CN112432634B - Harmonic vibration force suppression method based on multi-synchronous rotation coordinate transformation - Google Patents

Abstract

The invention discloses a method for suppressing the harmonic vibration force of a magnetic levitation rotor based on a multi-synchronous coordinate transformation method. A method for suppressing harmonic vibration force of a magnetic levitation rotor. Among them, MSRFT can accurately suppress harmonic vibration force, use a controller to suppress vibration in X and Y directions at the same time, use less hardware computing resources, and accelerate the dynamic process of suppression. At the same time, the introduction of phase compensation angle can ensure the absolute stability of the system in a larger frequency range. The MSRFT controller in the invention has a simple structure and is very convenient in practical application. It can suppress the harmonic vibration force in the magnetic levitation rotor, and is suitable for the suppression of the harmonic vibration force of the magnetic levitation rotor system with mass imbalance and sensor harmonics.

Description

A Harmonic Vibration Force Suppression Method Based on Multi-synchronous Rotational Coordinate Transformation

technical field

The invention relates to the technical field of harmonic vibration force suppression of magnetic suspension rotors, in particular to a method for suppression of harmonic vibration force of magnetic suspension rotors based on a multi-synchronous rotation coordinate transformation method, which is used to control the torque gyro rotor system of magnetic suspension within the full operating speed range The harmonic vibration force can be suppressed, providing technical support for the application of magnetic levitation control moment gyroscope on "ultra-quiet" and "ultra-stable" satellite platforms.

Background technique

The control moment gyroscope has the advantages of large output torque and fast response speed, and has become a key attitude control inertial actuator for high-performance satellites. Compared with traditional mechanical bearings, active magnetic bearings can realize the non-contact support of the rotor, so it has the advantages of no friction, no lubrication, high speed, etc., and the active vibration is controllable. Compared with the traditional mechanical gyroscope, the maglev control moment gyroscope has the characteristics of micro-vibration, and has been widely used in high-performance satellites.

However, due to the machining error of the rotor and the measurement error of the sensor, the magnetic levitation control torque gyro also inevitably has some vibrations. Two of the main vibration sources are rotor mass imbalance and sensor harmonics. Mass imbalance is manifested as the misalignment of the geometric center and mass center of the rotor. When the rotor rotates at high speed, a large centrifugal force will be generated, and its amplitude will increase with the rotation. As the speed increases, the frequency is the same as the rotational frequency; the sensor harmonics come from the roundness error of the measurement surface, so that the output signal of the displacement sensor contains harmonic interference with the same frequency and double frequency as the rotational speed, so that the active magnetic levitation control torque gyro Magnetic bearing electromagnetic coils generate harmonic currents of the same frequency and double frequency, thereby generating harmonic vibration force. These harmonic vibration forces are transmitted to the satellite platform through the base, which seriously affects the pointing accuracy and attitude stability of the satellite.

In order to solve these vibrations, the traditional method is to use a mechanical vibration isolation device to isolate the vibration source by adding a physical device. On the one hand, the vibration isolation device is expensive, bulky, and inconvenient to maintain. The vibration damping performance will inevitably be affected; on the other hand, the vibration isolation device cannot eliminate the vibration, but converts the low-frequency and high-amplitude vibration into high-frequency and low-amplitude vibration, and the vibration energy is not reduced. Therefore, the active vibration control of the maglev control moment gyroscope and the elimination of vibration through the vibration control algorithm are an effective method to solve the vibration.

Magnetic levitation control torque gyro active vibration control algorithms mainly include wave trap, resonance controller, repetitive controller and LMS, etc. The repetitive controller is an effective method to deal with harmonic interference, but the repetitive control has the disadvantage of slow response speed, LMS The calculation of the algorithm is large, and it is not easy to implement. Although the structure of the wave trap and the resonant controller is simple, when dealing with multiple frequencies, multiple controllers need to be connected in parallel, which increases the computational burden of the system.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art and propose a method for suppressing the harmonic vibration force of a magnetic levitation rotor based on a multi-synchronous rotating coordinate transformation method. The bearing force constructed by using the current and displacement according to the electromagnetic force model is used as the control Algorithm input can realize the complete suppression of vibration force. Using the orthogonal characteristics of X and Y direction signals, one controller can simultaneously suppress vibration force in two directions, reducing computing resources and improving dynamic response speed. By introducing phase compensation The angle compensates the phase in different frequency bands, realizing the absolute stability of the whole working frequency band.

The technical solution adopted in the present invention is: a method for suppressing harmonic vibration force of a magnetic levitation rotor based on a multi-synchronous coordinate transformation method, comprising the following steps:

Step (1) Establish a fully active maglev rotor dynamics model with mass unbalance and sensor harmonics

The application object of the invention is the active magnetic bearing system in the magnetic suspension control moment gyroscope. Suppose N is the geometric center of the stator, NXY is the inertial coordinate system, C and O are the mass center and geometric center of the rotor respectively, and Oεη is the rotating coordinate system. The present invention is mainly aimed at the suppression of the vibration force of two degrees of freedom in radial translation, so only the modeling of two degrees of freedom in translation is considered. According to Newton's second law, the following kinetic equation is obtained:

Where m is the mass of the rotor, x(t), y(t) represent the translational displacement of the rotor mass center in the X direction and Y direction, respectively, f _x (t), f _y (t) are the displacements in the X direction and Y direction, respectively The resultant force of bearing force, f _ax (t), f _bx (t), f _ay (t), f _by (t) is the bearing force of four pairs of radial magnetic bearings. When the rotor moves with small displacement, the nonlinear bearing force can be approximately linearized, which can be expressed as follows:

Where K _i , K _h are current stiffness and displacement stiffness respectively, i _ax (t), i _bx (t), i _ay (t), i _by (t) are four pairs of radial magnetic bearing coil currents, x _a ( t), x _b (t), y _a (t), y _b (t) are the displacements in the bearing coordinate system; the subscripts a and b represent the A and B ends of the rotor system;

Due to the unbalanced mass, the geometric center does not coincide with the mass center, and the displacement sensor measures the displacement of the rotor geometric center, which has the following relationship:

X(t)=x(t)+Θ _x (t)

Y(t)=y(t)+Θ _y (t)

Among them, X(t) and Y(t) respectively represent the displacement of the geometric center, which can be obtained from the geometric relationship:

Θ _x (t), Θ _y (t) represents the unbalanced quantity, which has the following form:

Θ _x (t) = ecos(Ωt+χ)

Θ _y (t) = esin(Ωt+χ)

e is the magnitude of the unbalance, χ is the initial phase, and Ω is the rotational speed of the rotor. It can be seen that the mass imbalance will generate the same frequency interference signal, so that the active magnetic bearing will generate the same frequency vibration force.

Due to the presence of sensor harmonics in the displacement sensors, the output signals of the four pairs of displacement sensors are not the real displacement signals of the rotor. The signals provided by the displacement sensors are as follows:

x _as (t), x _bs (t), y _as (t), y _bs (t) are displacement sensor output signals; d _axs (t), d _bxs (t), d _ays (t), d _bys ( t) is the sensor harmonic interference signal, which can be expressed as follows:

Among them, s _{ai and} s _bi are the sensor harmonic amplitudes, χ _i is the initial phase, and i is the harmonic order. The sensor harmonics will generate interference signals with the same frequency and double frequency as the rotational speed, which will cause the magnetic bearing system to generate harmonic vibration force.

Step (2) Design a method for suppressing the harmonic vibration force of the maglev rotor based on the multi-synchronous rotation coordinate transformation method

The controller takes vibration force at the same frequency and double-frequency current as input, and is connected to the original closed-loop system in parallel, and its output is fed back to the input terminal of the power amplifier of the original control system. The design of this module mainly includes the following two aspects:

①Multi-synchronous rotation coordinate transformation method: According to the different forms of vibration forces of the same frequency and double frequency generated by the actual magnetic levitation rotor system, the vibration of the same frequency includes the current stiffness force and the displacement stiffness force, and the double frequency vibration only includes the current stiffness force; according to the system electromagnetic The force model uses current and displacement to construct the same-frequency vibration force as the input of the same-frequency force suppression part of the multi-synchronous rotation coordinate transformation, and double-frequency vibration can be suppressed by suppressing the double-frequency current, so the current is used as the input of the double-frequency force suppression part ;

②Through theoretical analysis and proof, the stability conditions of the multi-synchronous rotating coordinate transformation system are obtained; according to the closed-loop characteristics of the actual maglev rotor system, the corresponding phase compensation angle is designed, and the absolute stability of the system within the operating speed range is realized through the phase compensation angle.

Further, the vibration force suppression algorithm of described step (2) is:

Harmonic suppression by synchronous rotating coordinate transformation mainly includes three parts, namely, the disturbance signal is transformed from a stationary coordinate system to a rotating coordinate system through synchronous rotating coordinate transformation. , and then identify the DC flow through low-pass filtering, and finally obtain the same-frequency/multiple-frequency interference signal in the stationary coordinate system through inverse transformation of synchronous rotating coordinates. The closed-loop structure formed by feeding back the output to the output terminal of the power amplifier can effectively suppress the same-frequency/double-frequency vibration force.

Since the phases of each frequency band of the system are inconsistent, to ensure the absolute stability of the system within the entire operating frequency range, it is necessary to introduce a phase compensation angle for phase compensation. The coordinate transformation equation of synchronous rotation with phase compensation angle is as follows:

是相位补偿角，用来确保闭环稳定性，i是正整数，当输入信号谐波频率为Ω的i倍时，经过同步旋转坐标变换后输出为直流信号，经过低通滤波即可提取原信号中的谐波成分，设低通滤波器有如下传递函数：Among them, u ₁ (t), u ₂ (t) are input signals, u _dc1 (t), u _dc2 (t) are output signals of synchronous rotation coordinate transformation; Ω is rotor rotation speed,

is the phase compensation angle, used to ensure the stability of the closed loop, i is a positive integer, when the harmonic frequency of the input signal is i times of Ω, the output is a DC signal after synchronous rotation coordinate transformation, and the original signal can be extracted by low-pass filtering The harmonic components of , the low-pass filter has the following transfer function:

Wherein k is the low-pass filter gain coefficient, ω _c is the cut-off frequency;

令u_dc1(t),u_dc2(t),

的拉普拉斯变换分别为u_dc1(s),u_dc2(s),

有以下等式成立：Suppose the signal after low-pass filtering is

Let u _dc1 (t), u _dc2 (t),

The Laplace transforms are respectively u _dc1 (s), u _dc2 (s),

The following equation holds:

Rewrite the above formula as follows:

Inverse Laplace transform of the above formula can get the following differential equation:

Let κ=kω _c , write the above formula in matrix form as follows:

The low-pass filtered signal needs to be inversely transformed from the synchronous rotating coordinates to the original stationary coordinate system, and the transformation relationship is expressed as follows:

x ₁ (t), x ₂ (t) are the output signals after synchronous rotation coordinate inverse transformation;

From the above formulas, the following state space expressions can be solved:

The transfer function matrix is derived from the state-space expression:

The corresponding input-output relationship is:

u ₁ (t), u ₂ (t) are orthogonal sinusoidal signals, assuming the following form:

A _m and γ represent the amplitude and initial phase of the signal, respectively;

It can be seen from the above formula that the following relationship exists:

iΩu ₁ (s)＝su ₂ (s)

According to the above formula, the equivalent single-input transfer function can be obtained:

Let s=jω, when ω=iΩ, we can get:

When ω _c <<κ, it can be considered that the synchronous rotation coordinate transformation produces a large gain at the harmonic frequency, and the effective suppression of the harmonic component can be realized after forming a closed loop with the original system. Harmonic vibration forces of the system are thus eliminated.

The basic principle of the invention is that the magnetic suspension control moment gyroscope is supported by magnetic suspension bearings, and for the magnetic suspension rotor, the main sources of its vibration are mass imbalance and sensor harmonics. Due to the existence of mass imbalance and sensor harmonics, the maglev rotor system contains harmonic vibration forces. The harmonic vibration force is transmitted to the spacecraft through the base, which seriously affects the performance of the spacecraft platform. Aiming at the harmonic vibration force of the magnetic levitation rotor of the magnetic levitation control moment gyroscope, the present invention proposes a harmonic vibration force suppression algorithm based on a multi-synchronous rotating coordinate transformation method by establishing a magnetic levitation rotor dynamics model including mass unbalance and sensor harmonics . Utilizing the orthogonal characteristics of the output signals of the displacement sensors in the X and Y directions, one controller is used to suppress the vibration force in both directions at the same time, and multiple algorithms with different frequencies are connected in parallel to realize the suppression of the vibration of the same frequency and double frequency, and phase compensation is introduced. Angle, by changing the phase angle in different frequency bands to ensure the stability of the system in the full speed range.

The advantage of the present invention compared with prior art is:

1) The traditional maglev rotor vibration suppression method is mostly zero-current control. Most vibration forces are suppressed by suppressing harmonic currents. However, suppressing harmonic currents can only suppress current stiffness forces, and there are also participating displacement stiffness forces that cannot be suppressed. . The present invention uses current and displacement to construct vibration force as an input signal, which can realize the suppression of all vibration forces.

2) The present invention utilizes the orthogonality characteristic of the output signal of the displacement sensor, uses one controller to realize vibration suppression in two directions at the same time, reduces system computing resources, and improves dynamic response speed. And through the phase compensation angle, different phase angles can be selected in different frequency bands, which can ensure the stability of the system in the full speed range.

Description of drawings

Fig. 1 is a flowchart of the present invention;

Fig. 2 is a schematic diagram of the structure of the magnetic levitation rotor system, where 1 is the active magnetic bearing, 2 is the rotor, 3 is the geometric axis of the rotor, and 4 is the inertial axis of the rotor;

Figure 3 is a block diagram of the basic control system of the maglev rotor;

Fig. 4 schematic diagram of synchronous selection coordinate transformation principle, wherein, 5 is a sensor probe, and 2 is a rotor;

Fig. 5 synchronous selection coordinate transformation algorithm principle block diagram;

Fig. 6 is a multi-synchronous rotating coordinate transformation method and a block diagram of the composite control system of the main controller;

Fig. 7 is a simplified block diagram of the composite control system of the equivalent single-input synchronous rotation coordinate transformation method and the main controller.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

According to an embodiment of the present invention, as shown in Fig. 1, the implementation process of a magnetic levitation rotor harmonic vibration force suppression method based on the multi-synchronous rotating coordinate transformation method is: firstly establish the magnetic levitation rotor dynamic force with mass unbalance and sensor harmonics Then design a controller based on multi-synchronous rotation coordinate transformation method to suppress the harmonic vibration force.

Step (1) Establish a maglev rotordynamics model with mass unbalance and sensor harmonics

The application object of the invention is the active magnetic bearing system in the magnetic suspension control moment gyroscope. The schematic diagram of its structure is shown in Figure 2. Let N be the geometric center of the stator, NXY be the inertial coordinate system, C and O be the mass center and geometric center of the rotor, respectively, and Oεη be the rotating coordinate system. The present invention is mainly aimed at the suppression of the vibration force of the two degrees of freedom in radial translation, so only the modeling of the two degrees of freedom in translation is considered. According to Newton's second law, the following kinetic equation is obtained:

Where m is the mass of the rotor, x(t), y(t) represent the translational displacement of the rotor mass center in the X direction and Y direction, respectively, f _x (t), f _y (t) are the displacements in the X direction and Y direction, respectively The resultant force of the bearing force, f _ax (t), f _bx (t), f _ay (t), f _by (t) are four pairs of radial magnetic bearings (two pairs at each end of A and B, the magnetic bearings in the figure are only Section, only one pair can be seen at both ends of A and B, so the figure only shows the bearing force of one pair). When the rotor moves with small displacement, the nonlinear bearing force can be approximately linearized, which can be expressed as follows:

Where K _i , K _h are current stiffness and displacement stiffness respectively, i _ax (t), i _bx (t), i _ay (t), i _by (t) are four pairs of radial magnetic bearing coil currents, x _a ( t), x _b (t), y _a (t), y _b (t) are the displacements in the bearing coordinate system.

It can be seen from Figure 2 that due to mass imbalance, the geometric center does not coincide with the mass center, and the displacement sensor measures the displacement of the rotor geometric center, which has the following relationship:

X(t)=x(t)+Θ _x (t)

Y(t)=y(t)+Θ _y (t)

Among them, X(t) and Y(t) respectively represent the displacement of the geometric center, which can be obtained from the geometric relationship:

Θ _x (t), Θ _y (t) represents the unbalanced quantity, which has the following form:

Θ _x (t) = ecos(Ωt+χ)

Θ _y (t) = esin(Ωt+χ)

e is the magnitude of the unbalance, χ is the initial phase, and Ω is the rotational speed of the rotor. It can be seen that the mass imbalance will generate the same frequency interference signal, so that the active magnetic bearing will generate the same frequency vibration force.

Due to the presence of sensor harmonics in the displacement sensors, the output signals of the four pairs of displacement sensors are not the real displacement signals of the rotor. The signals provided by the displacement sensors are as follows:

x _as (t), x _bs (t), y _as (t), y _bs (t) are displacement sensor output signals; d _axs (t), d _bxs (t), d _ays (t), d _bys ( t) is the sensor harmonic interference signal, which can be expressed as follows:

Among them, s _{ai and} s _bi are the sensor harmonic amplitudes, χ _i is the initial phase, and i is the harmonic order. The sensor harmonics will generate interference signals with the same frequency and double frequency as the rotational speed, which will cause the magnetic bearing system to generate harmonic vibration force. The control schematic diagram of the maglev rotor system with mass unbalance and sensor harmonics is shown in Fig. 3, where G _c (s), G _w (s) represent the transfer function of the controller and the transfer function of the power amplifier, respectively, and K _s represents the sensor gain factor.

Step (2): Design a method for suppressing the harmonic vibration force of the maglev rotor based on the multi-synchronous rotating coordinate transformation method

The controller takes vibration force at the same frequency and double-frequency current as input, and is connected to the original closed-loop system in parallel, and its output is fed back to the input terminal of the power amplifier of the original control system. The design of this module mainly includes the following two aspects:

①Multi-Synchronous Rotating Frame Transformation (Multi-Synchronous Rotating Frame Transformation, MSRFT): According to the different forms of vibration forces of the same frequency and double frequency generated by the actual magnetic levitation rotor system, the same frequency vibration includes current stiffness force and displacement stiffness force, double frequency vibration Only the current stiffness force is included; according to the model of the electromagnetic force of the system, the current and displacement are used to construct the same-frequency vibration force as the input of the same-frequency force suppression part of the multi-synchronous rotation coordinate transformation. The double-frequency vibration can be suppressed by suppressing the double-frequency current, so the The current is used as the input of the frequency doubling force suppression part;

②Through theoretical analysis and proof, the stability conditions of the multi-synchronous rotating coordinate transformation system are obtained; according to the closed-loop characteristics of the actual maglev rotor system, the corresponding phase compensation angle is designed, and the absolute stability of the system within the operating speed range is realized through the phase compensation angle.

Further, the vibration force suppression algorithm of described step (2) is:

Harmonic suppression by synchronous rotating coordinate transformation mainly includes three parts, namely, the disturbance signal is transformed from a stationary coordinate system to a rotating coordinate system through synchronous rotating coordinate transformation. , and then identify the DC flow through low-pass filtering, and finally obtain the same-frequency/multiple-frequency interference signal in the stationary coordinate system through inverse transformation of synchronous rotating coordinates. The schematic diagram of its principle is shown in Figure 4. M is the geometric center of the rotor, C is the center of mass, and ε is the amount of vibration. When the rotor rotates at high speed, it will rotate around the center of mass due to the principle of self-centering. CX _s Y _s is the stationary coordinate system, and CX _r Y _r is the rotating coordinate system, x _s , y _s are the vibration coordinates in the stationary coordinate system, x _r , y _r are the vibration coordinates in the rotating coordinates, and the rotating coordinates rotate synchronously with the rotor, so the vibration in the rotating coordinate system is Continuous flow, low-pass filtering in the rotating coordinate system, and then the inverse transformation of the synchronous rotating coordinates can realize the processing of harmonic components. The closed-loop structure formed by feeding back the output to the output terminal of the power amplifier can effectively suppress the same-frequency/double-frequency vibration force.

1. Analysis of synchronous rotation coordinate transformation algorithm

Since the phases of each frequency band of the system are inconsistent, to ensure the absolute stability of the system within the entire operating frequency range, it is necessary to introduce a phase compensation angle for phase compensation. As shown in Figure 5, the coordinate transformation equation of synchronous rotation with phase compensation angle is as follows:

是相位补偿角，用来确保闭环稳定性，当输入信号谐波频率为Ω的k倍时，经过同步旋转坐标变换后输出为直流信号，经过低通滤波即可提取原信号中的谐波成分，设低通滤波器有如下传递函数：Among them, u ₁ (t), u ₂ (t) are input signals, u _dc1 (t), u _dc2 (t) are output signals of synchronous rotation coordinate transformation; Ω is rotor rotation speed,

Is the phase compensation angle, which is used to ensure the stability of the closed loop. When the harmonic frequency of the input signal is k times of Ω, the output is a DC signal after the synchronous rotation coordinate transformation, and the harmonic component in the original signal can be extracted after low-pass filtering , let the low-pass filter have the following transfer function:

Wherein k is the low-pass filter gain coefficient, ω _c is the cut-off frequency;

令

的拉普拉斯变换分别为u_dc1(s),u_dc2(s),

有以下等式成立：Suppose the signal after low-pass filtering is

make

The Laplace transforms are respectively u _dc1 (s), u _dc2 (s),

The following equation holds:

Rewrite the above formula as follows:

Inverse Laplace transform of the above formula can get the following differential equation:

Let κ=kω _c , write the above formula in matrix form as follows:

The low-pass filtered signal needs to be inversely transformed from the synchronous rotating coordinates to the original stationary coordinate system, and the transformation relationship is expressed as follows:

x ₁ (t), x ₂ (t) are the output signals after synchronous rotation coordinate inverse transformation;

From the above formulas, the following state space expressions can be solved:

The transfer function matrix is derived from the state-space expression:

The corresponding input-output relationship is:

u ₁ (t), u ₂ (t) are orthogonal sinusoidal signals, assuming the following form:

A _m and γ represent the amplitude and initial phase of the signal, respectively;

It can be seen from the above formula that the following relationship exists:

iΩu ₁ (s)＝su ₂ (s)

According to the above formula, the equivalent single-input transfer function can be obtained:

Let s=jω, when ω=iΩ, we can get:

When ω _c <<κ, it can be considered that the synchronous rotation coordinate transformation produces a large gain at the harmonic frequency, and the effective suppression of the harmonic component can be realized after forming a closed loop with the original system.

As shown in Figure 6, the same-frequency vibration force and double-frequency current are used as the input of multi-synchronous rotation coordinate transformation, and the output is fed back to the input terminal of the power amplifier, which is added to the control signal of the main controller to eliminate the harmonic vibration force of the system .

2. Stability analysis

Because the X and Y directions are symmetrical in structure and have the same parameters, take the X direction as an example for stability analysis. The idea of the stability analysis in the present invention is that the insertion of each controller is based on the first stable system, that is, the insertion of the same-frequency vibration force algorithm is based on The original system is stable, and the multiplier suppression algorithm insertion is based on the system stability of the same frequency suppression algorithm. The present invention only analyzes the stability conditions of the insertion system of the same-frequency suppression algorithm, and the insertion of the frequency multiplication algorithm is similar, and the simplified block diagram is shown in FIG. 7 .

The closed-loop characteristic polynomial of the system obtained from Figure 7 is:

1+2K _s K _i G _c (s)G _w (s)P(s)-2K _h P(s)+2K _i G _w (s)G _SRFx (s)＝0

The above formula can be transformed into:

为系统函数。in,

is a system function.

When κ=0, there is s=-ω _c ±jΩ. When κ→0, there is a closed-loop pole moving in the field of -ω _c ±jΩ. In order to ensure that the system has sufficient stability margin, κ is used as an independent variable, and s is because Variable, get the differential at κ=0, s=jΩ, and get the following formula:

To ensure that the closed-loop characteristic functions all follow the left half plane of s after the algorithm is added to the system, the following conditions need to be met:

即上式约为

可以得到下列稳定性条件：Because ω _c ＜＜Ω, so

That is, the above formula is about

The following stability conditions can be obtained:

Properly adjusting the size of the phase compensation angle according to the phase of the system function at different frequencies can make the system stable in the full operating speed range.

Although the illustrative specific embodiments of the present invention have been described above, so that those skilled in the art can understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, As long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.

Claims (1)

1. A magnetic levitation rotor harmonic vibration force suppression method based on multi-synchronous coordinate transformation method, is characterized in that: comprise the following steps: Step (1): Building a maglev rotordynamic model with mass imbalance and sensor harmonics For the active magnetic bearing system in the magnetic levitation control moment gyro, let N be the geometric center of the stator, NXY be the inertial coordinate system, C and O be the mass center and geometric center of the rotor respectively, and Oεη be the rotating coordinate system. The suppression of the vibration force of 1 degree, the modeling of translational two degrees of freedom is carried out; the following dynamic equation is obtained by Newton's second law:

Where m is the mass of the rotor, x(t), y(t) represent the translational displacement of the rotor mass center in the X direction and Y direction, respectively, f _x (t), f _y (t) are the displacements in the X direction and Y direction, respectively The resultant force of the bearing force, f _ax (t), f _bx (t), f _ay (t), f _by (t) is the bearing force of four pairs of radial magnetic bearings, when the rotor performs a displacement movement less than a predetermined threshold, the nonlinear The approximate linearization of the bearing force is expressed as follows:

Where K _i , K _h are current stiffness and displacement stiffness respectively, i _ax (t), i _bx (t), i _ay (t), i _by (t) are four pairs of radial magnetic bearing coil currents, x _a ( t), x _b (t), y _a (t), y _b (t) are the displacements in the bearing coordinate system; the subscripts a and b represent the A and B ends of the rotor system; Due to the unbalanced mass, the geometric center does not coincide with the mass center, and the displacement sensor measures the displacement of the rotor geometric center, which has the following relationship: X(t)=x(t)+Θ _x (t) Y(t)=y(t)+Θ _y (t) Among them, X(t), Y(t) represent the displacement of the geometric center in the X direction and the Y direction, respectively, and can be obtained from the geometric relationship:

Θ _x (t), Θ _y (t) represents the unbalanced quantity, which has the following form; Θ _x (t) = ecos(Ωt+χ) Θ _y (t) = esin(Ωt+χ) e is the amplitude of unbalance, χ is the initial phase, and Ω is the rotating speed of the rotor. The unbalanced mass will generate the same frequency interference signal, so that the active magnetic bearing will generate the same frequency vibration force; Due to the presence of sensor harmonics in the displacement sensors, the output signals of the four pairs of displacement sensors are not the real displacement signals of the rotor. The signals provided by the displacement sensors are as follows:

x _as (t), x _bs (t), y _as (t), y _bs (t) are displacement sensor output signals; d _axs (t), d _bxs (t), d _ays (t), d _bys ( t) is the sensor harmonic interference signal, expressed as follows:

Among them, s _{ai and} s _bi are the harmonic amplitudes of the sensor, χ _i is the initial phase, i is the harmonic order, and n is the highest order of the harmonic. The sensor harmonics will generate interference signals with the same frequency and multiplied frequency as the rotational speed, Make the magnetic bearing system generate harmonic vibration force; Step (2): Design a harmonic vibration force suppression method based on multi-synchronous rotating coordinate transformation Design the controller, which takes the same-frequency vibration force and double-frequency current as input, connects to the original closed-loop system in parallel, and its output is fed back to the power amplifier input of the original control system, including the following two aspects: ①Multi-synchronous rotation coordinate transformation method: According to the different forms of vibration forces of the same frequency and double frequency generated by the actual magnetic levitation rotor system, the vibration of the same frequency includes the current stiffness force and the displacement stiffness force, and the double frequency vibration only includes the current stiffness force; according to the system electromagnetic The force model uses current and displacement to construct the same-frequency vibration force as the input of the same-frequency force suppression part of the multi-synchronous rotation coordinate transformation, and double-frequency vibration can be suppressed by suppressing the double-frequency current, so the current is used as the input of the double-frequency force suppression part ; ② Calculate the stability conditions of the multi-synchronous rotating coordinate transformation system; design the corresponding phase compensation angle according to the closed-loop characteristics of the actual maglev rotor system, and realize the absolute stability of the system within the operating speed range through the phase compensation angle.

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