A method for suppressing co-frequency vibration of electromagnetic bearing flexible rotor system based on disturbance compensation

Abstract

The present invention discloses a method for suppressing co-frequency vibration of an electromagnetic bearing flexible rotor system based on disturbance compensation. The method first establishes a mathematical model of a linear anti-disturbance controller, the main components of which are a linear extended state observer and a linear control law; then, a phase shift angle θ is introduced into the sine and cosine components of the standard LMS algorithm output signal to obtain a phase shift LMS algorithm; finally, the phase shift LMS algorithm is used to compensate for the disturbance observation value. After adding disturbance compensation, the linear extended state observer can accurately estimate the sinusoidal disturbance with the same frequency as the rotation speed, and the linear control law can be used to suppress the co-frequency vibration. The present invention can effectively suppress the co-frequency vibration of the flexible rotor system in the full speed range, including rigid body translation and cone critical, first-order and second-order multi-order bending critical speeds.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic bearing-flexible rotor system vibration control, and specifically to a method for suppressing the same-frequency vibration of an electromagnetic bearing flexible rotor system based on disturbance compensation when crossing critical zones of rigid body translation and cone motion, first-order and second-order bending, etc. Background Art

[0002] Due to machining errors, material unevenness and other reasons, the rotor is bound to be unbalanced, so an unbalanced excitation force synchronized with the speed is generated during the rotation process. The amplitude of the unbalanced excitation force is proportional to the square of the speed. On a flexible rotor with high speed, the unbalanced force will seriously affect the operation of the rotor. Electromagnetic bearings achieve stable suspension of the rotor through controllable electromagnetic force, and control algorithms can be designed to suppress the vibration of the rotor unbalanced excitation force in real time. It has the advantages of no friction, high efficiency, long service life, and low maintenance cost, and has been widely used in high-speed rotating equipment.

[0003] At present, the methods for controlling the same-frequency unbalanced vibration of electromagnetic bearing rigid rotor systems mainly include automatic balancing and unbalance compensation. Automatic balancing follows the principle of "minimum control force". Its principle is to use a same-frequency trap in the controller to eliminate the same-frequency current. The rotor will rotate around its inertia axis due to the self-centering effect, but the rotor system controlled by this method will still be displaced due to the unbalanced force, which limits the rotation accuracy. Unbalance compensation follows the principle of "minimum displacement". Its principle is to increase the output current of the controller so that an additional part of the current is used to offset the unbalanced force of the rotor. The rotor will rotate around its geometric axis. The rotor system controlled by this method has small displacement and high rotation accuracy.

[0004] The existing technologies mainly include a method of identifying the model parameters of the unbalanced force during the rotation process by modeling the unbalanced force and a method of suppressing the same-frequency vibration in the full speed range by inserting a variable polarity adaptive notch filter. The existing technologies have the following problems: (1) The method of modeling the unbalanced force requires an accurate mathematical calculation model of the unbalanced force, and the iterative search speed of the compensation algorithm is overly dependent on the system identification algorithm itself. (2) The method of inserting the adaptive notch filter requires polarity switching or step factor adjustment before and after crossing the rigid body critical speed, in order to change the output phase of the algorithm to adapt to the phase characteristics of the system after crossing the rigid body critical speed, but adjusting the phase of the algorithm when the rotor is running at high speed is extremely dangerous. (3) The above-mentioned unbalance compensation methods are mainly used for rigid rotors. For flexible rotors, due to the problems of high speed, large vibration, complex disturbance, rotor deformation, etc., the original compensation scheme is not applicable to flexible rotors after crossing the bending critical speeds of various orders. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the prior art and propose a method for suppressing the same-frequency vibration of an electromagnetic bearing flexible rotor system based on disturbance compensation. The method of observing disturbances is used to obtain the unbalanced force of the rotor system, and then accurately compensates for it. The method can effectively suppress vibrations in the full speed range, including rigid body translation and cone critical, first-order bending and second-order bending critical, and other multi-order bending critical speeds.

[0006] The object of the present invention is achieved through the following technical solution: a method for suppressing the same-frequency vibration of an electromagnetic bearing flexible rotor system based on disturbance compensation, the method comprising the following steps:

[0007] Step 1: Establish the mathematical model of linear ADRC

[0008] The main components of the linear ADRC are the linear extended state observer and the linear control law. For the electromagnetic bearing flexible rotor system, the internal dynamics of the system are unknown, and it will be subject to disturbances including unbalanced forces during operation. The unknown internal dynamics and disturbances of the system are collectively referred to as the total disturbance, and the total disturbance is taken as the third state variable. The state equation of the linear extended state observer is:

[0009]

[0010] Where, the state vector z = [z1 z2 z3] T , z1, z2, z3 are the flexible rotor displacement, the derivative of the flexible rotor displacement, and the observed value of the disturbance, respectively. The superscript T of the matrix indicates the transpose; C = [1 0 0], b0 is the control gain of the linear active disturbance rejection controller; u is the input of the linear active disturbance rejection controller; y is the true value of the flexible rotor displacement, is the observed value of the flexible rotor displacement; L is the gain matrix of the linear extended state observer;

[0011] All poles of the characteristic equation of the linear extended state observer are placed in the same position (–ω o ,0), the gain matrix L=[3ω o 3ω o 2 ω o 3 ] T ,ω o is the bandwidth of the linear extended state observer;

[0012] The linear control law is designed as u=[k p (Ref–z1)–k d z2–z3] / b0, where Ref is the reference value of displacement control of the electromagnetic bearing flexible rotor system; k p =ωc 2 , k d =2ω c ,ω c is the bandwidth of the linear ADRC controller.

[0013] Step 2: Introduce the phase shift angle θ into the sine and cosine components of the standard LMS algorithm output signal to obtain the phase shift least squares (Least Mean Square, LMS) algorithm. The iterative expression of the output signal from step k to step k+1 is:

[0014] y(k)=w1(k)sin(ω r k+θ)+w2(k)cos(ω r k+θ)

[0015] w1(k+1)=w1(k)+2UX(k)sin(ω r k)

[0016] w2(k+1)=w2(k)+2UX(k)cos(ω r k)

[0017] Among them, X(k) is the input signal of the kth step, y(k) is the output signal of the kth step, w1 and w2 are weight coefficients, ω r is the center frequency, U is the step size; the calculation method of the weight coefficient is the same as the standard LMS algorithm; the phase offset angle introduced by the phase offset LMS algorithm will affect the phase of the output signal.

[0018] Step 3: Suppression of co-frequency vibration of electromagnetic bearing flexible rotor system based on disturbance compensation

[0019] In order to solve the problem that the linear extended state observer cannot accurately estimate the sinusoidal disturbance with high speed frequency in step 1, the phase shift LMS algorithm is used to compensate the disturbance observation value. The input signal of the phase shift LMS algorithm is the derivative of the disturbance observation value in the linear extended state observer, and its output signal is inserted into the disturbance observation value as disturbance compensation. After adding disturbance compensation, the linear extended state observer can accurately estimate the sinusoidal disturbance with the same frequency as the speed, and the linear control law can be used to suppress the vibration of the same frequency.

[0020] Furthermore, before establishing the mathematical model of the linear active disturbance rejection controller, a dynamic model of the electromagnetic bearing flexible rotor system is established, specifically:

[0021] Since the flexible rotor has infinite degrees of freedom due to its axially varying stiffness and mass, the finite element method is used for modeling. Set n nodes in the axial direction of the flexible rotor, and regard the electromagnetic force of the electromagnetic bearing as a generalized external force, that is, the electromagnetic force of the electromagnetic bearing is the external force exerted on the rotor at the electromagnetic bearing node. The unbalanced force is also regarded as the external force exerted on the rotor at the rigid disk node. The dynamic equation of the electromagnetic bearing flexible rotor system modeled by the finite element method at a constant speed is:

[0022]

[0023] Among them, M, D, G, K are the 4n×4n-dimensional mass matrix, damping matrix, gyro matrix and stiffness matrix respectively; Ω is the rotation speed, F MAG is the electromagnetic force vector of the 4n×1 dimensional electromagnetic bearing, F u is a 4n×1 dimensional unbalanced force vector, G m is the 4n×1 dimensional gravity vector, q is the generalized displacement vector;

[0024] The electromagnetic force of the electromagnetic bearing is a nonlinear function of the coil current i and the displacement vector q. By linear expansion near the working point (q0, i0), the linearized expression of the electromagnetic force of the electromagnetic bearing is obtained as follows:

[0025] F MAG =F MAG,0 +K i (i–i0)+K x (q–q0)

[0026] Among them, F MAG,0 is the electromagnetic force at the working point (q0,i0), K i is the current stiffness coefficient matrix of the electromagnetic bearing, K x is the displacement stiffness coefficient matrix of the electromagnetic bearing; in general, F MAG,0 Just with the gravity vector G m balance;

[0027] At the rigid disk node, the horizontal and vertical unbalanced forces F ux and F uy The expression is:

[0028]

[0029]

[0030] Among them, e is the eccentricity, m is the mass of the disk, t is the time, is the eccentric angle.

[0031] Furthermore, a phase shift angle θ is introduced into the output signal of the phase shift LMS algorithm, and the phase shift angle is set to -90°, so that within the full speed range of the flexible rotor, the phase difference between the phase of the output signal of the phase shift LMS algorithm and the phase of the actual unbalanced force falls between -90° and 90°, thereby achieving the effects of disturbance compensation and co-frequency vibration suppression.

[0032] Furthermore, the continuous domain transfer function H of the phase shift LMS algorithm is θ (s) is:

[0033]

[0034] Where s is the Laplace operator, T z is the sampling time;

[0035] The disturbance estimation equation of the linear extended state observer is changed to:

[0036]

[0037] Transfer function H from unbalanced force vector to disturbance estimation error of electromagnetic bearing flexible rotor system e (s) is:

[0038]

[0039] Where, L = [β1 β2 β3] T =[3ω o 3ω o 2 ω o 3 ] T ;

[0040] The phase shift LMS algorithm makes the transfer function H e (s) has a zero at the operating frequency, so the disturbance estimation error is reduced to zero.

[0041] The basic principle of the present invention is that for an electromagnetic bearing flexible rotor system, an unbalanced force with the same frequency as the rotational speed will increase the rotor vibration, and the vibration must be suppressed. By establishing a dynamic model of an electromagnetic bearing flexible rotor system, a mathematical model of a linear anti-disturbance controller, and a phase-shifted LMS algorithm, a method for suppressing the same-frequency vibration of an electromagnetic bearing flexible rotor system based on disturbance compensation is proposed. The linear extended state observer inside the linear anti-disturbance controller can observe disturbances such as unknown dynamic characteristics and unbalanced forces of the rotor, but the linear extended state observer will have a lag when observing high-speed frequency sinusoidal disturbances. The present invention uses a phase-shifted LMS algorithm to extract the same-frequency amount in the disturbance, and compensates with the disturbance observation item as the compensation object. The linear extended state observer after adding disturbance compensation can accurately estimate the sinusoidal disturbance with the same frequency as the rotational speed, and at the same time, through the linear control law, it can suppress the same-frequency vibration in the rotational speed range including rigid body translation and cone critical, first-order and second-order bending critical, etc.

[0042] The advantages of the present invention compared with the prior art are:

[0043] (1) In order to avoid the problem in the prior art that the polarity needs to be switched when the rotor crosses the rigid body critical point, the present invention proposes a method for suppressing the same-frequency vibration of an electromagnetic bearing flexible rotor system based on disturbance compensation, which can enable a linear extended state observer to accurately observe the same-frequency sinusoidal disturbance and accurately control the vibration of the rotor system without switching polarity.

[0044] (2) The same frequency vibration suppression method of the present invention is applicable to an electromagnetic bearing flexible rotor system, and its operating speed includes the full speed range including rigid body translation and cone motion critical, first-order and second-order bending critical. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of the present invention;

[0046] Figure 2 It is the block diagram of linear active disturbance rejection controller;

[0047] Figure 3 It is the block diagram of LMS algorithm;

[0048] Figure 4 The frequency characteristic diagram of the error in estimating the unbalanced force to disturbance;

[0049] Figure 5 Block diagram of the linear extended state observer for the LMS algorithm with phase offset insertion;

[0050] Figure 6 is the frequency characteristic diagram of disturbance estimation error with and without disturbance compensation;

[0051] Figure 7 is the phase diagram of the phase shift LMS algorithm. DETAILED DESCRIPTION

[0052] In order to better understand the technical solution of the present application, the embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0053] It should be clear that the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present application.

[0054] The terms used in the embodiments of the present application are only for the purpose of describing specific embodiments, and are not intended to limit the present application. The singular forms "a", "said" and "the" used in the embodiments of the present application and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings.

[0055] like Figure 1 As shown in the figure, the implementation process of a synchronous vibration suppression method of an electromagnetic bearing flexible rotor system based on disturbance compensation is: first, a mathematical model of a linear anti-disturbance controller and a phase shift LMS algorithm model are established, and then a synchronous vibration suppression method of an electromagnetic bearing flexible rotor system based on disturbance compensation is designed in a speed range including rigid body translation and cone critical, first-order and second-order bending critical.

[0056] Step 1: Before establishing the mathematical model of the linear ADRC, establish the dynamic model of the electromagnetic bearing flexible rotor system. Take an electromagnetic bearing flexible rotor system with multiple rigid disks as an example. The mass and stiffness vary along the axial direction. To analyze the dynamics of this system, it is necessary to solve the partial differential equations about time and space. Therefore, a discretization method is usually used for modeling. Set n nodes on the rotor, and treat the electromagnetic force of the active magnetic bearing (AMB) as a generalized external force. It is considered that the electromagnetic force of the electromagnetic bearing is the external force exerted on the rotor at the electromagnetic bearing node. It only needs to be superimposed on the electromagnetic bearing node. Similarly, the unbalanced force is regarded as the external force exerted on the flexible rotor at the rigid disk node.

[0057] Using the shaft unit model, the dynamic equation of the electromagnetic bearing flexible rotor system at a constant speed can be obtained as follows:

[0058]

[0059] Among them, M, D, G, and K are the 4n×4n-dimensional mass matrix, damping matrix, gyro matrix, and stiffness matrix, respectively. Ω is the rotation speed, and F MAG is the electromagnetic force vector of the 4n×1 dimensional electromagnetic bearing, F u is the 4n×1 dimensional unbalanced excitation force vector, Gm is the 4n×1 dimensional gravity vector, and q is the generalized displacement vector.

[0060] The electromagnetic force of the electromagnetic bearing is a nonlinear function of the coil current i and the rotor displacement q. For the convenience of analysis, a linear expansion is performed near the working point (q0, i0), and the linearized expression of the electromagnetic force of the electromagnetic bearing is obtained as follows:

[0061] F MAG =F MAG,0 +K i (i–i0)+K x (q–q0)

[0062] Among them, F MAG,0 is the electromagnetic force at the working point (q0, i0), i is the control current vector, K i is the current stiffness coefficient matrix of the electromagnetic bearing, K x is the displacement stiffness coefficient matrix of the electromagnetic bearing. In general, F MAG,0 Just with the gravity vector G m balance.

[0063] At the rigid disk node, the expressions of the unbalanced forces in the horizontal and vertical directions are:

[0064]

[0065]

[0066] Among them, e is the eccentricity, m is the mass of the disk, is the eccentric angle.

[0067] The electromagnetic bearing flexible rotor system is a multi-input multi-output system. In order to use the analysis method of multi-input multi-output system, the dynamic equation of the electromagnetic bearing flexible rotor system is expressed as the state space equation:

[0068]

[0069] in, C s =[C m O], T s is the position matrix of the electromagnetic bearing, C m is the sensor output matrix.

[0070] Then, a linear ADRC model is established. In the concept of ADRC, the system is subject to "internal disturbance" consisting of internal unmodeled dynamics and "external disturbance" consisting of external disturbances during operation. Even if the object model is unknown, it can be observed through the disturbance observer, and then the disturbance can be compensated in the controller to reduce the impact of the disturbance on the system. The main components of the structure of the linear ADRC are the linear extended state observer and the linear control law, such as Figure 2 shown.

[0071] The second-order controlled object can be described by the following differential equation:

[0072]

[0073] Among them, y is the displacement, a1 and a0 are the model information, ω is the external disturbance force, b is the system control gain of the controlled object, and u is the control input.

[0074] Since the model information is unknown, the perturbation term expression is defined as:

[0075]

[0076] This disturbance term contains model information and external disturbance force, which is called total disturbance. In order to observe the disturbance, the disturbance is taken as the third state variable, and the state equation of the linear extended state observer is:

[0077]

[0078] in, C=[1 0 0]

[0079] After parameterization, the poles of the characteristic equation of the linear extended state observer are configured to the same position (–ω o , 0), we can solve the gain matrix L = [3ω o 3ω o 2 ω o 3 ] T ,ω o is the observer bandwidth.

[0080] The linear control rate is designed as u = [k p (Ref–z1)–k d z2–z3] / b0. Ref is the reference value of displacement control of electromagnetic bearing flexible rotor system. k p =ω c 2 , k d =2ω c ,ω c is the controller bandwidth.

[0081] Step 2: The structure of the standard LMS algorithm is as follows Figure 3 As shown, the iterative expression from step k to step k+1 is:

[0082] y(k)=w1(k)sin(ω r k)+w2(k)cos(ω r k),

[0083] w1(k+1)=w1(k)+2u x (k)sin(ω r k),

[0084] w2(k+1)=w2(k)+2u x (k)cos(ω r k)

[0085] Among them, x is the input, y is the output, w1 and w2 are weight coefficients, ω r is the center frequency of the algorithm, and u is the step size.

[0086] By performing Z transform on the discrete expression, the transfer function of the standard LMS algorithm is obtained as follows:

[0087]

[0088] The algorithm has a peak z = e jωrTz , indicating that the gain at the algorithm center frequency is infinite, where T z is the sampling time. Based on the structure of the standard LMS algorithm, the phase shift angle θ is introduced into the sine and cosine components of the algorithm output information, and its iterative expression is:

[0089] y(k)=w1(k)sin(ω r k+θ)+w2(k)cos(ω r k+θ)

[0090] The calculation method of the weight coefficient is the same as the standard LMS algorithm. This algorithm is called the phase offset LMS algorithm, and the introduction of the phase offset angle will affect the phase of the output signal.

[0091] Step 3: Design a co-frequency vibration suppression method based on disturbance compensation

[0092] The linear extended state observer established in step 1 cannot accurately estimate high-frequency sinusoidal disturbances. The frequency characteristics of the unbalanced force to disturbance estimation error are as follows: Figure 4As shown. As the frequency increases, the disturbance estimation error gradually increases and the phase lags. To address this problem, the present invention adopts a method based on disturbance compensation, using the phase offset LMS algorithm to track the same-frequency vibration signal and insert it into the disturbance observation value as disturbance compensation, so that the extended state observer can accurately estimate the high-frequency sinusoidal disturbance. Its principle block diagram is shown in Figure 5 shown.

[0093] The continuous domain transfer function of the phase shift LMS algorithm model established in step 2 is:

[0094]

[0095] After embedding the LMS algorithm, the disturbance estimation term equation of the linear extended state observer is changed to:

[0096]

[0097] The transfer function from the unbalanced force vector to the disturbance estimation error is:

[0098]

[0099] Where, L = [β1 β2 β3] T This transfer function will add a zero at the center frequency of the phase offset LMS algorithm, making the disturbance estimation error zero at this frequency. Figure 6 As shown in the figure, the center frequency is set to 100 Hz. Therefore, after adding disturbance compensation, the disturbance estimation can accurately track the unbalanced force vector. After the extended state observer obtains an accurate disturbance estimate, the disturbance estimate is controlled in the linear control rate part to reduce the same-frequency vibration.

[0100] The above process is called co-frequency vibration suppression based on disturbance compensation, and its effective condition is that the phase difference between the output signal of the phase-shifted LMS algorithm and the unbalanced force vector is between –90° and 90°. The phase difference between the unbalanced force vector and the increment of the disturbance observation term in the linear extended state observer is greater than 90° in the range of 0 to 15 Hz, and less than 90° in the range greater than 15 Hz. Therefore, compared with the phase of the unbalanced force vector, the phase of the output signal of the standard LMS algorithm without a phase shift angle in the range of 0 to 15 Hz is greater than 90°, so that the standard LMS algorithm cannot effectively compensate for disturbances in this range, such as Figure 7 As shown. The present invention adopts a phase shift method, and by introducing a -90° phase shift angle, the phase of the output signal of the phase shift LMS algorithm in the entire rotation range of the flexible rotor falls within the range of -90° to 90°. Therefore, in the entire rotation range of the flexible rotor system including the rigid body translation and cone critical, first-order and second-order bending critical, the phase shift LMS algorithm can effectively compensate for disturbances.

[0101] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0102] The above is a description of a specific embodiment of the specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the embodiments and still achieve the desired results. In addition, the processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0103] The terms used in one or more embodiments of this specification are only for the purpose of describing specific embodiments, and are not intended to limit one or more embodiments of this specification. The singular forms of "a", "said" and "the" used in one or more embodiments of this specification and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0104] It should be understood that although the terms first, second, third, etc. may be used to describe various information in one or more embodiments of this specification, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of one or more embodiments of this specification, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0105] The above description is merely a preferred embodiment of one or more embodiments of the present specification and is not intended to limit one or more embodiments of the present specification. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of one or more embodiments of the present specification shall be included in the scope of protection of one or more embodiments of the present specification.

Claims

1. A method for suppressing the same-frequency vibration of an electromagnetic bearing flexible rotor system based on disturbance compensation, characterized in that: The following steps are involved: Step 1: Establish the mathematical model of linear ADRC The main components of the linear active disturbance rejection controller are a linear extended state observer and a linear control law; The state equation of the linear extended state observer is: Where, the state vector z = [z1 z2 z3] T , z1, z2, z3 are the flexible rotor displacement, the derivative of the flexible rotor displacement, and the observed value of the disturbance, respectively. The superscript T of the matrix indicates the transpose; C = [1 0 0], b0 is the control gain of the linear active disturbance rejection controller; u is the input of the linear active disturbance rejection controller; y is the true value of the flexible rotor displacement, is the observed value of the flexible rotor displacement; L is the gain matrix of the linear extended state observer; All poles of the characteristic equation of the linear extended state observer are placed in the same position (–ω o ,0), the gain matrix L=[3ω o 3ω o 2 ω o 3 ] T ,ω o is the bandwidth of the linear extended state observer; The linear control law is designed as u=[k p (Ref-z1)-k d z2–z3] / b0, where Ref is the reference value of displacement control of the electromagnetic bearing flexible rotor system; k p =ω c 2 , k d =2ω c ,ω c is the bandwidth of the linear ADRC controller; Step 2: Introduce the phase shift angle θ into the sine and cosine components of the standard LMS algorithm output signal to obtain the phase shift LMS algorithm. The iterative expression of the output signal from step k to step k+1 is: y(k)=w1(k)sin(ω r k+θ)+w2(k)cos(ω r k+θ) w1(k+1)=w1(k)+2UX(k)sin(ω r k) w2(k+1)=w2(k)+2UX(k)cos(ω r k) Among them, X(k) is the input signal of the kth step, y(k) is the output signal of the kth step, w1 and w2 are weight coefficients, ω r is the center frequency, U is the step size; Step 3: Suppression of co-frequency vibration of electromagnetic bearing flexible rotor system based on disturbance compensation Aiming at the problem that the linear extended state observer cannot accurately estimate the sinusoidal disturbance of high speed frequency in step 1, a phase shift LMS algorithm is used to compensate the disturbance observation value. The input signal of the phase shift LMS algorithm is the derivative of the disturbance observation value in the linear extended state observer, and its output signal is inserted into the disturbance observation value as disturbance compensation. After adding disturbance compensation, the linear extended state observer can accurately estimate the sinusoidal disturbance with the same frequency as the speed, and at the same time, the linear control law can be used to suppress the same frequency vibration. The continuous domain transfer function H of the phase-shift LMS algorithm θ (s) is: Where s is the Laplace operator, T z is the sampling time; The disturbance estimation equation of the linear extended state observer is changed to: Transfer function H from unbalanced force vector to disturbance estimation error of electromagnetic bearing flexible rotor system e (s) is: Where, L=[β1 β2 β3] T =[3h o 3h o 2 oh o 3 ] T ; The phase shift LMS algorithm makes the transfer function H e (s) has a zero point at the operating frequency, so the disturbance estimation error is reduced to 0; The effective condition for the same-frequency vibration suppression of the electromagnetic bearing flexible rotor system based on disturbance compensation is that the phase difference between the output signal of the phase-shifted LMS algorithm and the unbalanced force vector is between -90° and 90°.

2. The same frequency vibration suppression method according to claim 1, characterized in that: Before establishing the mathematical model of the linear active disturbance rejection controller, the dynamic model of the electromagnetic bearing flexible rotor system is established, specifically: Set n nodes in the axial direction of the flexible rotor, and use the finite element method to model the dynamic equation of the electromagnetic bearing flexible rotor system: Among them, M, D, G, K are the 4n×4n-dimensional mass matrix, damping matrix, gyro matrix and stiffness matrix respectively; Ω is the rotation speed, F MAG is the electromagnetic force vector of the 4n×1 dimensional electromagnetic bearing, F u is a 4n×1 dimensional unbalanced force vector, G m is the 4n×1 dimensional gravity vector, q is the generalized displacement vector; The electromagnetic force of the electromagnetic bearing is a nonlinear function of the coil current i and the displacement vector q. By linear expansion near the working point (q0, i0), the linearized expression of the electromagnetic force of the electromagnetic bearing is obtained as follows: F MAG =F MAG,0 +K i (i–i0)+K x (q–q0) Among them, F MAG,0 is the electromagnetic force at the working point (q0,i0), K i is the current stiffness coefficient matrix of the electromagnetic bearing, K x is the displacement stiffness coefficient matrix of the electromagnetic bearing; At the rigid disk node, the horizontal and vertical unbalanced forces F ux and F uy The expression is: Among them, e is the eccentricity, m is the mass of the disk, t is the time, is the eccentric angle.

3. The same frequency vibration suppression method according to claim 1, characterized in that: A phase shift angle θ is introduced into the output signal of the phase shift LMS algorithm, and the phase shift angle is set to -90°, so that within the full speed range of the flexible rotor, the phase difference between the phase of the output signal of the phase shift LMS algorithm and the phase of the actual unbalanced force falls between -90° and 90°, thereby achieving the effects of disturbance compensation and co-frequency vibration suppression.

4. The same frequency vibration suppression method according to claim 1, characterized in that: The output signal in the phase shift LMS algorithm is a sinusoidal signal with the same frequency as the rotation speed and a phase shift angle of θ.

5. The same frequency vibration suppression method according to claim 1, characterized in that: For the phase difference between the unbalanced force of the electromagnetic bearing flexible rotor system and the derivative of the disturbance observation value in the linear expansion state observer, the phase difference is not less than 90° within a frequency range not greater than 15 Hz, and the phase difference is less than 90° within a frequency range greater than 15 Hz.

6. The same frequency vibration suppression method according to claim 1, characterized in that: The method estimates and compensates for unbalanced forces in an electromagnetic bearing flexible rotor system.

7. The same frequency vibration suppression method according to claim 1, characterized in that: The method is used to cross the multi-order rigid body and multi-order bending critical speed regions of the electromagnetic bearing flexible rotor system.

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