CN108716471B - Active control method for minimum displacement of rotor of magnetic suspension molecular pump - Google Patents

Active control method for minimum displacement of rotor of magnetic suspension molecular pump Download PDF

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CN108716471B
CN108716471B CN201810285534.1A CN201810285534A CN108716471B CN 108716471 B CN108716471 B CN 108716471B CN 201810285534 A CN201810285534 A CN 201810285534A CN 108716471 B CN108716471 B CN 108716471B
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rotor
magnetic suspension
displacement
disturbance
linear
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CN108716471A (en
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郑世强
王灿
韩邦成
宋欣达
孟云平
陈诚
周冲
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Beijing University of Aeronautics and Astronautics
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D19/00—Axial-flow pumps
    • F04D19/02—Multi-stage pumps
    • F04D19/04—Multi-stage pumps specially adapted to the production of a high vacuum, e.g. molecular pumps
    • F04D19/042—Turbomolecular vacuum pumps
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D19/00—Axial-flow pumps
    • F04D19/02—Multi-stage pumps
    • F04D19/04—Multi-stage pumps specially adapted to the production of a high vacuum, e.g. molecular pumps
    • F04D19/048—Multi-stage pumps specially adapted to the production of a high vacuum, e.g. molecular pumps comprising magnetic bearings
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D27/00—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/05—Shafts or bearings, or assemblies thereof, specially adapted for elastic fluid pumps
    • F04D29/056—Bearings
    • F04D29/058—Bearings magnetic; electromagnetic
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/66—Combating cavitation, whirls, noise, vibration or the like; Balancing
    • F04D29/661—Combating cavitation, whirls, noise, vibration or the like; Balancing especially adapted for elastic fluid pumps

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

Abstract

The invention relates to an active control method for minimum displacement of a rotor of a magnetic suspension molecular pump. A generalized controlled object mathematical model of the magnetic suspension rotor system is established by analyzing the unbalanced vibration forming mechanism of the magnetic suspension rotor system. The method is characterized in that each channel controller is designed based on a linear active disturbance rejection control principle, unbalanced vibration of a system is regarded as external disturbance, and the disturbance is estimated and compensated in real time by using a linear extended state observer, so that a same-frequency compensation signal with proper amplitude and phase is superposed in a control signal to counteract unbalanced excitation force of a rotor, the high-speed and high-precision rotation of the rotor around a geometric axis is realized, and the purpose of actively controlling the minimum displacement of a magnetic suspension rotor system is achieved. Compared with the traditional control method, the method has the advantages of simple parameter conditioning, easy realization, great reduction of the rotation speed same-frequency component in the displacement signal, small rotor whirling radius, high rotation precision and great significance for improving the performance and reliability of the magnetic suspension rotor system.

Description

Active control method for minimum displacement of rotor of magnetic suspension molecular pump
Technical Field
The invention relates to a magnetic suspension molecular pump rotor minimum displacement active vibration control method, which can be applied to high-precision and strong robust control of a high-speed magnetic suspension rotor system and belongs to the field of motion control.
Background
The magnetic suspension molecular pump is an important device for obtaining high vacuum, and is widely applied to various high vacuum occasions. Compared with the traditional mechanical bearing, the magnetic suspension bearing is a novel bearing, and has wide application prospect because of the special advantages of non-contact, no friction, high rotating speed, high precision, long service life, capability of actively controlling the dynamic unbalance of the rotor and the like. The control accuracy of the magnetic suspension rotor system is an important factor for determining whether the molecular pump can stably and reliably operate at a high speed for a long time, and the magnetic suspension rotor has various complex vibration problems in the actual operation process, wherein the most important reason is that the dynamic imbalance with the same frequency as the rotor brings great challenges to the high accuracy and high stability control of the system. The fundamental reason for the generation of dynamic unbalance is rotor mass unbalance, and due to the reasons of machining accuracy and the like, the mass distribution of the rotor is not uniform, and a geometric axis and an inertia main shaft are not coincident, so that centrifugal force is generated. Because the magnitude of the centrifugal force is in direct proportion to the square of the rotating speed of the rotor, particularly, the unbalanced vibration force is increased rapidly along with the increase of the rotating speed of the rotor, so that the displacement precision of the rotor is reduced, and the rotor can collide with a mechanical protection bearing in serious conditions to influence the stable operation of a system. The magnetic suspension rotor system has real-time active control capability, provides unique advantages for implementing unbalanced vibration control, and has important significance for improving the control precision and reliability of the magnetic suspension rotor system by inhibiting unbalanced vibration.
At present, two active control methods for unbalanced vibration of a magnetic suspension rotor exist, namely: self-balancing active vibration control, namely eliminating the same-frequency component of the rotating speed in the output signal of the displacement sensor in a feedback channel, thereby eliminating the synchronous exciting force transmitted to the magnetic bearing and enabling the rotor to rotate around an inertia main shaft; the second method comprises the following steps: self-centering active vibration control is carried out, so that the coil generates additional compensation electromagnetic force to counteract unbalanced excitation force, the same-frequency vibration of rotor displacement is inhibited, and the rotor rotates around a geometric main shaft. The first method has the advantages of low operation noise, small moving base effect and the like, but the rotation speed same-frequency whirl in the rotor displacement signal cannot be inhibited, the rotor whirl radius is increased along with the increase of the rotation speed, and the rotor whirl radius is possibly collided with a protective bearing to cause system instability; the second scheme can ensure that the rotor has high rotation precision and small whirling radius, but because the same-frequency bearing force is reacted on the magnetic bearing, the system noise and the effect of the movable base are obvious, and the system power consumption is increased.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problem that the displacement precision is reduced due to unbalanced vibration of a magnetic suspension molecular pump rotor system, a rotor minimum displacement active control method based on a linear active disturbance rejection controller is provided. The method treats the unbalanced vibration of the system as external disturbance, carries out real-time estimation and compensation on the disturbance through the linear extended state observer, and realizes high-speed and high-precision rotation of the rotor around a geometric axis, thereby achieving the purpose of actively controlling the minimum displacement of the magnetic suspension rotor system and providing an effective control method for the stable and reliable operation of the magnetic suspension molecular pump.
The technical scheme adopted by the invention for solving the technical problems is as follows: a magnetic suspension molecular pump rotor minimum displacement active control method comprises the following steps:
(1) rotor dynamics model of magnetic suspension molecular pump
The rotor of the magnetic suspension molecular pump is regarded as a rigid rotor, the dynamic unbalance of the magnetic suspension rotor is composed of a static unbalance part and an even unbalance part, wherein the static unbalance is caused by the fact that the rotor has mass eccentricity, namely an inertia shaft and a geometric shaft are not overlapped with each other, so that a static unbalance force is generated; the even unbalance is caused by the fact that an inertia shaft of the rotor is not parallel to a geometric shaft, so that disturbance torque is generated; establishing a generalized coordinate system by taking the mass center of the dynamic unbalance rotor as an origin to obtain a dynamic equation of the magnetic suspension rotor:
Figure BDA0001615883940000021
in the formula: m is rotor mass, Jx、JyAnd JzThe moments of inertia of the rotor about the x, y and z axes, respectively; fxThe rotor is subjected to a magnetic force in the x-direction, FyThe rotor being subjected to magnetic forces in the y-direction, MxThe rotor is subjected to magnetic moment in the x direction, MyThe rotor is subjected to magnetic moment in the y direction; Ω is the rotor rotational angular velocity; alpha is alphaG、βGIs that the rotor is in the wideAngular displacement around an x axis and a y axis under a sense coordinate system; x is the number ofG、yGRespectively, the displacement of the rotor under a generalized coordinate system; f. ofxdIs the static unbalance force in the x-direction, fydIs a static imbalance force in the y-direction; p is a radical ofxdIs the disturbance torque in the x-direction, pydIs the disturbance torque in the y-direction;
wherein:
Figure BDA0001615883940000022
in the formula: epsilon is static unbalance eccentricity; sigma is an included angle between the rotating shaft and the coordinate axis; theta is the static imbalance angular position;
Figure BDA0001615883940000023
an even unbalanced angular position.
Considering that a power amplifier system is a first-order inertia link, a sensor is a proportion link, and combining a kinetic equation of the magnetic suspension rotor, a generalized controlled object mathematical model of four radial channels of the magnetic suspension rotor system is obtained:
Figure BDA0001615883940000031
in the formula: x is the number ofa、xb、yaAnd ybThe linear displacement of the magnetic suspension rotor in the Ax, Bx, Ay and By directions respectively is measured; f (-) is the total disturbance of the system, where ω isi(i ═ 1,2,3,4) is the unbalance disturbance variable of the magnetic levitation rotor; b0i(i-1, 2,3,4) is a control signal ui(t) (i ═ 1,2,3, 4).
(2) Designing a linear active disturbance rejection controller
The four channels of the magnetic suspension rotor system adopt controllers with the same structure, and for an Ax channel, the magnetic suspension rotor system has a model-assisted linear extended state observer expression form:
Figure BDA0001615883940000032
in the formula: y is AxDisplacement output of channel sensor, y ═ xa(ii) a u is a control signal output by the controller; z is a radical of1Is the tracking signal of y, z2Is that
Figure BDA0001615883940000033
Of the tracking signal z3Is that
Figure BDA0001615883940000034
Of the tracking signal z4A tracking signal that is the total disturbance f (·); a is0Is a coefficient of y, a1Is that
Figure BDA0001615883940000035
Coefficient of (a)2Is that
Figure BDA0001615883940000036
The coefficient of (a); b0Is the Ax channel control signal coefficient b01An estimated value of (d); l ═ beta1 β2 β3 β4]Is a linear extended state observer gain.
The expression form of the linear state error feedback control law is as follows:
Figure BDA0001615883940000037
in the formula: u. of0Is a linear combination of errors; u is the output of the controller; kPIs the proportionality coefficient, Kd1Is a first order differential coefficient, Kd2Are second order differential coefficients, all of which are controller adjustment parameters; y isspIs the set displacement tracking target value.
The principle of the invention is as follows: according to a special processing mode of the active disturbance rejection controller on system disturbance, unbalanced vibration received by the magnetic suspension rotor system is regarded as external disturbance, and the external disturbance is estimated and compensated in real time through a linear extended state observer with model assistance, so that a same-frequency compensation signal with proper amplitude and phase is superposed in a control signal to counteract unbalanced excitation force of the rotor, and active vibration control of minimum displacement of the magnetic suspension rotor system is realized. On the basis of establishing a generalized controlled object mathematical model of the magnetic suspension rotor system, the invention designs the linear active-disturbance-rejection controllers of all subsystems based on the linear active-disturbance-rejection control principle, and finally realizes the active control of the minimum displacement of the rotor system.
Compared with the existing control scheme, the invention has the advantages that:
(1) the invention provides a magnetic suspension molecular pump rotor minimum displacement active control method based on a linear active disturbance rejection controller, which has the advantages of simple structure, easy parameter conditioning and easy realization, and can be applied to occasions with higher requirements on the displacement vibration amplitude of a high-speed magnetic suspension rotor.
(2) The method provided by the invention does not need an accurate model of the controlled object, and can estimate and compensate the uncertainty of the system model and the gyro effect, thereby effectively improving the robustness of the system.
Drawings
FIG. 1 is a block flow diagram of an aspect of the present invention;
fig. 2 is a structural view of a magnetic levitation rotor system, in which 1 represents a rotor, 2 represents a sensor a, 3 represents a magnetic bearing a, 4 represents a magnetic bearing B, and 5 represents a sensor B;
FIG. 3 is a block diagram of a magnetic bearing control system configuration;
FIG. 4 is a block diagram of a single channel linear active disturbance rejection controller;
FIG. 5 is a block diagram of a linear extended state observer with model assistance;
FIG. 6 is a graph of the spectrum of the Ax channel shift signal of the linear ADRC;
FIG. 7 is a graph of the frequency spectrum of the Ax channel shift signal of a conventional PID controller;
FIG. 8 is a graph of the spectrum of the Ax channel shift signal of the linear ADRC including random noise;
FIG. 9 is a graph of the spectrum of a conventional PID controller Ax channel displacement signal containing random noise.
Detailed description of the preferred embodiments
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1 to 9, the active control method for the minimum displacement of the rotor of the magnetic suspension molecular pump of the present invention comprises the following specific steps:
(1) as shown in figure 1, the method firstly analyzes the unbalanced vibration forming mechanism of the magnetic suspension rotor system, establishes the dynamic unbalanced magnetic suspension rotor dynamic equation, then considers the power amplifier link and the sensor link to obtain the generalized controlled object mathematical model of the magnetic suspension rotor system, and finally designs the linear active disturbance rejection controller with model assistance based on the linear active disturbance rejection control principle and the generalized controlled object mathematical model, and the linear active disturbance rejection controller is used for the active control of the minimum displacement of the magnetic suspension rotor system.
(2) As shown in FIG. 2, the rotor of the magnetic suspension molecular pump is regarded as a rigid rotor, and the dynamic unbalance of the magnetic suspension rotor is composed of a static unbalance part and an even unbalance part and is mainly caused by the reasons of uneven mass distribution of the rotor, processing and installation errors and the like. The static unbalance is caused by the fact that mass eccentricity exists in the rotor, namely, an inertia shaft and a geometric shaft are not overlapped with each other, and static unbalance force is caused; even imbalance is due to the rotor inertia axis not being parallel to the geometric axis, causing a disturbing moment. Establishing a generalized coordinate system by taking the mass center of the dynamic unbalance rotor as an origin to obtain a dynamic equation of the magnetic suspension rotor:
Figure BDA0001615883940000051
in the formula: m is rotor mass, Jx、JyAnd JzThe moments of inertia of the rotor about the x, y and z axes, respectively; fxThe rotor is subjected to a magnetic force in the x-direction, FyThe rotor being subjected to magnetic forces in the y-direction, MxThe rotor is subjected to magnetic moment in the x direction, MyThe rotor is subjected to magnetic moment in the y direction; Ω is the rotor rotational angular velocity; alpha is alphaG、βGIs the angular displacement of the rotor around the x-axis and the y-axis under a generalized coordinate system; x is the number ofG、yGRespectively, the displacement of the rotor under a generalized coordinate system; f. ofxdIs the static unbalance force in the x-direction, fydIs a static imbalance force in the y-direction; p is a radical ofxdIs the disturbance torque in the x-direction, pydIs the disturbance torque in the y-direction.
Wherein:
Figure BDA0001615883940000052
in the formula: epsilon is static unbalance eccentricity; sigma is an included angle between the rotating shaft and the coordinate axis; theta is the static imbalance angular position;
Figure BDA0001615883940000055
an even unbalanced angular position.
Converting the coordinate to obtain a generalized force vector F ═ F in the generalized coordinate systemx Mx Fy My]And generalized displacement vector q ═ xG αG yG βG]Using magnetic axis force vector f ═ f under magnetic bearing coordinate systemax fbx fay fby]And a displacement vector qh＝[xaxb ya yb]Respectively expressed as:
the nearly linear relationship of the magnetic bearing forces at the magnetic bearing A, B at the operating point is then obtained by a taylor series expansion:
Figure BDA0001615883940000054
in the formula: k is a radical ofi＝[kiax kibx kiay kiby]Is the displacement stiffness, k, at the working point of the magnetic bearingh＝[khax khbx khaykhby]Is the current stiffness at the working point of the magnetic bearing.
And finally, obtaining a kinetic equation of the magnetic suspension rotor under a magnetic bearing coordinate system:
Figure BDA0001615883940000061
in the formula: omegaiAnd (i ═ 1,2,3 and 4) is the unbalanced vibration quantity of the magnetic suspension rotor system, and is equivalent to an external disturbance of the system. Omegai(i ═ 1,2,3, 4):
Figure BDA0001615883940000062
(3) as shown in fig. 3, the power amplifier link and the sensor link are considered, and the power amplifier is equivalent to an inertial linkThe sensor is equivalent to a proportional element Gs(s)＝ks. Order to
Figure BDA0001615883940000064
Figure BDA0001615883940000065
Obtaining a generalized controlled object mathematical model of the magnetic suspension rotor system:
Figure BDA0001615883940000066
(4) as shown in fig. 4, the basic structure of the linear active disturbance rejection controller is mainly composed of two parts: the linear error combination control law and the linear extended state observer rewrite a generalized controlled object mathematical model of a magnetic suspension rotor system into the following formula according to a linear active disturbance rejection control theory:
Figure BDA0001615883940000067
in the formula: x is the number ofa、xb、yaAnd ybThe linear displacement of the magnetic suspension rotor in the Ax, Bx, Ay and By directions respectively is measured; f (-) is the total disturbance of the system, which contains the uncertainty of the system model and the unbalance disturbance amount ωi(i＝1,2,3,4)；b0i(i-1, 2,3,4) is a control signal ui(t) (i ═ 1,2,3, 4). Each sub-type of four channels of magnetic suspension rotor system canAnd for an Ax channel, designing a linear active disturbance rejection controller as follows, and estimating and compensating total disturbance f (·) containing the unbalance of the rotor in real time by using a linear extended state observer so as to realize the active control of the minimum displacement of the magnetic suspension rotor system.
(5) As shown in fig. 5, a linear extended state observer with model assistance is adopted, and part of known information obtained by mathematical modeling of a magnetic suspension rotor system is incorporated into the design of the linear extended state observer, so that the computational load of the observer can be reduced, or the estimation precision of disturbance can be improved on the premise of not reducing the bandwidth of the extended state observer, and the high-precision control effect on the rotor can be achieved. The specific expression is as follows:
Figure BDA0001615883940000071
in the formula: y is the displacement output of the Ax channel sensor, y ═ xa(ii) a u is a control signal output by the controller; z is a radical of1Is the tracking signal of y, z2Is that
Figure BDA0001615883940000072
Of the tracking signal z3Is that
Figure BDA0001615883940000073
Of the tracking signal z4A tracking signal that is the total disturbance f (·); a is0Is a coefficient of y, a1Is that
Figure BDA0001615883940000074
Coefficient of (a)2Is that
Figure BDA0001615883940000075
The coefficient of (a); b0Is the Ax channel control signal coefficient b01Estimated value of (b) obtained by modeling0＝b1kwkswwkiax，b0The closer to b01The linear extended observer estimates the disturbance f (-) more accurately; l ═ beta1 β2 β3 β4]For linear extended state observer gain, which is a parameter to be determined, β is generally taken1＝4ω0,β2＝6ω0 2,β3＝4ω0 3,β4＝ω0 4，ω0Is the linear extended state observer bandwidth.
The expression of the linear state error feedback control law is as follows:
Figure BDA0001615883940000076
in the formula: u. of0Is a linear combination of errors; u is the output of the controller; y isspIs a set displacement tracking target value; kPIs the proportionality coefficient, Kd1Is a first order differential coefficient, Kd2Is a second order differential coefficient, is a parameter to be determined, and generally takes Kp＝ωc 3,Kd1＝3ωc 2,Kd2＝3ωc，ωcIs the controller bandwidth.
The method can obtain the control parameter b through modeling0Is also due to ωcAnd omega0There is an empirical relationship: omega0＝5～10ωcOnly the parameter omega needs to be adjustedcThe parameter conditioning of the linear active disturbance rejection controller can be finished, and the method has the advantages of simple structure, easy parameter conditioning and easy realization.
(6) In order to verify the effectiveness of the active control method provided by the invention, a Simulink simulation model is set up, the method is used for carrying out comparative simulation with a traditional PID controller, and simulation parameters are as follows: m 19.6kg, Jx＝0.2039，Jy＝0.2039，Jz＝0.1268，lma＝0.0279m，lmb＝0.1251m，kia＝400N/A，kib＝115N/A，kha＝1.4N/um，khb＝0.4N/um。
(7) The comparative simulation results are as follows:
referring to fig. 6 and 7, graphs of Ax channel displacement signals are shown for a magnetic levitation molecular pump operating at 24000r/min using the method of the present invention (fig. 6) and a conventional PID controller (fig. 7). The comparison can be carried out as follows: the amplitude of the same-frequency vibration frequency of the displacement of the method is 0.06, while the amplitude of the same-frequency vibration frequency of the displacement of the traditional PID controller is 0.18, obviously, the inhibition effect of the same-frequency vibration of the displacement of the method of the invention is obviously better than that of the traditional PID control method.
Referring to FIG. 8 and FIG. 9, the graph of Ax channel displacement signal spectrum of the magnetic suspension molecular pump operated at 27000r/min and added with random noise signals of 1e-5 is shown by using the method of the present invention (FIG. 8) and the conventional PID controller (FIG. 9). The comparison can be carried out as follows: the suppression effect of the method on the system random noise is obviously superior to that of the traditional PID control method; secondly, with the increase of the rotating speed, due to the gyro effect, the magnetic suspension rotor system has the nutation frequency, if the magnetic suspension rotor system is not controlled, the system is unstable, compared with the traditional PID control scheme, the method has the advantages that the effect of inhibiting the nutation frequency is obvious, and the robustness of the system can be greatly improved.
The invention has not been described in detail and is within the skill of the art.

Claims (1)

1. A magnetic suspension molecular pump rotor minimum displacement active control method is characterized in that: the method comprises the following steps:
(1) rotor dynamics model of magnetic suspension molecular pump
The rotor of the magnetic suspension molecular pump is regarded as a rigid rotor, the dynamic unbalance of the magnetic suspension rotor is composed of a static unbalance part and an even unbalance part, wherein the static unbalance is caused by the fact that the rotor has mass eccentricity, namely an inertia shaft and a geometric shaft are not overlapped with each other, so that a static unbalance force is generated; the even unbalance is caused by the fact that an inertia shaft of the rotor is not parallel to a geometric shaft, so that disturbance torque is generated; establishing a generalized coordinate system by taking the mass center of the dynamic unbalance rotor as an origin to obtain a dynamic equation of the magnetic suspension rotor:
Figure FDA0002143146030000011
in the formula: m is rotor mass, Jx、JyAnd JzThe moments of inertia of the rotor about the x, y and z axes, respectively; fxThe rotor is subjected to a magnetic force in the x-direction, FyThe rotor being subjected to magnetic forces in the y-direction, MxThe rotor is subjected to magnetic moment in the x direction, MyThe rotor is subjected to magnetic moment in the y direction; Ω is the rotor rotational angular velocity; alpha is alphaG、βGIs the angular displacement of the rotor around the x-axis and the y-axis under a generalized coordinate system; x is the number ofG、yGRespectively, the displacement of the rotor under a generalized coordinate system; f. ofxdIs the static unbalance force in the x-direction, fydIs a static imbalance force in the y-direction; p is a radical ofxdIs the disturbance torque in the x-direction, pydIs the disturbance torque in the y-direction;
wherein:
Figure FDA0002143146030000012
in the formula: epsilon is static unbalance eccentricity; sigma is an included angle between the rotating shaft and the coordinate axis; theta is the static imbalance angular position;
Figure FDA0002143146030000014
an angular position that is even unbalanced;
considering that a power amplifier system is a first-order inertia link, a sensor is a proportion link, and combining a kinetic equation of the magnetic suspension rotor, a generalized controlled object mathematical model of four radial channels of the magnetic suspension rotor system is obtained:
Figure FDA0002143146030000013
in the formula: x is the number ofa、xb、yaAnd ybThe linear displacement of the magnetic suspension rotor in the Ax, Bx, Ay and By directions respectively is measured; f (-) is the total disturbance of the system, where ω isi(i ═ 1,2,3,4) is the unbalance disturbance variable of the magnetic levitation rotor; b0i(i-1, 2,3,4) is a control signal ui(t) (i ═ 1,2,3, 4); the sub-type of four channels of the magnetic suspension rotor system can be regarded as a single channel needing active disturbance rejection controllerThe system carries out linear active disturbance rejection controller design on an Ax channel, and carries out real-time estimation and compensation on total disturbance f (-) including the unbalance amount of a rotor by utilizing a linear extended state observer, so that the active control of the minimum displacement of the magnetic suspension rotor system is realized;
(2) designing a linear active disturbance rejection controller
The four channels of the magnetic suspension rotor system adopt controllers with the same structure, and for an Ax channel, the magnetic suspension rotor system has a model-assisted linear extended state observer expression form:
Figure FDA0002143146030000021
in the formula: y is the displacement output of the Ax channel sensor, y ═ xa(ii) a u is a control signal output by the controller; z is a radical of1Is the tracking signal of y, z2Is that
Figure FDA0002143146030000022
Of the tracking signal z3Is that
Figure FDA0002143146030000023
Of the tracking signal z4A tracking signal that is the total disturbance f (·); a is0Is a coefficient of y, a1Is that
Figure FDA0002143146030000024
Coefficient of (a)2Is thatThe coefficient of (a); b0Is the Ax channel control signal coefficient b01An estimated value of (d); l ═ beta1 β2 β3 β4]Linear extended state observer gain;
the expression form of the linear state error feedback control law is as follows:
in the formula: u. of0Is a linear combination of errors; u is the output of the controller; kPIs the proportionality coefficient, Kd1Is a first order differential coefficient, Kd2Are second order differential coefficients, all of which are controller adjustment parameters; y isspIs the set displacement tracking target value.
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