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CN113565874A - An interference suppression method for magnetic levitation sensor based on variable step size minimum mean square error - Google Patents

An interference suppression method for magnetic levitation sensor based on variable step size minimum mean square error Download PDF

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CN113565874A
CN113565874A CN202110842736.3A CN202110842736A CN113565874A CN 113565874 A CN113565874 A CN 113565874A CN 202110842736 A CN202110842736 A CN 202110842736A CN 113565874 A CN113565874 A CN 113565874A
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rotor
magnetic suspension
step size
mean square
square error
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刘昆
王雨楠
曾塬
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Sun Yat Sen University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C32/00—Bearings not otherwise provided for
    • F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
    • F16C32/0406—Magnetic bearings
    • F16C32/044—Active magnetic bearings
    • F16C32/0444—Details of devices to control the actuation of the electromagnets
    • F16C32/0446—Determination of the actual position of the moving member, e.g. details of sensors
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C32/00—Bearings not otherwise provided for
    • F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
    • F16C32/0406—Magnetic bearings
    • F16C32/044—Active magnetic bearings
    • F16C32/0444—Details of devices to control the actuation of the electromagnets
    • F16C32/0451—Details of controllers, i.e. the units determining the power to be supplied, e.g. comparing elements, feedback arrangements with P.I.D. control
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C32/00—Bearings not otherwise provided for
    • F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
    • F16C32/0406—Magnetic bearings
    • F16C32/044—Active magnetic bearings
    • F16C32/0459—Details of the magnetic circuit
    • F16C32/0468—Details of the magnetic circuit of moving parts of the magnetic circuit, e.g. of the rotor
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/002—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion characterised by the control method or circuitry
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/02—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

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  • General Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Mechanical Engineering (AREA)
  • Aviation & Aerospace Engineering (AREA)
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  • General Physics & Mathematics (AREA)
  • Magnetic Bearings And Hydrostatic Bearings (AREA)

Abstract

本发明公开了一种基于变步长最小均方差的磁悬浮传感器干扰抑制方法，该方法包括：对转子进行受力分析和建模，并识别转子磁悬浮轴承系统的参数；引入变步长最小均方差算法并设定步长因子抑制干扰。通过使用本发明，能够实现磁悬浮飞轮的传感器干扰振动抑制。本发明作为一种基于变步长最小均方差的磁悬浮传感器干扰抑制方法，可广泛应用于磁悬浮转子振动控制领域。

Figure 202110842736

The invention discloses a magnetic suspension sensor interference suppression method based on variable step size minimum mean square error. The method includes: performing force analysis and modeling on a rotor, and identifying parameters of a rotor magnetic suspension bearing system; introducing variable step size minimum mean square error algorithm and set the step size factor to suppress interference. By using the present invention, the sensor disturbance vibration suppression of the magnetic suspension flywheel can be realized. As a method for suppressing interference of a magnetic suspension sensor based on the minimum mean square error of variable step size, the invention can be widely used in the field of vibration control of a magnetic suspension rotor.

Figure 202110842736

Description

Magnetic suspension sensor interference suppression method based on variable step length minimum mean square error
Technical Field
The invention relates to the field of vibration control of magnetic suspension rotors, in particular to a magnetic suspension sensor interference suppression method based on variable step length minimum mean square error.
Background
Electromagnetic bearings have two major sources of vibration, rotor mass imbalance and sensor run-out. However, since the mass imbalance is due to practical manufacturing limitations, the inertial axis of the main shaft does not coincide with the geometric axis, and unbalanced vibration occurs when the rotor rotates at high speed. The sensor vibration is caused by the fact that the surface of the sensor is not uniform, interference is introduced in a measuring link of the sensor, and harmonic interference is mainly caused by the sensor vibration.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a magnetic suspension sensor interference suppression method based on variable step length minimum mean square error, and the method is used for realizing the sensor interference vibration suppression of a magnetic suspension flywheel.
The first technical scheme adopted by the invention is as follows: a magnetic suspension sensor interference suppression method based on variable step length minimum mean square error comprises the following steps:
carrying out stress analysis and modeling on the rotor, and identifying parameters of a rotor magnetic suspension bearing system;
and introducing a variable step size minimum mean square error algorithm and setting a step size factor to suppress interference.
Further, the step of analyzing and modeling the stress of the rotor and identifying the parameters of the rotor magnetic suspension bearing system specifically further comprises:
carrying out stress analysis on the rotor, and obtaining a rotor dynamics equation according to a Newton's law and a Lagrange equation;
constructing a rotor magnetic suspension bearing system model according to a dynamic equation;
and identifying parameters of the rotor magnetic suspension bearing system.
Further, the rotor dynamics equation is formulated as follows:
Figure BDA0003179480060000011
Figure BDA0003179480060000012
Figure BDA0003179480060000013
Figure BDA0003179480060000014
in the above formula, FAX、FBXFor the electromagnetic force of the rotor in the x-direction, FAY、FBYThe electromagnetic force of the rotor along the y direction, alpha and beta are the angular displacement of the rotor rotating around the x and y axes, omega is the rotating speed, l is the length of the rotor, and m is the mass of the rotor.
Further, the expression of the rotor magnetic suspension bearing system model is as follows:
F＝kii+kxx
in the above formula, kiAs a current stiffness system, kxIs the displacement stiffness coefficient.
Further, the parameter for identifying the rotor magnetic suspension bearing system is specifically the displacement stiffness coefficient k of the identification systemxAnd current stiffness coefficient kiThe method specifically comprises the following steps:
horizontally placing the rotor on a test bed and respectively calculating the ratio of the current rigidity coefficient and the displacement rigidity coefficient of the X channel and the Y channel according to the stable suspension of the rotor;
vertically installing a rotor and respectively calculating the current rigidity coefficient and the displacement rigidity coefficient of an X channel and a Y channel according to the stable suspension of the rotor;
and measuring the vertical offset displacement, the horizontal offset displacement, the rotor mass and the vertical angle between the normal direction of the magnetic pole surface and the ground, calculating the current rigidity coefficient and the displacement rigidity coefficient of the X channel, and calculating the current rigidity coefficient and the displacement rigidity coefficient of the Y channel.
Further, the step factor is expressed as follows:
Figure BDA0003179480060000021
in the above formula, f represents the rotor rotation frequency, μ1' denotes a positive parameter, | e (k) | denotes signal error.
The method and the system have the beneficial effects that: the method identifies the displacement stiffness coefficient and the current stiffness coefficient by establishing a model, introduces a variable step length minimum mean square error algorithm to realize suppression of vibration caused by sensor disturbance, and adopts a variable step length factor which changes along with the change of the rotor displacement signal frequency to realize balance, thereby realizing suppression of sensor disturbance vibration of the magnetic suspension flywheel.
Drawings
FIG. 1 is a schematic diagram of steps of a magnetic levitation sensor interference suppression method based on variable step size minimum mean square error of the invention;
FIG. 2 is a force analysis diagram of a rotor according to an embodiment of the present invention;
FIG. 3 is a schematic view of a magnetic bearing incorporating a variable step size minimum mean square error algorithm in accordance with a specific embodiment of the present invention;
FIG. 4 is a block diagram of a least mean square error (LMS) algorithm in accordance with an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments. The step numbers in the following embodiments are provided only for convenience of illustration, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.
The invention provides a magnetic suspension sensor interference suppression method based on variable step length minimum mean square error, which comprises the following steps:
carrying out stress analysis and modeling on the rotor, and identifying parameters of a rotor magnetic suspension bearing system;
and introducing a variable step size minimum mean square error algorithm and setting a step size factor to suppress interference.
Specifically, for different rotation frequencies, a proper step factor needs to be selected to effectively filter the unbalanced interference, so that the fixed-step LMS algorithm can only have a good compensation effect on some fixed rotation frequencies.
Further, as a preferred embodiment of the method, the step of analyzing and modeling the stress of the rotor and identifying the parameters of the rotor magnetic suspension bearing system specifically further includes:
carrying out stress analysis on the rotor, and obtaining a rotor dynamics equation according to a Newton's law and a Lagrange equation;
constructing a rotor magnetic suspension bearing system model according to a dynamic equation;
and identifying parameters of the rotor magnetic suspension bearing system.
Specifically, the force analysis diagram refers to fig. 2.
Further as a preferred embodiment of the method, the rotor dynamics equation has the formula:
Figure BDA0003179480060000031
in the above formula, FAX、FBXFor the electromagnetic force of the rotor in the x-direction, FAY、FBYThe electromagnetic force of the rotor along the y direction, alpha and beta are the angular displacement of the rotor rotating around the x and y axes, omega is the rotating speed, l is the length of the rotor, and m is the mass of the rotor.
Further as a preferred embodiment of the method, the expression of the rotor magnetic suspension bearing system model is as follows:
F＝kii+kxx (2)
in the above formula, kiAs a current stiffness system, kxIs the displacement stiffness coefficient.
In addition, referring to fig. 3, many interference sources exist in the magnetic suspension GMW control system, unbalanced interference force is vibration interference introduced in a rotor dynamics link and is influenced by factors such as a processing technology and installation errors, and interference is also introduced in a sensor measurement link and a magnetic force generation link.
Sensor runout (Sensor disturbance) is expressed in Sensor coordinates as:
Figure BDA0003179480060000032
in the above formula, i is the harmonic order, i is 1,2, … … n; x is the number ofai,xbiAmplitude of ith harmonic of output signal of sensor at two ends of magnetic bearings A and BValue of thetaai,θbiRespectively, corresponding to the initial phase.
Further as a preferred embodiment of the method, the parameter for identifying the rotor magnetic suspension bearing system is specifically a displacement stiffness coefficient k of the identification systemxAnd current stiffness coefficient kiThe method specifically comprises the following steps:
horizontally placing the rotor on a test bed and respectively calculating the ratio of the current rigidity coefficient and the displacement rigidity coefficient of the X channel and the Y channel according to the stable suspension of the rotor;
Figure BDA0003179480060000041
Figure BDA0003179480060000042
vertically installing a rotor and respectively calculating the current rigidity coefficient and the displacement rigidity coefficient of an X channel and a Y channel according to the stable suspension of the rotor;
Figure BDA0003179480060000043
Figure BDA0003179480060000044
measuring vertically displaced offset displacement E [ i ]vx(t)]Horizontally placed offset displacement E [ i ]hx(t)]The rotor mass m and the vertical angle theta between the normal direction of the magnetic pole surface and the ground front surface are calculated, and the current rigidity coefficient k of the X channel is calculatedixAnd coefficient of displacement stiffness khxCalculating the current rigidity coefficient k of the Y channeliyAnd coefficient of displacement stiffness khy。
In particular, the coefficient of stiffness k for displacementxAnd current stiffness coefficient kiAnd (5) performing identification. When the rotor is horizontally placed on the test bed, the kinetic equation is:
Figure BDA0003179480060000045
when the rotor was stably suspended, it was considered that:
Figure BDA0003179480060000046
taking the average value of two sides of the formula (4):
Figure BDA0003179480060000047
according to formula (6):
Figure BDA0003179480060000051
for the X channel, E [ i ] is measuredhx(t)]And E [ x ]h(t)]Then, the ratio of the current stiffness coefficient to the displacement stiffness coefficient can be calculated, and the Y channel is the same as the current stiffness coefficient and the displacement stiffness coefficient.
When the rotor is vertically mounted, the kinetic equation:
Figure BDA0003179480060000052
when the rotor was stably suspended, it was considered that:
Figure BDA0003179480060000053
average value of two sides of formula (8)
Figure BDA0003179480060000054
Due to the existence of the control action, the displacement rigidity force generated by the offset displacement is the same as that generated when the control current is horizontally placed, and the control current additionally comprises a part which is excessive by overcoming the component force of gravity. Subtracting equation (6) from equation (10):
Figure BDA0003179480060000055
influenced by an integral term in a PID controller, after a displacement offset instruction is given, the final steady-state displacement deviation is 0, the given offset displacement instruction is equal, and the method comprises the following steps:
Figure BDA0003179480060000056
the following can be obtained:
Figure BDA0003179480060000057
measured to obtain E [ ivx(t)]、E[ivx(t)]M and theta, k can be calculatedixIn order to improve the accuracy, the average value can be obtained by multipoint measurement, and k can be obtained from the equations (7) and (13)hx。
Further as a preferred embodiment of the method, referring to fig. 3 and fig. 4, a variable step minimum mean square error algorithm is introduced to define x (t) ═ sin (ω)0t) cos(ω0t)]TFor the input signal vector, W (t) ═ wL1(t) wL2(t)]TIs a weight vector, d (t) is a signal to be filtered, Y (t) is an algorithm input signal, e (t) is an error signal, ω is0For filtering angular frequencies, μ is the step size. Then there are:
e(t)＝d(t)-Y(t)＝d(t)-XT(t)W(t)
Y(t)＝Y1(t)wL1(t)+Y2wL2(t)
Wk+1(t)＝Wk(t)+μe(t)X(t)
the closed loop transfer function from d (t) to e (t) is known as:
Figure BDA0003179480060000061
in the above formula, ω0＝2πf0T and T are system sampling periods.
To ensure convergence, the step length should satisfy the condition:
Figure BDA0003179480060000062
zero of the function is
Figure BDA0003179480060000063
When the frequency f of d (t) is equal to the algorithm input signal frequency f0When there is HLWhere (z) ═ 0, filtering of d (t) can be achieved.
Further as a preferred embodiment of the method, for convenient parameter design, an improved variable step length minimum mean square error algorithm is provided, and the step length factor is set as:
Figure BDA0003179480060000064
in the above formula, f represents the rotor rotation frequency, μ1' denotes a positive parameter, | e (k) | denotes signal error.
A magnetic suspension sensor interference suppression device based on variable step length minimum mean square error comprises:
at least one processor;
at least one memory for storing at least one program;
when the at least one program is executed by the at least one processor, the at least one processor is enabled to implement the method for magnetic levitation sensor interference suppression based on variable step size minimum mean square error as described above.
The contents in the above method embodiments are all applicable to the present system embodiment, the functions specifically implemented by the present system embodiment are the same as those in the above method embodiment, and the beneficial effects achieved by the present system embodiment are also the same as those achieved by the above method embodiment.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (6)

1. A magnetic suspension sensor interference suppression method based on variable step length minimum mean square error is characterized by comprising the following steps:
carrying out stress analysis and modeling on the rotor, and identifying parameters of a rotor magnetic suspension bearing system;
and introducing a variable step size minimum mean square error algorithm and setting a step size factor to suppress interference.
2. The method for suppressing the interference of the magnetic suspension sensor based on the variable step size minimum mean square error as claimed in claim 1, wherein the step of performing the stress analysis and modeling on the rotor and identifying the parameters of the magnetic suspension bearing system of the rotor further comprises:
carrying out stress analysis on the rotor, and obtaining a rotor dynamics equation according to a Newton's law and a Lagrange equation;
constructing a rotor magnetic suspension bearing system model according to a dynamic equation;
and identifying parameters of the rotor magnetic suspension bearing system.
3. The method for suppressing the interference of the magnetic suspension sensor based on the variable step size minimum mean square error as claimed in claim 2, wherein the formula of the rotor dynamics equation is as follows:
Figure FDA0003179480050000011
Figure FDA0003179480050000012
Figure FDA0003179480050000013
Figure FDA0003179480050000014
in the above formula, FAX、FBXFor the electromagnetic force of the rotor in the x-direction, FAY、FBYThe electromagnetic force of the rotor along the y direction, alpha and beta are the angular displacement of the rotor rotating around the x and y axes, omega is the rotating speed, l is the length of the rotor, and m is the mass of the rotor.
4. The method for suppressing the interference of the magnetic suspension sensor based on the variable step size minimum mean square error as claimed in claim 3, wherein the expression of the rotor magnetic suspension bearing system model is as follows:
F＝kii+kxx
in the above formula, kiAs a current stiffness system, kxIs the displacement stiffness coefficient.
5. The method for suppressing interference of a magnetic suspension sensor based on variable step size minimum mean square error as claimed in claim 4, wherein the parameter for identifying the rotor magnetic suspension bearing system is specifically a displacement stiffness coefficient k of the identification systemxAnd current stiffness coefficient kiThe method specifically comprises the following steps:
horizontally placing the rotor on a test bed and respectively calculating the ratio of the current rigidity coefficient and the displacement rigidity coefficient of the X channel and the Y channel according to the stable suspension of the rotor;
vertically installing a rotor and respectively calculating the current rigidity coefficient and the displacement rigidity coefficient of an X channel and a Y channel according to the stable suspension of the rotor;
and measuring the vertical offset displacement, the horizontal offset displacement, the rotor mass and the vertical angle between the normal direction of the magnetic pole surface and the ground, calculating the current rigidity coefficient and the displacement rigidity coefficient of the X channel, and calculating the current rigidity coefficient and the displacement rigidity coefficient of the Y channel.
6. The method for suppressing the interference of the magnetic levitation sensor based on the variable step size minimum mean square error as claimed in claim 5, wherein the expression of the step size factor is as follows:
Figure FDA0003179480050000021
in the above formula, f represents the rotor rotation frequency, μ1' denotes a positive parameter, | e (k) | denotes signal error.
CN202110842736.3A 2021-07-26 2021-07-26 An interference suppression method for magnetic levitation sensor based on variable step size minimum mean square error Pending CN113565874A (en)

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CN116292622A (en) * 2023-05-11 2023-06-23 长江三峡集团实业发展(北京)有限公司 Magnetic suspension flexible rotor full-rotation-speed vibration control method and device
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CN116292622A (en) * 2023-05-11 2023-06-23 长江三峡集团实业发展(北京)有限公司 Magnetic suspension flexible rotor full-rotation-speed vibration control method and device
CN116292622B (en) * 2023-05-11 2023-08-18 长江三峡集团实业发展(北京)有限公司 Magnetic suspension flexible rotor full-rotation-speed vibration control method and device
CN118050991A (en) * 2024-02-20 2024-05-17 江苏大学 Construction method of magnetic suspension electric spindle rotor vibration suppression controller

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Application publication date: 20211029