CN113485472B - Magnetic suspension rotor same-frequency vibration torque suppression method based on double-channel wave trap - Google Patents
Magnetic suspension rotor same-frequency vibration torque suppression method based on double-channel wave trap Download PDFInfo
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- CN113485472B CN113485472B CN202110890520.4A CN202110890520A CN113485472B CN 113485472 B CN113485472 B CN 113485472B CN 202110890520 A CN202110890520 A CN 202110890520A CN 113485472 B CN113485472 B CN 113485472B
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- G05D17/02—Control of torque; Control of mechanical power characterised by the use of electric means
Abstract
The invention discloses a method for inhibiting same-frequency vibration torque of a magnetic suspension rotor based on a double-channel wave trap, which comprises the following steps of: firstly, a magnetic suspension rotor dynamic model considering rotor dynamic unbalance is established, and then a magnetic suspension rotor same-frequency vibration moment suppression method based on a double-channel wave trap is adopted. The dual-channel wave trap can accurately restrain the same-frequency vibration moment, one controller is used for restraining vibration in the X direction and the Y direction, and hardware computing resources are small. Meanwhile, the absolute stability of the system in a larger frequency range can be ensured by introducing a phase compensation angle. The dual-channel wave trap controller has a simple structure, is very convenient in practical application, and is suitable for inhibiting the same-frequency vibration moment of the magnetic suspension control moment gyroscope with rotor dynamic unbalance.
Description
Technical Field
The invention relates to the technical field of vibration suppression of a magnetic suspension control moment gyroscope, in particular to a magnetic suspension rotor same-frequency vibration moment suppression method based on a double-channel wave trap, which is used for suppressing the same-frequency vibration moment of a magnetic suspension control moment gyroscope rotor system in a full working rotating speed range and providing technical support for the application of the magnetic suspension control moment gyroscope on an ultra-static satellite platform and an ultra-stable satellite platform.
Background
The control moment gyroscope has the characteristics of large output moment and high response speed, and is an ideal attitude control actuating mechanism of an agile maneuvering satellite. The magnetic suspension control moment gyroscope uses the active magnetic bearing to realize the non-contact support of the rotor, has the advantages of no friction, high rotating speed and the like, and can realize active vibration control. The MSCMG has wide application prospect in the future hypersensitive maneuvering satellite.
Due to the deflection and offset of the geometric and inertial axes caused by the rotor mass imbalance, co-frequency vibrations are generated when the rotor rotates at high speeds. Rotor mass unbalance is divided into static unbalance and dynamic unbalance, and static unbalance can produce same frequency vibration power, and dynamic unbalance can produce same frequency vibration moment. The performance of the hypersensitive maneuvering satellite is reduced due to the same-frequency vibration force and moment, so that the suppression of the same-frequency vibration force and moment is a critical technology to be solved urgently in technical application of the magnetic bearing.
The common-frequency current of the system is eliminated, so that most common-frequency vibration can be reduced, and specific frequency is restrained. Suppression of the coil current can achieve suppression of most vibrations, but some residual displacement stiffness force still exists. In addition, many methods aim at the suppression of the same-frequency vibration force, the same-frequency vibration moment has coupling in the X direction and the Y direction due to the strong gyro effect of the rotor at high speed, so that the design of a suppression algorithm is difficult, and the research on the suppression of the vibration moment still needs to be deep.
Disclosure of Invention
The purpose of the invention is as follows: the method for restraining the same-frequency vibration torque of the magnetic suspension rotor based on the dual-channel wave trap is characterized in that vibration torque constructed by current and displacement according to an electromagnetic force model is used as control algorithm input, the same-frequency torque can be completely restrained, vibration forces in two directions can be restrained by one controller by utilizing the orthogonal characteristic of X, Y direction signals, computing resources are reduced, phase compensation is carried out on phases in different frequency bands by introducing a phase compensation angle, and absolute stability of the full working frequency band is achieved.
The technical scheme adopted by the invention is as follows: a magnetic suspension rotor same-frequency vibration torque suppression method based on a double-channel wave trap comprises the following steps:
step (1): establishing a magnetic suspension rotor dynamic model containing rotor dynamic unbalance by taking the vibration torque as a suppression target;
step (2): designing an improved double-channel phase shift wave trap based on the dynamics model established in the step (1), adding a phase compensation angle and a damping factor into the improved double-channel phase shift wave trap, using a complex coefficient to simplify, obtaining a complex coefficient transfer function of the double-channel wave trap, using current and displacement to construct same-frequency vibration torque as input, enabling the double-channel wave trap to generate a preset gain at the same frequency of the rotating speed of the rotor by adjusting the ratio of a convergence factor and the damping factor in the double-channel wave trap, and accessing the double-channel wave trap into a magnetic suspension rotor control system in a feedback mode to realize effective suppression of the same frequency quantity;
and (3): determining the stable condition of the magnetic suspension rotor control system after the improved double-channel phase shift wave trap is added based on the double-channel wave trap complex coefficient transfer function obtained in the step (2); and designing a phase compensation angle according to the stable condition, ensuring the stability of the magnetic suspension rotor control system within the working rotating speed range through the phase compensation angle, and finishing the suppression of the same-frequency vibration torque within the full rotating speed range of the magnetic suspension rotor.
In the step (1), the magnetic suspension rotor magnetic bearing system comprises four pairs of radial magnetic bearings and four pairs of radial displacement sensors. Let N be the geometric center of the stator, NXY be the inertial coordinate system, C and O be the center of mass and the geometric center of the rotor, respectively, and O ε η be the rotational coordinate system.
Let alpha and beta be the displacement of rotor inertia axis in two degrees of freedom of radial deflection respectively. From newton's second law, a dynamic model of the radial deflection freedom can be obtained, expressed as follows:
wherein, JxAnd JyIs the radial moment of inertia, JzIs the axial moment of inertia. MxAnd MyIs the torque provided by the radial magnetic bearing and omega is the high speed rotor rotational speed.
The electromagnetic torque expression can be known by the magnetic bearing electromagnetic force approximate linearization formula as follows:
Mx＝(fby-fay)lm＝[Ki(iby-iay)+Kh(xby-xay)]lm
My＝(fax-fbx)lm＝[Ki(iax-ibx)+Kh(xax-xbx)]lm
wherein f isax，fbx，fayAnd fbyIs the bearing force of four pairs of radial magnetic bearings. lmIs the distance from the plane of the magnetic bearings to the plane of the rotor centroid. KiAnd KhCurrent stiffness and displacement stiffness are indicated, respectively. i.e. iax，iay，ibxAnd ibyIs four pairs of magnetic bearing coil currents. x is the number ofax，xay，xbxAnd xbyIs the displacement of the geometric axis of the rotor at four pairs of radial magnetic bearings.
Due to the existence of the dynamic unbalance, the geometric axis and the inertia axis of the rotor are not coincident. The disturbance caused by the dynamic imbalance can be expressed as follows:
Θα＝e cos(Ωt+χ)
Θβ＝e sin(Ωt+χ)
wherein, thetaα，ΘβRepresenting the dynamic unbalance amount, e representing the dynamic unbalance amplitude, and x representing the initial dynamic unbalance phase.
According to the geometric relationship, the relationship between the displacement at the magnetic bearing and the deflection and angular displacement of the inertial shaft is as follows:
similarly, the relationship between the rotor displacement at the displacement sensor and the displacement of the deflection angle of the inertial shaft is as follows:
wherein lsIs the distance of the plane of the sensor from the plane of the rotor centroid. sax，sbx，say，sbyIs the displacement at the four pairs of displacement sensors.
A. And B, carrying out signal difference on the displacement sensors at the two ends to obtain output angular displacement, which specifically comprises the following steps:
sα(s)＝sbyKs-sayKs＝2Ksls(β+Θα)
sβ(s)＝saxKs-sbxKs＝2Ksls(β+Θβ)
wherein s isα(s),sβ(s) is the angular displacement of the sensor output, KsIs the displacement sensor coefficient.
The analysis shows that the dynamic unbalance of the rotor can generate the same-frequency displacement interference, and the displacement sensor can output the same-frequency noise, so that the rotor can generate the same-frequency vibration torque.
Finally, a magnetic suspension rotor dynamic model containing rotor dynamic unbalance is established as follows:
wherein alpha and beta are respectively the displacement of the rotor inertia shaft in two degrees of freedom of radial deflection; j. the design is a squarexAnd JyIs the radial moment of inertia, JzIs the axial moment of inertia; mxAnd MyIs the torque provided by the radial magnetic bearing; Ω is the high speed rotor rotational speed; f. ofax，fbx，fayAnd fbyIs the bearing force of four pairs of radial magnetic bearings; lmThe distance between the plane of the magnetic bearing and the plane of the mass center of the rotor; kiAnd KhCurrent stiffness and displacement stiffness, respectively; i.e. iax，iay，ibxAnd ibyIs four pairs of magnetic bearing coil currents; thetaα，ΘβIs the dynamic unbalance amount which is respectively as follows:
Θα＝e cos(Ωt+χ)
Θβ＝e sin(Ωt+χ)
wherein e represents the amplitude of the dynamic unbalance, and x represents the initial phase of the dynamic unbalance; therefore, the dynamic unbalance of the rotor is represented as interference with the same frequency of the rotating speed of the rotor, and the rotor system can generate the same frequency torque.
The advantages of the model are as follows: according to Newton's second law and vibration mechanism of dynamic unbalance, from the angle of the rotation model of the magnetic suspension rotor, a dynamic model of the magnetic suspension rotor containing the dynamic unbalance of the rotor is established.
In the step (2), a dual-channel wave trap is designed, the algorithm takes equivalent torque as input, is accessed to the original closed-loop system in a parallel connection mode, and the output of the algorithm is fed back to the power amplifier input end of the original control system, and the method comprises the following two aspects:
two-channel wave trap: the common-frequency vibration moment of the actual magnetic suspension rotor system comprises a current rigidity moment and a displacement rigidity moment; constructing a same-frequency vibration moment by using current and displacement according to a model of system electromagnetic force as an input of a dual-channel wave trap, and simplifying analysis by using a complex coefficient transfer function;
secondly, obtaining the system stable condition of the dual-channel wave trap by using the complex coefficient transfer function; and designing a corresponding phase compensation angle according to the closed-loop characteristic of the actual magnetic suspension rotor system, and realizing the absolute stability of the system in the working rotating speed range through the phase compensation angle.
The dual-channel wave trap in the step (2) is as follows:
in order to improve the stability margin of a system and enable the system to realize the stability of a full rotating speed range, a phase compensation angle and a damping factor are added into a traditional double-input wave trap, and the state space model of the improved double-channel phase-shift wave trap can be represented as follows:
where ε is a convergence factor, the convergence rate may be adjusted. Ω is the rotor speed. γ is the damping factor and θ is the phase compensation angle. u. of1(t),u2(t) is the input signal of the dual channel trap, x1(t),x2(t) is the output signal of the dual channel trap.
The differential equation is obtained from the above equation as follows:
because the input and output signals of the dual-channel wave trap have the characteristics of equal amplitude and 90 degrees phase difference. And (3) introducing a complex variable to equivalently simplify the double-input system into a complex coefficient single-input system. Let xc＝x2+jx1，uc＝u2+ju1And j is an imaginary unit. The above equation can be simplified as follows:
wherein x isc(t) being dual channel trapsComplex coefficient input signal uc(t) is the complex coefficient output signal of the dual channel trap.
The zero initial condition pull-down plateau transform is performed on the above equation:
sxc(s)＝-γxc(s)+jΩxc(s)+εcosθuc(s)+jεsinθuc(s)
s is the laplacian operator.
The complex coefficient input variable x of the dual-channel wave trap can be solvedc(s) and a complex coefficient output variable ucThe relationship of(s) is as follows:
double channel trap complex coefficient transfer function GDNF(s) the following:
let s ═ j ω, ω be the angular frequency, and ε ≠ 0. It is possible to obtain:
when ω is Ω, there are:
when ω < Ω or ω > Ω, there are:
|xc(jω)|＝0
from the above analysis, it can be seen that by adjusting the ratio of ε to γ, the controller can be made to produce a predetermined gain at the same frequency. The controller is connected to the system in a feedback mode, so that the effective suppression of the same frequency quantity can be realized.
The final improved dual-channel phase shift trap in the step (2) is represented as a state space model as follows:
wherein epsilon is a convergence factor, and the convergence speed is adjusted; Ω is the rotor speed; γ is a damping factor; θ is the phase compensation angle; u. of1(t),u2(t) is the input signal of the dual channel phase shift trap; x is the number of1(t),x2(t) is the output signal of the trap;
double channel trap complex coefficient transfer function GDNF(s) the following:
double-channel wave trap complex coefficient output variable xc(s) and input variable ucThe relationship of(s) is as follows:
where s is the laplace operator, let s ═ j ω, and ≠ 0, yielding:
when ω is Ω, there are:
when ω < Ω or ω > Ω, there are:
|xc(jω)|＝0
the improved dual-channel phase shift trap has the advantages that: by utilizing the orthogonal characteristic of the output signal of the displacement sensor, the improved double-channel phase shift wave trap is used for simultaneously realizing the vibration suppression in two directions, and the computing resource of the magnetic suspension rotor control system is reduced.
In the step (3), the stable conditions of the magnetic suspension rotor control system after the double-channel wave trap is added are established as follows:
where θ is the phase compensation angle; Ω is the rotor speed; arg [. cndot ] is argument; s(s) is a sensitivity function of the original magnetically levitated rotor control system, s(s) is expressed as:
wherein G isc(s) is a PID controller; gcr(s) is a cross-feedback controller that suppresses the vortex mode; gw(s) is a power amplifier; ksIs the displacement sensor coefficient; lsIs the distance from the plane of the sensor to the plane of the center of mass of the rotor; lmThe distance between the plane of the magnetic bearing and the plane of the mass center of the rotor; kiAnd KhRespectively representing current stiffness and displacement stiffness; p(s) is active magnetic bearing-rotor.
The advantages of the above-mentioned stable conditions are: according to different frequency bands of the rotor rotating speed, corresponding phase compensation angles are designed to meet the proposed stability conditions, the stability of a magnetic suspension rotor control system in a working rotating speed range is guaranteed, and the suppression of same-frequency vibration torque is finally achieved.
The basic principle of the invention is as follows: the magnetic suspension control moment gyroscope is supported by a magnetic suspension bearing, and for a magnetic suspension rotor, the main vibration source of the magnetic suspension control moment gyroscope is unbalanced by the mass of the rotor. Rotor mass unbalance is divided into static unbalance and dynamic unbalance, wherein dynamic unbalance can produce same-frequency vibration torque, and same-frequency vibration torque is transmitted to the spacecraft through the base, seriously influences spacecraft platform performance. The invention provides a method for inhibiting same-frequency vibration torque based on a dual-channel wave trap by establishing a magnetic suspension rotor dynamic model considering rotor dynamic unbalance aiming at the same-frequency vibration torque of a magnetic suspension rotor of a magnetic suspension control torque gyroscope. By utilizing the orthogonal characteristic of the output signals of the displacement sensors in the X direction and the Y direction, the controller is used for simultaneously inhibiting the vibration moments in the two directions, and a phase compensation angle is introduced to ensure that the magnetic suspension rotor control system is stable in the full rotating speed range.
Compared with the prior art, the invention has the advantages that:
(1) most of the existing methods for suppressing vibration of a magnetic suspension rotor are methods for suppressing vibration force, and the research on suppression of vibration moment is very little. The invention takes the vibration moment as the suppression target, uses the current and the displacement to construct the vibration moment as the input signal, and can realize the suppression of the same-frequency vibration moment.
(2) According to the Newton's second law and the vibration mechanism of dynamic unbalance, a magnetic suspension rotor dynamic model containing rotor dynamic unbalance is established, and the mechanical characteristics of a magnetic suspension rotor control system containing unbalance are accurately reflected from the angle of the magnetic suspension rotor rotation model; the linear bearing force of the rotor near the balance position is adopted to represent the magnetic suspension rotor dynamic model, and the balance between the accuracy and the complexity of the model is realized.
(3) According to the invention, a phase compensation angle and a damping factor are added into an improved dual-channel phase shift wave trap; by utilizing the orthogonal characteristic of the output signal of the displacement sensor, the improved double-channel phase shift wave trap is used for simultaneously realizing the vibration suppression in two directions, and the computing resource of the magnetic suspension rotor control system is reduced.
(4) According to the invention, the stability condition of the magnetic suspension rotor control system after the double-channel wave trap is added is established, and the corresponding phase compensation angle is designed according to the frequency bands with different rotor rotating speeds so as to meet the proposed stability condition, ensure the stability of the magnetic suspension rotor control system within the working rotating speed range, and finally realize the suppression of the same-frequency vibration torque.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a schematic structural diagram of a magnetic suspension rotor system, wherein 1 is an active magnetic bearing, 2 is a displacement sensor, 3 is a rotor inertia shaft, and 4 is a rotor geometric shaft;
FIG. 3 is a block diagram of a basic control system of a magnetic levitation rotor;
FIG. 4 is a schematic block diagram of a dual channel trap;
FIG. 5 is a block diagram of a dual channel trap and master controller combined control system;
fig. 6 is a simplified block diagram of a complex coefficient equivalent single input system.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
As shown in fig. 1 and fig. 2, according to an embodiment of the present invention, an implementation process of a magnetic suspension rotor co-frequency vibration torque suppression method based on a dual-channel wave trap is as follows: firstly, establishing a magnetic suspension rotor dynamic model considering rotor dynamic unbalance; then designing a controller based on a dual-channel wave trap to suppress the same-frequency vibration moment.
Step (1) establishing a magnetic suspension rotor dynamic model considering rotor dynamic unbalance
The magnetic levitation rotor magnetic bearing system comprises four pairs of radial magnetic bearings and four pairs of radial displacement sensors. The structure is shown in fig. 2, wherein N is the geometric center of the stator, NXY is the inertial coordinate system, C and O are the mass center and the geometric center of the rotor respectively, and O epsilon eta is the rotating coordinate system. 1 is an active magnetic bearing, 2 is a displacement sensor, 3 is a rotor inertia shaft, and 4 is a rotor geometric shaft. lmThe distance between the plane of the magnetic bearing and the plane of the mass center of the rotor; lsIs the distance of the plane of the sensor from the plane of the rotor centroid.
Let alpha and beta be the displacement of rotor inertia axis in two degrees of freedom of radial deflection respectively. From newton's second law, a dynamic model of the radial deflection freedom can be obtained, expressed as follows:
wherein, JxAnd JyIs a radial rotationMoment of inertia, JzIs the axial moment of inertia. MxAnd MyIs the torque provided by the radial magnetic bearing and omega is the high speed rotor rotational speed.
The electromagnetic torque expression can be known by the magnetic bearing electromagnetic force approximate linearization formula as follows:
Mx＝(fby-fay)lm＝[Ki(iby-iay)+Kh(xby-xay)]lm
My＝(fax-fbx)lm＝[Ki(iax-ibx)+Kh(xax-xbx)]lm
wherein f isax，fbx，fayAnd fbyIs the bearing force of four pairs of radial magnetic bearings. lmIs the distance from the plane of the magnetic bearings to the plane of the rotor centroid. KiAnd KhCurrent stiffness and displacement stiffness are indicated, respectively. i.e. iax，iay，ibxAnd ibyIs four pairs of magnetic bearing coil currents. x is the number ofax，xay，xbxAnd xbyIs the displacement of the geometric axis of the rotor at four pairs of radial magnetic bearings.
Due to the existence of the dynamic unbalance, the geometric axis and the inertia axis of the rotor are not coincident. The disturbance caused by the dynamic imbalance can be expressed as follows:
Θα＝e cos(Ωt+χ)
Θβ＝e sin(Ωt+χ)
wherein e represents the amplitude of the dynamic unbalance, and χ represents the initial phase of the dynamic unbalance.
According to the geometric relationship, the relationship between the displacement at the magnetic bearing and the deflection and angular displacement of the inertial shaft is as follows:
similarly, the relationship between the rotor displacement at the displacement sensor and the displacement of the deflection angle of the inertial shaft is as follows:
wherein lsIs the distance of the plane of the sensor from the plane of the rotor centroid. sax(s)，sbx(s)，say(s)，sby(s) is the displacement at the four pairs of displacement sensors.
A. And B, carrying out signal difference on the displacement sensors at the two ends to obtain output angular displacement, which specifically comprises the following steps:
sα(s)＝sbyKs-sayKs＝2Ksls(β+Θα)
sβ(s)＝saxKs-sbxKs＝2Ksls(β+Θβ)
wherein s isα(s),sβ(s) is the sensor output angular displacement, Ks is the displacement sensor coefficient.
From the above analysis, it can be known that the dynamic unbalance of the rotor can generate the same frequency interference, so that the rotor generates the same frequency vibration moment. The control block diagram of the deflection two-degree-of-freedom magnetic suspension rotor system is shown in figure 3. The system control block diagram is composed of four parts of a controller, a power amplifier, a magnetic bearing and a magnetic suspension rotor. In the figure Gc(s) is a PID controller; gcr(s) is a cross-feedback controller that suppresses the vortex mode; gw(s) is a power amplifier; ksIs the displacement sensor coefficient; kiAnd KhRespectively representing current stiffness and displacement stiffness; lmThe distance between the plane of the magnetic bearing and the plane of the mass center of the rotor; lsIs the distance from the plane of the sensor to the plane of the center of mass of the rotor; j. the design is a squarexAnd JyIs the radial moment of inertia; j. the design is a squarezIs the axial moment of inertia; alpha and beta are respectively the displacement of the rotor inertia shaft in two degrees of freedom of radial deflection; thetaαAnd ΘβIs the amount of dynamic unbalance; i.e. iαAnd iβIs a deflection mode current, iα＝iay-iby，iβ＝iax-ibx；sα(s) and sβ(s) is the displacement sensor output angular displacement. The error signal obtained by comparing the displacement signal of the magnetic suspension rotor in the displacement sensor with the given suspension position is used as the input signal of a PID controller and a cross feedback controller, the controller outputs a control signal to be sent to a power amplifier to output a control current, and the magnetic bearing coil generates corresponding electromagnetic force through the output control current to act on the magnetic suspension rotor to continuously adjust the suspension position of the magnetic suspension rotor until the magnetic suspension rotor is stably suspended at the given position.
Step (2): design method for inhibiting same-frequency vibration moment based on dual-channel wave trap
The method comprises the following steps that a double-channel wave trap is designed, equivalent torque is used as input in the algorithm, the algorithm is connected into an original closed-loop system in a parallel mode, the output of the algorithm is fed back to the power amplifier input end of an original control system, and the method comprises the following two aspects:
two-channel wave trap: the common-frequency vibration moment of the actual magnetic suspension rotor system comprises a current rigidity moment and a displacement rigidity moment; constructing a same-frequency vibration moment by using current and displacement according to a model of system electromagnetic force as an input of a dual-channel wave trap, and simplifying analysis by using a complex coefficient transfer function;
secondly, obtaining the system stable condition of the dual-channel wave trap by using the complex coefficient transfer function; and designing a corresponding phase compensation angle according to the closed-loop characteristic of the actual magnetic suspension rotor system, and realizing the absolute stability of the system in the working rotating speed range through the phase compensation angle.
Further, the dual-channel wave trap in the step (2) is:
1. algorithmic analysis
In order to improve the stability margin of a system and realize the stability of the system in a full rotating speed range, the invention adds a phase compensation angle and a damping factor into the traditional double-input wave trap to obtain an improved double-channel phase-shift wave trap. The state space model can be represented as follows:
where ε is a convergence factor, the convergence rate may be adjusted. Ω is the rotor speed. γ is the damping factor and θ is the phase compensation angle. u. of1(t),u2(t) is the input signal of the dual channel trap, x1(t),x2(t) is the output signal of the dual channel trap.
The differential equation is obtained from the above equation as follows:
because the input and output signals of the dual-channel wave trap have the characteristics of equal amplitude and 90 degrees phase difference. And (3) introducing a complex variable to equivalently simplify the double-input system into a complex coefficient single-input system. Let xc＝x2+jx1，uc＝u2+ju1And j is an imaginary unit. The above equation can be simplified as follows:
the zero initial condition pull-down plateau transform is performed on the above equation:
sxc(s)＝-γxc(s)+jΩxc(s)+εcosθuc(s)+jεsinθuc(s)
s is the laplacian operator.
The variable x can be solvedc(s) and ucThe relationship of(s) is as follows:
double channel trap complex coefficient transfer function GDNF(s) the following:
let s be j ω and ε ≠ 0. It is possible to obtain:
when ω is Ω, there are:
when ω < Ω or ω > Ω, there are:
|xc(jω)|＝0
from the above analysis, it can be seen that by adjusting the ratio of ε to γ, the controller can be made to produce a predetermined gain at the same frequency. The controller is connected to the system in a feedback mode, so that the effective suppression of the same frequency quantity can be realized. A schematic block diagram of a dual channel trap is shown in figure 4. U in the figure1,u2Is the input signal of the dual channel trap; x is the number of1,x2Is the output signal of the dual channel trap; ε is a convergence factor; Ω is the rotor speed; γ is a damping factor; θ is the phase compensation angle.
As shown in fig. 5, the equivalent vibration moment is used as the input of the dual-channel wave trap, the output is fed back to the input end of the power amplifier and added with the control signal of the main controller, and the same-frequency vibration moment of the system is eliminated. In the figure, DNF is a dual-channel phase shift trap; gc(s) is a PID controller; gcr(s) is a cross-feedback controller that suppresses the vortex mode; gw(s) is a power amplifier; ksIs the displacement sensor coefficient; kiAnd KhRespectively representing current stiffness and displacement stiffness; lmThe distance between the plane of the magnetic bearing and the plane of the mass center of the rotor; lsIs the distance from the plane of the sensor to the plane of the center of mass of the rotor; j. the design is a squarexAnd JyIs the radial moment of inertia; j. the design is a squarezIs the axial moment of inertia; alpha and beta are respectively the displacement of the rotor inertia shaft in two degrees of freedom of radial deflection; thetaα、ΘβIs the amount of dynamic unbalance; sα(s) and sβ(s) is the displacement sensor output angular displacement.
2. Stability analysis
For convenience of analysis, a complex coefficient transfer function is introduced to enable a real coefficient dual-input system to be equivalent to a complex coefficient single-input system, and a simplified block diagram is shown in fig. 6. In the figure, DNF is a dual-channel phase shift trap; gc(s) is a PID controller; gcr(s) is a cross-feedback controller that suppresses the vortex mode; gw(s) is a power amplifier; ksIs the displacement sensor coefficient; kiAnd KhRespectively representing current stiffness and displacement stiffness; lmThe distance between the plane of the magnetic bearing and the plane of the mass center of the rotor; lsIs the distance from the plane of the sensor to the plane of the center of mass of the rotor; j. the design is a squarerrIs the radial complex coefficient moment of inertia; j. the design is a squarezIs the axial moment of inertia; j is an imaginary unit.
The closed-loop characteristic polynomial of the system obtained from fig. 6 is:
wherein G isANF(s) is the dual channel trap equivalent transfer function.
The original system sensitivity function is defined as follows:
the above equation can be converted into:
s+γ-jΩ+ε(cosθ+jsinθ)·S(s)＝0
wherein ε is a convergence factor; Ω is the rotor speed; γ is a damping factor; θ is the phase compensation angle.
When ε is equal to 0, s is equal to γ + j Ω. With epsilon as an independent variable and s as a dependent variable, the partial differential equation of the above equation is expressed as follows:
to ensure that the closed-loop eigenfunctions all follow the s-left half-plane after the algorithm is added to the system, the following conditions need to be satisfied:
wherein arg [. cndot. ] is argument.
The phase compensation angle is adjusted to ensure that the magnetic bearing control system realizes the stability of a closed-loop system at different rotating speeds.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but various changes may be apparent to those skilled in the art, and it is intended that all inventive concepts utilizing the inventive concepts set forth herein be protected without departing from the spirit and scope of the present invention as defined and limited by the appended claims.
Claims (2)
1. A magnetic suspension rotor same-frequency vibration torque suppression method based on a double-channel wave trap is characterized by comprising the following steps: the method comprises the following steps:
step (1): establishing a magnetic suspension rotor dynamic model containing rotor dynamic unbalance by taking the vibration torque as a suppression target;
step (2): designing an improved double-channel phase shift wave trap based on the dynamics model established in the step (1), adding a phase compensation angle and a damping factor into the improved double-channel phase shift wave trap, using a complex coefficient to simplify, obtaining a complex coefficient transfer function of the double-channel wave trap, using current and displacement to construct same-frequency vibration torque as input, enabling the double-channel wave trap to generate a preset gain at the same frequency of the rotating speed of the rotor by adjusting the ratio of a convergence factor and the damping factor in the double-channel wave trap, and accessing the double-channel wave trap into a magnetic suspension rotor control system in a feedback mode to realize effective suppression of the same frequency quantity;
and (3): determining the stable condition of the magnetic suspension rotor control system after the improved double-channel phase shift wave trap is added based on the double-channel wave trap complex coefficient transfer function obtained in the step (2); designing a phase compensation angle according to a stable condition, ensuring the stability of a magnetic suspension rotor control system within a working rotating speed range through the phase compensation angle, and finishing the suppression of the same-frequency vibration torque within the full rotating speed range of the magnetic suspension rotor;
in the step (1), a magnetic suspension rotor dynamics model including rotor dynamic unbalance is established as follows:
wherein alpha and beta are respectively the displacement of the rotor inertia shaft in two degrees of freedom of radial deflection; j. the design is a squarexAnd JyIs the radial moment of inertia, JzIs the axial moment of inertia; mxAnd MyIs the torque provided by the radial magnetic bearing; Ω is the high speed rotor rotational speed; f. ofax，fbx，fayAnd fbyIs the bearing force of four pairs of radial magnetic bearings; lmThe distance between the plane of the magnetic bearing and the plane of the mass center of the rotor; kiAnd KhCurrent stiffness and displacement stiffness, respectively; i.e. iax，iay，ibxAnd ibyIs four pairs of magnetic bearing coil currents; thetaα，ΘβIs the dynamic unbalance amount which is respectively as follows:
Θα＝e cos(Ωt+χ)
Θβ＝e sin(Ωt+χ)
wherein e represents the amplitude of the dynamic unbalance, and x represents the initial phase of the dynamic unbalance; therefore, the dynamic unbalance of the rotor is represented as interference with the same frequency of the rotating speed of the rotor, so that the rotor system can generate the same frequency torque;
in the step (2), an improved dual-channel phase shift trap is designed, and the improved dual-channel phase shift trap is represented as a state space model as follows:
wherein epsilon is a convergence factor, and the convergence speed is adjusted; Ω is the rotor speed; γ is a damping factor; θ is the phase compensation angle; u. of1(t),u2(t) is the input signal of the dual channel phase shift trap; x is the number of1(t),x2(t) is the output signal of the trap;
double channel trap complex coefficient transfer function GDNF(s) the following:
double-channel wave trap complex coefficient output variable xc(s) and input variable ucThe relationship of(s) is as follows:
where s is the laplace operator, let s ═ j ω, and ≠ 0, yielding:
when ω is Ω, there are:
when ω < Ω or ω > Ω, there are:
|xc(jω)|＝0。
2. the method for suppressing the same-frequency vibration torque of the magnetic suspension rotor based on the dual-channel wave trap as claimed in claim 1, is characterized in that: in the step (3), the stable conditions of the magnetic suspension rotor control system after the double-channel wave trap is added are established as follows:
where θ is the phase compensation angle; Ω is the rotor speed; arg [. cndot ] is argument; s(s) is a sensitivity function of the original magnetically levitated rotor control system, s(s) is expressed as:
wherein G isc(s) is a PID controller; gcr(s) is a cross-feedback controller that suppresses the vortex mode; gw(s) is a power amplifier; ksIs the displacement sensor coefficient; lsIs the distance from the plane of the sensor to the plane of the center of mass of the rotor; lmThe distance between the plane of the magnetic bearing and the plane of the mass center of the rotor; kiAnd KhRespectively representing current stiffness and displacement stiffness; p(s) is active magnetic bearing-rotor.
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