram of the control algorithm shown is shown below.

[0047] Figure 6 The dual-frequency Bode plot of the complex LMS algorithm with error in this embodiment of the invention;

[0048] Figure 7 This is a simulation effect diagram at 200Hz in an embodiment of the present invention. Detailed Implementation

[0049] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0050] Example 1

[0051] This invention provides a complex LMS algorithm with steady-state error compensation for suppressing vibration forces at the same frequency, characterized by the following steps:

[0052] (1) First, establish a dynamic model of the magnetic levitation bearing-rotor system containing rotor mass imbalance:

[0053] According to Newton's second law, the force on the rotor's center of mass is:

[0054]

[0055]

[0056] Where m is the rotor mass, x and y are the displacements of the center of mass in the center-of-mass coordinate system, and f xa f xb f ya f yb It is the magnetic levitation electromagnetic force F acting on the rotor's center of mass. x and F y It is the projection of the equivalent mass imbalance onto the center-of-mass plane, and can be expressed as:

[0057] F x =mεω 2 cos(β+ωt)

[0058] F y =mεω 2sin(β+ωt)

[0059] When the rotor moves within a small range around the equilibrium position, the electromagnetic force on the magnetic bearing plane can be considered as a linear model:

[0060]

[0061] Where K i It is the current stiffness force matrix, K h This is the displacement stiffness force matrix. The displacement sensor detects the centroid coordinates of the rotor, and the electromagnetic force can be directly calculated from the centroid coordinates (x, y, y). s ,y s ) Calculation. The relationship between the geometric coordinates and the coordinates of the rotor's center of mass is as follows:

[0062] x = x s +εcos(β+Ωt)

[0063] y = y s +εsin(β+Ωt)

[0064] Based on force balance, the expression for the output electromagnetic force of the magnetic bearing can be rewritten as:

[0065]

[0066] (2) In order to suppress the same frequency component in the displacement signal, the complex LMS algorithm with error compensation is used to extract and suppress the same frequency component in the displacement signal under the asymmetric displacement condition.

[0067] The complex LMS algorithm consists of three parts: weight update, error calculation, and filtered output. Compared to the traditional single-channel LMS algorithm, both its input and output signals are complex numbers. The equations for the complex LMS algorithm with error compensation are as follows:

[0068]

[0069] Wherein, the reference input signal X n Take the unit circle X n =x R (n)+jx I (n), where x R (n) = cos(nΩT), x I (n)=sin(nΩT),x' R (n)=cos(nΩT+θ),x' I (n) = sin(nΩT + θ) is the reference signal after adding the phase compensation angle θ. The rotor displacement signal is represented as d. n =d R (n)+jd I (n), the estimation error is expressed as en =e R (n)+je I (n), W n W' represents the weight. n The value represents the weight of the compensation channel, μ represents the step size factor, T represents the transpose operation, the subscripts R and I represent the real and imaginary parts of the complex number respectively, and j represents the imaginary unit. The complex number calculation form is converted into a real number calculation form:

[0070] Original channel weight update:

[0071]

[0072] Weight update of the compensation channel:

[0073]

[0074] The filtered outputs of the original channel and the compensated channel are superimposed:

[0075]

[0076] Error calculation:

[0077]

[0078] Let the rotor displacement signal be represented as:

[0079]

[0080] Where γ1≠γ2. The rotor displacement signal, after passing through the transformation matrices of the original channel and the compensated channel in the complex LMS algorithm with error compensation, is represented as:

[0081]

[0082] The transfer function of the weight update process can be expressed as 1 / (z-1), which can be regarded as a digital integrator. After the weight update, the part containing the second harmonic of u1, u2, u3, and u4 is filtered out, and the converged weights can be simplified as follows:

[0083]

[0084] Where A = (γ1 + γ2) / 2, B = (γ1 - γ2) / 2. Ignoring the effect of the phase compensation angle for now, the weights, after being processed again through the output transformation matrix, yield the filtered outputs for the positive and negative order components:

[0085]

[0086] By adding the output of the original channel filter to the output of the error compensation channel pairwise, the steady-state output of the algorithm can be obtained:

[0087]

[0088] The expression for the filtered output is exactly the same as the expression for the displacement input. After the filtered output is introduced into the displacement input through a closed loop, the converged error signal will tend to 0, which can achieve error-free control and completely filter out the unbalance signal in the rotor displacement signal.

[0089] Performing a z-transform on the real expression of the complex LMS algorithm, we obtain the transfer function of the algorithm from the error input to the filter output as follows:

[0090]

[0091] The equivalent transfer function from rotor displacement input to error is expressed as:

[0092]

[0093] From the relationship between the discrete domain operator z and the Laplace operator s, we know that z = e sT =e jωt Where ω is an arbitrary frequency, and Δω is a very small frequency fluctuation range, i.e., Δω << Ω, and the step size factor μ satisfies μ << 1. Then, the frequency characteristic of the algorithm's transfer function is:

[0094]

[0095] In summary, the complex LMS algorithm with error compensation can not only eliminate the same-frequency quantity in the displacement signal that is in the same frequency as the rotation speed signal at the positive frequency, but also suppress the negative frequency component caused by the asymmetry of displacement amplitude to the same extent. This effectively suppresses the current error and achieves complete suppression of the same-frequency signal in the rotor current stiffness force under the condition of asymmetric displacement amplitude.

[0096] (3) To completely suppress the same-frequency vibration force, high-precision compensation is also needed for the same-frequency component of the negative displacement stiffness force. The expression for the same-frequency component of the negative displacement stiffness force is:

[0097]

[0098] For this component of vibration at the same frequency, a controller can be used to control the power amplifier to output a corresponding compensation current -K. h Θ / K i , where Θ represents the unbalance in the displacement signal.

[0099] However, due to the low-pass characteristic of the power amplifier, there is significant phase lag and amplitude attenuation at higher speeds. In this case, directly using -K... h Θ / K iGenerating compensation current will cause a decrease in compensation accuracy.

[0100] The unbalance in the displacement signal is identified by the first complex LMS algorithm when performing notch filtering at the same frequency. The desired current is generated and the difference between the desired current and the actual current is calculated to obtain the current deviation signal. This signal is then fed into the second complex LMS algorithm to obtain the corresponding control quantity. When the control quantity is superimposed on the controller output, high-precision compensation of negative displacement stiffness force can be achieved.

[0101] Equivalent single-channel control algorithm with current notch filtering and negative displacement stiffness compensation:

[0102]

[0103] The equivalent transfer function H'(z) from error e to current i:

[0104]

[0105] After applying the negative displacement stiffness compensation algorithm, the coil output current i can be expressed as:

[0106]

[0107] Where i d (z) represents the desired current signal calculated from the displacement signal imbalance identified in real time using the first complex LMS algorithm.

[0108] After the first complex LMS algorithm converges, e(z) is approximately 0, and at this point, near the rotational speed, there is... This indicates that after applying the second complex LMS algorithm to compensate for the negative displacement stiffness force, the actual current generated by the power amplifier is always equal to the expected compensation current. Therefore, the algorithm can overcome the low-pass characteristic of the power amplifier and achieve the expected effect across the entire speed range.

[0109] The principle of this invention is as follows: Due to rotor machining errors and material inhomogeneity, the rotor's inertial axis and geometric axis may not coincide, leading to mass imbalance. During high-speed rotation, this generates a synchronous vibration force proportional to the square of the rotational speed, producing vibration and noise, affecting the reliable operation of the equipment. While dynamic balancing technology can mitigate this mass imbalance, residual mass imbalance still exists, and dynamic balancing requires multiple offline trials at different speeds, resulting in low efficiency. This invention leverages the strong electromechanical characteristics of magnetic levitation bearings, using a complex LMS algorithm in the control system to suppress synchronous vibration forces. The complex LMS algorithm couples the rotor's single-end radial dual-channel displacement into a complex number for calculation. Unlike traditional dual-channel controllers that suffer from residual errors when the rotor's radial displacement amplitude is asymmetrical, this invention designs an error compensation channel to extract the negative sequence component and superimposes the filtered output of the error compensation channel with the output of the original channel to obtain the final output. This enables high-precision suppression of synchronous vibration forces even under conditions of asymmetrical rotor radial displacement amplitude.

[0110] Example 2

[0111] like Figure 1-7 As shown, this embodiment provides a method for suppressing the same-frequency vibration force of magnetic bearings based on the complex LMS algorithm, including:

[0112] Figure 1 In (a), the mass imbalance of the system is described by simplified point masses, with the unbalanced force provided by a point mass ms on the geometric center plane. Assume the unbalanced point masses are all distributed along the edge of the shaft, i.e., the radius during rotation is rm, the shaft length is l, and the initial mass imbalance phase angle is φs. When the rotor rotates about the z-axis, the equivalent unbalanced point masses will be subjected to centrifugal force, thus generating an unbalanced disturbance force:

[0113]

[0114] Figure 1 (b) shows the rotor cross-section considering unbalanced vibration. XNY is the fixed coordinate system, and XrOYr is the rotating coordinate system. C is the plane centroid, O is the geometric center of the plane, ε is the eccentricity between the geometric center and the centroid, and s0 represents the single-sided protective gap; r is the rotation vector of the geometric center in the fixed coordinate system, and the coordinates of O and C in the fixed coordinate system are (x... s ,y s (x,y). The rotor speed is Ω, and the initial phase is β. The geometric relationship between the centroid coordinates and the mass center coordinates is:

[0115]

[0116] When the rotor moves within a small range around the equilibrium position, the electromagnetic force on the magnetic bearing plane can be considered as a linear model:

[0117]

[0118] Where K i It is the current stiffness force matrix, K x This is the displacement stiffness force matrix. The displacement sensor detects the centroid coordinates of the rotor, and the electromagnetic force can be directly calculated from the centroid coordinates (x, y, y). s ,y s )calculate.

[0119] Based on force balance, the expression for the output electromagnetic force of a magnetic bearing with mass imbalance can be rewritten as:

[0120]

[0121] (2) Assume the displacement signal obtained by the rotor radial displacement sensor through AD sampling is:

[0122]

[0123] Where x and y are the vibration signals sampled by the displacement sensor, γ1, γ2、 These represent the amplitude and phase of the displacement in the x and y channels, respectively. Using Euler's formula, the rotor shaft center coordinates can be expressed in complex number form: in,

[0124]

[0125] When γ1≠γ2, the axis center coordinates are equivalent to the orthogonal sum of positive and negative sequences, containing not only a positive component with the same frequency as the rotational speed but also a negative frequency component. The negative frequency indicates that the rotational direction of the signal is reversed. The transfer function of the dual-channel controller only suppresses the positive frequency component, ensuring that when the axis center coordinates x+jy pass through the dual-channel controller, the vibration signal... Some were sufficiently attenuated, while The components remain unchanged, but the algorithm's effectiveness will inevitably be weakened.

[0126] Considering factors such as the rotor's circumferential error and differences between displacement sensor channels, γ1≠γ2 in this case. in Represents phase error, generally considered Considering only the effect of inconsistent radial amplitudes:

[0127]

[0128] in, The rotor displacement signal, after passing through the transformation matrices of the original channel and the compensated channel in the complex LMS algorithm with error compensation, is represented as follows:

[0129]

[0130] Where u1 and u2 are the output signals of the original CLMS algorithm after transformation matrix, and u3 and u4 are the output signals of the compensation channel after transformation matrix. Simplified using the double-angle formula, we get:

[0131]

[0132] Where A = (γ1 + γ2) / 2, B = (γ1 - γ2) / 2. The transfer function of the weight update process can be expressed as 1 / (z-1), which can be regarded as a digital integrator. After the weight update, the part containing the second harmonic of u1, u2, u3, and u4 is filtered out, and the converged weights can be simplified as:

[0133]

[0134] Among them, w1 and w2 are the weight outputs of the original complex LMS algorithm, and w3 and w4 are the weight outputs of the compensation channel.

[0135] Ignoring the effect of phase compensation angle, the weights, after being transformed again by the output matrix, yield the filtered outputs for the positive and negative order components:

[0136]

[0137] like Figure 2 As shown, by adding the output of the original channel filter to the output of the error compensation channel pairwise, the steady-state output of the algorithm can be obtained:

[0138]

[0139] The expression for the filtered output is exactly the same as the expression for the displacement input. After the filtered output is introduced into the displacement input through a closed loop, the converged error signal will tend to 0, which can achieve error-free control and completely filter out the unbalance signal in the rotor displacement signal.

[0140] (3) Figure 3 The weight update process of the compensation channel is as follows:

[0141]

[0142] Taking the Z-transform of the above equation, we get:

[0143]

[0144] Among them, z[e R (n)x R (n)+e I (n)x I (n)] and z[eI (n)x R (n)-e R (n)x I [n] represents the values ​​of e respectively. R (n)x R (n), e I (n)x I (n), e I (n)x R (n), e R (n)x I (n) Perform a Z-transform, using Euler's formula: x R (n)=cos(nΩT)=(e jn ΩT +e -jnΩT ) / 2x I (n)=sin(nΩT)=(-e jnΩT +e -jnΩT )j / 2

[0145] It can be known that:

[0146]

[0147] By convention, uppercase letters are used to denote the Z-transform of a signal, where E(ze) jΩT E(z) represents E(z) rotating clockwise around the unit circle by an angle ΩT. -jΩT Let ) represent E(z) rotating counterclockwise around the unit circle. Combining the above two equations, we can obtain:

[0148]

[0149] The filtering output process of the original channel is as follows:

[0150]

[0151] Performing a Z-transform on the filtered output of the original channel yields:

[0152]

[0153] By using the algorithm's output and error signals as complex numbers, the original channel transfer function G of the complex LMS algorithm from error to filtered output is obtained. clms (z):

[0154]

[0155] The weight update process for the compensation channel is as follows:

[0156]

[0157] The filtered output of the compensation channel is:

[0158]

[0159] Using the same calculation method, the transfer function from the error to the filter output of the compensation channel can be obtained.

[0160]

[0161] Therefore, the transfer function from the displacement input to the error in the complex LMS algorithm with error compensation... It is obtained by superimposing the original channel and the compensated channel:

[0162]

[0163] It can be seen that, The zero point is z = e ±jΩt From the relationship between the discrete-domain operator z and the Laplace operator s, we know that z = e sT =e jωt Where ω is an arbitrary frequency, and Δω is a very small frequency fluctuation interval, i.e., Δω << Ω, and the step size factor μ satisfies μ << 1, then The amplitude can be simplified as follows:

[0164]

[0165] in,

[0166] In summary, by incorporating the complex LMS algorithm with error compensation, the system not only exhibits good displacement notch filtering capability at the same frequency as the rotational speed, but also suppresses the negative frequency component caused by displacement amplitude asymmetry to the same extent, without attenuating signals at other frequency bands. This eliminates displacement signals at the same frequency as the rotational speed, thereby achieving the effect of suppressing current at the same frequency. The two-frequency Bode plot of the transfer function is as follows Figure 6 As shown.

[0167] (4) Figure 4-5 As shown, after the same-frequency current is sufficiently suppressed, it is also necessary to suppress the negative displacement stiffness force. This part of the same-frequency vibration force is introduced by the same-frequency component in the displacement signal present in the linearized expression of the electromagnetic force, and its form is:

[0168]

[0169] For this component of vibration at the same frequency, a controller can be used to control the power amplifier to output a corresponding compensation current -K. h Θ / K iΘ represents the unbalance in the displacement signal. The power amplifier has a low-pass characteristic. If the control quantity calculated based solely on the current rotor displacement is applied to the controller and then passes through the power amplifier, the amplitude attenuation of the power amplifier at high speeds will lead to a decrease in the accuracy of the compensation negative displacement stiffness force.

[0170] In order to overcome the adverse effects of the low-pass characteristics of the power amplifier stage on the algorithm, this invention uses the difference between the identified unbalance quantity and the desired current signal as the input of the second complex LMS algorithm. The output of this complex LMS algorithm is directly compensated to the controller output, thereby overcoming the low-pass characteristics of the power amplifier while achieving negative displacement stiffness compensation.

[0171] Specific control algorithm with current notch filtering and negative displacement stiffness compensation:

[0172]

[0173] The equivalent transfer function H'(z) from error e to current i:

[0174]

[0175] After applying the negative displacement stiffness compensation algorithm, the coil output current i can be expressed as:

[0176]

[0177] Where i d (z) represents the desired current signal calculated from the displacement signal imbalance identified in real time using the first complex LMS algorithm. After the first complex LMS algorithm converges, e(z) is approximately 0, and at this point, near the rotational speed, there is... This indicates that after applying the second complex LMS algorithm to compensate for the negative displacement stiffness force, the actual current generated by the power amplifier is always equal to the expected compensation current. Therefore, the algorithm can overcome the low-pass characteristic of the power amplifier and achieve the expected effect across the entire speed range.

[0178] Figure 7 The simulation results are based on a Simulink-built simulation model of coil control current and vibration force at 200Hz. No control algorithm is applied within 0-2s. The complex LMS algorithm with error compensation proposed in this paper is applied within 2-5s. It can be seen that the current is close to 0A after notch filtering, but vibration force still exists. After adding the negative displacement stiffness force compensation algorithm within 5-10s to suppress zero vibration force, the current increases to compensate for the negative displacement stiffness force. At this time, the vibration force can be close to 0N. The simulation results prove the effectiveness of the present invention.

[0179] The present invention obtains the current output of the power amplifier by means of a sampling resistor in conjunction with an operational amplifier, and the sensor for obtaining the displacement signal is an eddy current sensor.

[0180] The above description is merely a preferred embodiment of this application, but the scope of protection of this application 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 this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for suppressing synchronous vibration force of magnetic bearings based on complex LMS algorithm, characterized in that, Includes the following steps: Based on Newton's second law, a dynamic model of a magnetic levitation bearing-rotor system with rotor mass imbalance disturbance force is constructed, wherein the dynamic model of the magnetic levitation bearing-rotor system with rotor mass imbalance disturbance force includes imbalance disturbance force and magnetic levitation electromagnetic force. The first signal is obtained based on the rotor radial displacement sensor; A complex LMS algorithm with steady-state error compensation is constructed, wherein the complex LMS algorithm with steady-state error compensation includes a first complex LMS algorithm and a second complex LMS algorithm, both of which include an original channel and a compensation channel; the first signal is input into the first complex LMS algorithm to obtain a steady-state output, and the weights are updated based on the steady-state output and the calculation error of the first signal until convergence; The actual current is obtained, and the desired current is calculated based on the steady-state output. The difference between the desired current and the actual current is input into the second complex number LMS algorithm to obtain the compensation output, thereby achieving high-precision compensation of negative displacement stiffness force. The process of completely filtering out the unbalanced signal in the first signal includes: inputting the first signal into the first complex LMS algorithm, and obtaining a second signal through matrix transformation of the original channel and the compensation channel in the first complex LMS algorithm; obtaining weights based on the second signal, wherein the weights include the original channel weights and the compensation channel weights; obtaining filtered outputs of positive and negative order components by matrix transformation of the weights, wherein the filtered outputs include filtered outputs of the positive order components of the original channel and filtered outputs of the negative order components of the compensation channel, wherein both the filtered outputs of the positive order components of the original channel and the filtered outputs of the negative order components of the compensation channel include real and imaginary parts; superimposing the real part of the filtered output of the original channel with the real part of the filtered output of the compensation channel to obtain the real part of the final filtered output, and superimposing the imaginary part of the filtered output of the original channel with the imaginary part of the filtered output of the compensation channel to obtain the imaginary part of the final filtered output; obtaining a steady-state output based on the real and imaginary parts of the final filtered output; updating the weights based on the error between the first signal and the steady-state output, and iterating until the unbalanced signal is completely filtered out. The first complex LMS algorithm process includes: in, For the input signal, take the unit circle. , , , and To add phase compensation angle The reference signal after that, As the first signal, , To estimate the error, , Indicates the weight. This represents the weight of the compensation channel. Indicates the step size factor. Indicates the transpose operation, subscript and Let them represent the real and imaginary parts of a complex number, respectively. It represents the imaginary unit.

2. The method for suppressing synchronous vibration force of magnetic bearings based on the complex LMS algorithm according to claim 1, characterized in that, The unbalanced disturbance force is expressed as: in, , It is an unbalanced disturbance force in shaft and Projection on the axis It is the rotor mass. It's the rotational speed. It is the distance between the rotor's center of mass and its centroid. It is the initial phase angle of the rotor's center of mass position.

3. The method for suppressing synchronous vibration force of magnetic bearings based on the complex LMS algorithm according to claim 2, characterized in that, The calculation process for the magnetic levitation electromagnetic force includes: The electromagnetic force on the magnetic bearing plane is considered as a linear model: in It is the current stiffness force matrix. It is the displacement stiffness force matrix. , , , for , On the end magnetic bearing plane direction and Electromagnetic force in the direction, , , , for , end magnetic bearings in direction and The coil controls the current in the direction of the direction. , , , for , The end rotor displacement sensor detected direction and Rotor displacement in the direction; The rotor displacement sensor detects the centroid coordinates of the rotor, and the coordinate transformation relationship between the centroid coordinates and the mass center coordinates is expressed as follows: Based on force balance, the coordinate transformation relationship expression is input into the linear model to obtain the electromagnetic force expression for magnetic levitation: 。 4. The method for suppressing synchronous vibration force of magnetic bearings based on the complex LMS algorithm according to claim 1, characterized in that, The process of obtaining the first signal using a rotor radial displacement sensor includes: Based on the rotor radial displacement sensor, displacement signals on the x-channel and y-channel are collected respectively, and the displacement signals on the x-channel and y-channel are used as the real part and imaginary part of the complex number respectively to obtain the first signal.

5. The method for suppressing synchronous vibration force of magnetic bearings based on the complex LMS algorithm according to claim 1, characterized in that, The weights are updated based on the Z-transform, including the weight updates for the original channels and the weight updates for the compensated channels.

6. The method for suppressing synchronous vibration force of magnetic bearings based on the complex LMS algorithm according to claim 1, characterized in that, The second complex LMS algorithm process includes: in, It is the Z-transform of the coil output control current. This is the steady-state output of the first complex LMS algorithm. It is the Z-transform of the error between the first signal and the steady-state output. It is the Z-transform of the difference between the desired current and the actual current. This is the steady-state output of the second complex LMS algorithm. It is the displacement stiffness coefficient. It is the current stiffness coefficient. It is the displacement sensor gain. These are the AD conversion coefficients. It is the transfer function of the controller. It is the transfer function of the power amplifier. and These are the transfer functions for the first complex LMS algorithm and the second complex LMS algorithm, respectively.

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