CN114109887B - Double-steering variable-step-size vibration suppression method and system for magnetic suspension molecular pump - Google Patents
Double-steering variable-step-size vibration suppression method and system for magnetic suspension molecular pump Download PDFInfo
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- CN114109887B CN114109887B CN202111411653.5A CN202111411653A CN114109887B CN 114109887 B CN114109887 B CN 114109887B CN 202111411653 A CN202111411653 A CN 202111411653A CN 114109887 B CN114109887 B CN 114109887B
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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
- F04D27/00—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids
- F04D27/02—Surge control
- F04D27/0261—Surge control by varying driving speed
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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
- 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
- F04D29/668—Combating cavitation, whirls, noise, vibration or the like; Balancing especially adapted for elastic fluid pumps damping or preventing mechanical vibrations
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2260/00—Function
- F05D2260/81—Modelling or simulation
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
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Abstract
The invention discloses a double-steering variable-step-size vibration suppression method of a magnetic suspension molecular pump, which comprises the steps of constructing a state space equation of a rotor of the magnetic suspension molecular pump in an unbalanced vibration state by acquiring an adjustable phase angle of the rotor of the magnetic suspension molecular pump, and the rotating speed and the same-frequency signals of the rotor in the unbalanced vibration state; constructing a transfer function model for inhibiting the unbalanced vibration state according to the unbalanced quantity matrix of the magnetic suspension molecular pump rotor in the unbalanced vibration state, wherein the function model is used for inhibiting the same-frequency signals of the magnetic suspension molecular pump rotor in the unbalanced vibration state; the invention also discloses a double-steering variable-step-size vibration suppression system which comprises a suppression module for realizing the vibration suppression method, and a controller, a power amplifier, a sensor and the like which are connected with the suppression module in parallel.
Description
Technical Field
The invention relates to the technical field of magnetic bearing control, in particular to a double-steering variable-step-size vibration suppression method and system for a magnetic suspension molecular pump.
Background
The ultra-high vacuum molecular pump is core instrument equipment for obtaining an ultra-high vacuum environment, and plays a decisive role in obtaining the ultra-high vacuum. The traditional mechanical bearing molecular pump has the advantages of large vibration noise, short service life and low pumping speed and compression ratio. The magnetic suspension bearing has the characteristics of high rotating speed, no need of lubrication and no friction, and can meet the performance indexes of ultra-high vacuum, ultra-clean and ultra-static, and becomes the best choice for the rotor support of the ultra-high vacuum molecular pump.
When the rotor of the molecular pump runs at a stable suspension acceleration speed, the vibration of the magnetic suspension molecular pump system is mainly caused by unbalanced vibration of the rotor, and the improvement of the performance index of the molecular pump can be seriously influenced by the unbalanced vibration, so that the unbalanced vibration suppression is a key technology for realizing the engineering application of the magnetic suspension molecular pump.
For the unbalanced vibration control of a magnetically suspended rotor, a number of control methods have been proposed, which can be divided into two main categories. One is unbalance compensation, which rotates the rotor around the geometric axis by compensating for unbalance forces, but this method requires a larger control current, which may lead to saturation of the power amplification circuit; the second type is a method based on a self-centering theory for zero co-frequency current and zero bearing force, so that the rotor rotates around an approximate inertia shaft and an inertia shaft. The method comprises an adaptive controller, repetitive control, an H infinity robust controller and some nonlinear control methods, but the methods only aim at single-channel serial processing, have large computation amount and complex algorithm and are not easy to realize engineering application.
Disclosure of Invention
In order to overcome the defects of the prior art. The invention aims to provide a method for inhibiting double-steering variable-step-length vibration of a magnetic bearing control system, which has the characteristics of realizing different control strategies aiming at two steering directions of clockwise rotation and anticlockwise rotation, realizing double-channel parallel processing and reducing the calculation amount. The unbalanced vibration force can be quickly and effectively inhibited, and the position precision of the magnetic suspension rotor is improved.
In order to achieve the above object, the present invention provides a method for suppressing dual-steering variable-step-size vibration of a magnetic suspension molecular pump, comprising the following steps:
acquiring an adjustable phase angle of a rotor of the magnetic suspension molecular pump, and a rotor rotating speed and a same-frequency signal in an unbalanced vibration state, and constructing a state space equation of the rotor of the magnetic suspension molecular pump in the unbalanced vibration state;
based on a state space equation, a transfer function model for suppressing the unbalanced vibration state is constructed according to an unbalanced quantity matrix of the magnetic suspension molecular pump rotor in the unbalanced vibration state, wherein the function model is used for suppressing the same-frequency signals of the magnetic suspension molecular pump rotor in the unbalanced vibration state.
Preferably, in the process of constructing the state space equation, the following steps are further included:
taking the same-frequency signals as input signals of a state space equation, collecting state variables of the same-frequency signals, and acquiring output signals of the state space equation;
and acquiring the cut-off frequency and the gain of the low-pass filter for processing the same-frequency signals, and constructing a state space equation according to the cut-off frequency, the gain of the low-pass filter, the input signal, the state variable, the adjustable phase angle and the rotor rotating speed.
Preferably, the state space equation is:
wherein, x in the formula0(t)、y0(t) is an input signal, x1(t) and y1(t) is a state variable, cx(t) and cy(t) is the output signal, Ω is the rotor speed, w0The cutoff frequency of the low-pass filter, K the gain of the low-pass filter, and theta the adjustable phase angle.
Preferably, in the process of constructing the transfer function model, the unbalance amount matrix comprises a first unbalance amount matrix for representing the corresponding situation when the rotor rotates anticlockwise and a second unbalance amount matrix for representing the corresponding situation when the rotor rotates clockwise;
the matrix expression of the first unbalance amount matrix is:
the matrix expression of the second unbalance amount matrix is:
wherein, the lambda is the amplitude of the unbalance amount,
is the phase angle of the unbalance.
Preferably, based on the state space equation, the first unbalance matrix, the second unbalance matrix, according to formula g(s) ═ C (sI-a)-1B, respectively constructing a first open-loop transfer function corresponding to the rotor rotating anticlockwise and a second open-loop transfer function corresponding to the rotor rotating clockwise, wherein,
the functional expression of the first open-loop transfer function is:
a functional expression of the second open-loop transfer function:
wherein M(s) ═ Kw0[-sinθs2+(2Ωcosθ-w0sinθ)s+Ωw0cosθ+Ω2sinθ]，N(s)＝[(s+w0)2+Ω2]Ω，M′(s)＝Kw0[sinθs2+w0sinθs+Ωw0cosθ+Ω2sinθ]，N′(s)＝[(s+w0)2+Ω2]Ω。
Preferably, based on a first open-loop transfer function and a second open-loop transfer function, obtaining a first closed-loop transfer function corresponding to the first open-loop transfer function and a second closed-loop transfer function corresponding to the second open-loop transfer function according to the fact that a pole of the open-loop transfer function is a zero point of the closed-loop transfer function, and constructing a transfer function model, wherein the same-frequency signals are suppressed by adjusting the value of s of the transfer function model;
and when s is equal to j omega, the first closed-loop transfer function and the second closed-loop transfer function are equal to 0 approximately, and the suppression on the same-frequency signals is realized.
A double-steering variable-step-size vibration suppression system of a magnetic levitation molecular pump comprises:
the first sensor is used for acquiring a first signal of the rotor of the magnetic suspension molecular pump in an unbalanced vibration state;
the second sensor is used for acquiring a second signal of the rotor of the magnetic suspension molecular pump in an unbalanced vibration state;
the signal suppression module is used for suppressing the first signal and the second signal and acquiring a third signal and a fourth signal after suppression;
the first controller is used for sending a first control signal to a rotor system of a magnetic suspension molecular pump rotor through the first power amplifier according to the third signal;
and the second controller is used for sending a second control signal to the rotor system through the second power amplifier according to the fourth signal.
Preferably, the signal suppression module comprises at least one of,
a signal suppression unit for implementing the dual steering step-change vibration suppression method according to any one of claims 1 to 6;
the rotor steering simulation unit is used for respectively arranging coefficient switching units at a signal input end and a signal output end of the signal suppression unit and realizing the simulation of the steering of the rotor of the magnetic suspension molecular pump by adjusting the coefficient switching units, wherein the steering comprises clockwise rotation and anticlockwise rotation;
the coefficient switching unit comprises switching coefficients epsilon 1 and epsilon 2;
when the rotor of the magnetic suspension molecular pump rotates clockwise, the epsilon 1 is equal to 1, and the epsilon 2 is equal to 0;
when the rotor of the magnetic suspension molecular pump rotates anticlockwise, epsilon 1 is 0, and epsilon 2 is 1.
Preferably, the coefficient switching unit includes a first coefficient switching unit, a second coefficient switching unit, a third coefficient switching unit, and a fourth coefficient switching unit;
the coefficient switching unit is composed of an epsilon 1 coefficient subunit and an epsilon 2 coefficient subunit;
the first controller is respectively connected with the first coefficient switching unit and the third coefficient switching unit;
the second controller is respectively connected with the second coefficient switching unit and the fourth coefficient switching unit;
the epsilon 1 coefficient subunit of the first coefficient switching unit and the epsilon 2 coefficient subunit of the second coefficient switching unit form a first signal input channel of the signal suppression unit;
the epsilon 1 coefficient subunit of the second coefficient switching unit and the epsilon 2 coefficient subunit of the first coefficient switching unit form a second signal input channel of the signal suppression unit;
the first signal input channel and the second signal input channel form a signal input end of the signal suppression unit;
the epsilon 1 coefficient subunit of the third coefficient switching unit and the epsilon 2 coefficient subunit of the fourth coefficient switching unit form a first signal output channel of the signal suppression unit;
the epsilon 1 coefficient subunit of the fourth coefficient switching unit and the epsilon 2 coefficient subunit of the third coefficient switching unit form a second signal output channel of the signal suppression unit;
the first signal output channel and the second signal output channel form a signal output end of the signal suppression unit.
Preferably, the signal suppression unit is connected in parallel with the first controller and the second controller, respectively;
the functional expression of the closed loop transfer function of the signal suppression unit is:
the transfer function expression of the first controller or the second controller is as follows:
wherein, C2(s) is the output of the rotor of the magnetic molecular pump, Re2(s) is the input of the rotor of the magnetic molecular pump, KsFor sensingCoefficient of device, KADIs an analog-to-digital conversion coefficient;
the first controller and the second controller are PID controllers, and transfer functions of the PID controllers are as follows:
in the formula KpIs a proportional element gain, KIFor integral element gain, KDAnd KFThe parameters of the incomplete differential link.
The invention discloses the following technical effects:
the double-steering variable-step-size vibration suppression method for the magnetic bearing control system can be switched between a clockwise rotation mode and a counterclockwise rotation mode without re-setting parameters, and the trap depth can be increased along with the increase of the rotating speed in a medium-high speed range by adopting a structure connected with the controller in parallel, so that the effect of variable step size is achieved, and the response speed of the unbalanced vibration suppression method at high rotating speed is increased.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a closed-loop control block diagram of a magnetic bearing control system with dual channel variable step synchronous reference coordinate transformation with channel switching of the present invention;
FIG. 2 is a magnitude-phase characteristic curve corresponding to PID control used in the present invention;
FIG. 3 is a graph comparing the amplitude-frequency characteristic curves of the closed-loop transfer function of the original control system, the closed-loop transfer function of the magnetic bearing control system with the two-channel variable-step synchronous reference coordinate transformation and the closed-loop transfer function of the magnetic bearing control system with the two-channel series synchronous reference coordinate transformation according to the present invention;
FIG. 4 is a graph showing the convergence rate of rotor displacement obtained by the two-channel variable-step synchronous reference coordinate transformation and the two-channel series synchronous reference coordinate transformation performed in the magnetic suspension molecular pump.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments. The components of the embodiments of the present application, as generally described and illustrated in the figures herein, could be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.
As shown in fig. 1-4, the present invention provides a dual-steering variable-step-size vibration suppression method for a magnetic levitation molecular pump, comprising the following steps:
acquiring an adjustable phase angle of a rotor of the magnetic suspension molecular pump, and the rotor rotating speed and the same-frequency signals in an unbalanced vibration state, and constructing a state space equation of the rotor of the magnetic suspension molecular pump in the unbalanced vibration state;
based on a state space equation, a transfer function model for suppressing the unbalanced vibration state is constructed according to an unbalanced quantity matrix of the magnetic suspension molecular pump rotor in the unbalanced vibration state, wherein the function model is used for suppressing the same-frequency signals of the magnetic suspension molecular pump rotor in the unbalanced vibration state.
Further preferably, in the process of constructing the state space equation, the following steps are also included:
taking the same-frequency signals as input signals of a state space equation, collecting state variables of the same-frequency signals, and acquiring output signals of the state space equation;
and acquiring the cut-off frequency and the gain of the low-pass filter for processing the same-frequency signals, and constructing a state space equation according to the cut-off frequency, the gain of the low-pass filter, the input signal, the state variable, the adjustable phase angle and the rotor rotating speed.
Preferably, the state space equation is:
wherein, x in the formula0(t)、y0(t) is an input signal, x1(t) and y1(t) is a state variable, cx(t) and cy(t) is the output signal, Ω is the rotor speed, w0The cutoff frequency of the low-pass filter, K is the gain of the low-pass filter, and theta is the adjustable phase angle.
Further preferably, in the process of constructing the transfer function model, the unbalance amount matrix includes a first unbalance amount matrix for representing the correspondence when the rotor rotates counterclockwise and a second unbalance amount matrix for representing the correspondence when the rotor rotates clockwise;
the matrix expression of the first unbalance amount matrix is:
the matrix expression of the second unbalance amount matrix is:
wherein, the lambda is the amplitude of the unbalance amount,
is the phase angle of the unbalance.
Further preferably, the first imbalance is based on a state space equationA quantity matrix, a second averaging matrix, according to formula G(s) ═ C (sI-A)-1B, respectively constructing a first open-loop transfer function corresponding to the rotor rotating anticlockwise and a second open-loop transfer function corresponding to the rotor rotating clockwise, wherein,
the functional expression of the first open-loop transfer function is:
a functional expression of the second open-loop transfer function:
wherein M(s) ═ Kw0[-sinθs2+(2Ωcosθ-w0sinθ)s+Ωw0cosθ+Ω2sinθ]，
N(s)＝[(s+w0)2+Ω2]Ω，
M′(s)＝Kw0[sinθs2+w0sinθs+Ωw0cosθ+Ω2sinθ]，
N′(s)＝[(s+w0)2+Ω2]Ω。
Further preferably, based on the first open-loop transfer function and the second open-loop transfer function, obtaining a first closed-loop transfer function corresponding to the first open-loop transfer function and a second closed-loop transfer function corresponding to the second open-loop transfer function according to the pole of the open-loop transfer function as the zero of the closed-loop transfer function, and constructing a transfer function model, wherein the same-frequency signals are suppressed by adjusting the value of s of the transfer function model;
and when s is equal to j omega, the first closed-loop transfer function and the second closed-loop transfer function are equal to 0 approximately, and the suppression on the same-frequency signals is realized.
A dual-steering variable-step-size vibration suppression system of a magnetic levitation molecular pump comprises:
the first sensor is used for acquiring a first signal of a rotor of the magnetic suspension molecular pump in an unbalanced vibration state;
the second sensor is used for acquiring a second signal of the rotor of the magnetic suspension molecular pump in an unbalanced vibration state;
the signal suppression module is used for suppressing the first signal and the second signal and acquiring a third signal and a fourth signal after suppression;
the first controller is used for sending a first control signal to a rotor system of a magnetic suspension molecular pump rotor through the first power amplifier according to the third signal;
and the second controller is used for sending a second control signal to the rotor system through the second power amplifier according to the fourth signal.
Further preferably, the signal suppression module comprises,
a signal suppression unit for implementing the dual steering step-change vibration suppression method according to any one of claims 1 to 6;
the rotor steering simulation unit is used for respectively arranging coefficient switching units at a signal input end and a signal output end of the signal suppression unit and realizing the simulation of the steering of the rotor of the magnetic suspension molecular pump by adjusting the coefficient switching units, wherein the steering comprises clockwise rotation and anticlockwise rotation;
the coefficient switching unit comprises switching coefficients epsilon 1 and epsilon 2;
when the rotor of the magnetic suspension molecular pump rotates clockwise, the epsilon 1 is equal to 1, and the epsilon 2 is equal to 0;
when the rotor of the magnetic suspension molecular pump rotates anticlockwise, epsilon 1 is 0, and epsilon 2 is 1.
Further preferably, the coefficient switching unit includes a first coefficient switching unit, a second coefficient switching unit, a third coefficient switching unit, and a fourth coefficient switching unit;
the coefficient switching unit is composed of an epsilon 1 coefficient subunit and an epsilon 2 coefficient subunit;
the first controller is respectively connected with the first coefficient switching unit and the third coefficient switching unit;
the second controller is respectively connected with the second coefficient switching unit and the fourth coefficient switching unit;
the epsilon 1 coefficient subunit of the first coefficient switching unit and the epsilon 2 coefficient subunit of the second coefficient switching unit form a first signal input channel of the signal suppression unit;
the epsilon 1 coefficient subunit of the second coefficient switching unit and the epsilon 2 coefficient subunit of the first coefficient switching unit form a second signal input channel of the signal suppression unit;
the first signal input channel and the second signal input channel form a signal input end of the signal suppression unit;
the epsilon 1 coefficient subunit of the third coefficient switching unit and the epsilon 2 coefficient subunit of the fourth coefficient switching unit form a first signal output channel of the signal suppression unit;
the epsilon 1 coefficient subunit of the fourth coefficient switching unit and the epsilon 2 coefficient subunit of the third coefficient switching unit form a second signal output channel of the signal suppression unit;
the first signal output channel and the second signal output channel form a signal output end of the signal suppression unit.
Further preferably, the signal suppression unit is connected in parallel with the first controller and the second controller, respectively;
the functional expression of the closed loop transfer function of the signal suppression unit is:
the transfer function expression of the first controller or the second controller is as follows:
wherein, C2(s) is the output of the rotor of the magnetic molecular pump, Re2(s) is the input of the rotor of the magnetic molecular pump, KsIs the sensor coefficient, KADIs an analog-to-digital conversion coefficient;
the first controller and the second controller are PID controllers, the transfer functions of which are as follows:
in the formula KpIs a proportional element gain, KIGain of integral element, KDAnd KFThe parameters of the incomplete differential link.
The invention is further described with reference to the following figures and detailed description.
1) The state space equation is established by the open-loop block diagram of the two-channel synchronous reference coordinate transformation in FIG. 1:
in the formula x0(t)、y0(t) is an input signal for synchronous reference coordinate transformation, x1(t) and y1(t) is a state variable, cx(t) and cy(t) is the output signal of the synchronous reference coordinate transformation, omega is the rotation speed of the rotor, w0The cut-off frequency of the low-pass filter in the synchronous reference coordinate transformation is shown, K is the gain of the low-pass filter, and theta is the adjustable phase angle of the synchronous reference coordinate transformation.
2) When the vane rotor rotates counterclockwise, the corresponding unbalance amount matrix is:
when the vane rotor rotates clockwise, the corresponding unbalance amount matrix is:
in the above two equations λ is the magnitude of the unbalance,
to be out of balancePhase angle of the quantity. The state space equation of the formula (1) is combined with the formula G(s) ═ C (sI-A)-1B, wherein s is a complex parameter, I is an identity matrix, A is a system matrix, B is an input coefficient matrix, C is an output coefficient matrix, and G (S) is a transfer function; the open-loop transfer function matrix corresponding to the counterclockwise rotation of the synchronous coordinate transformation can be obtained as follows:
wherein M(s) ═ Kw0[-sinθs2+(2Ωcosθ-w0sinθ)s+Ωw0cosθ+Ω2sinθ]，N(s)＝[(s+w0)2+Ω2]Omega. Taking the open-loop transfer function of the anticlockwise synchronous reference coordinate transformation as
The open loop transfer function matrix corresponding to a clockwise rotation is:
wherein M'(s) ═ Kw0[sinθs2+w0sinθs+Ωw0cosθ+Ω2sinθ]，N′(s)＝[(s+w0)2+Ω2]Omega; taking the open-loop transfer function of the clockwise synchronous reference coordinate transformation as
From the transfer functions of N(s) and N'(s), when w is0When "Ω, s ═ j Ω, N(s) ≈ N'(s) ≈ 0.
To sum up, the denominator of the open-loop transfer function corresponding to the clockwise rotation and the counterclockwise rotation are different, and the numerator is the same, so that under the condition of appropriate parameters, the pole of the open-loop transfer function is the zero point of the closed-loop transfer function, and when s equals to j Ω, the magnetic suspension numerator corresponding to the counterclockwise rotation and the clockwise rotation of the rotor is obtainedPump system closed loop transfer function satisfying phi1(jΩ)≈0，Φ2And (j omega) is approximately equal to 0, so that the suppression of the same-frequency signals is realized.
3) In order to optimize the method of the synchronous reference coordinate transformation, switching coefficients epsilon 1 and epsilon 2 are respectively added at the input end and the output end of the synchronous reference coordinate transformation, namely, the original anticlockwise rotation control scheme is used, when a rotor rotates clockwise, epsilon 1 is equal to 1, and epsilon 2 is equal to 0; when the rotor rotates anticlockwise, epsilon 1 is equal to 0, and epsilon 2 is equal to 1. Therefore, the unbalanced vibration control under different steering can be realized by only changing the switching coefficient without repeatedly adjusting parameters.
4) When the reference coordinate transformation and the controller G are synchronizedcWhen the magnetic suspension molecular pump systems are connected in series, the single-channel closed-loop transfer function of the magnetic suspension molecular pump system is as follows:
(6) middle GsThe transfer function of(s) is as follows:
when the reference coordinate transformation and the controller G are synchronizedc(s) when connected in parallel, the single-channel closed-loop transfer function of the magnetic suspension molecular pump system is as follows:
(8) middle Gp(s) the corresponding transfer function is as follows:
(6) (7), (8) and (9) wherein C is1(s) is the output Re of the magnetic molecular pump system under the transformation of the series synchronous reference coordinate1(s) is a magnetic suspension molecular pump under the transformation of a series synchronous reference coordinateInput of the system, C2(s) is the output Re of the magnetic suspension molecular pump system under the transformation of the parallel synchronous reference coordinate2(s) is input of the magnetic suspension molecular pump system under the transformation of the parallel synchronous reference coordinate, KsIs the sensor coefficient, KADAre analog-to-digital conversion coefficients.
The ratio of the closed-loop transfer functions corresponding to the serial synchronous reference coordinate transformation and the parallel synchronous reference coordinate transformation is:
when w is0When < Ω, s ═ j Ω, n(s) ≈ 0 can be obtained:
GB(s)＝Gc(s) (11)
namely, the amplitude difference between the series type synchronous reference coordinate transformation amplitude and the parallel type synchronous coordinate transformation at the position where s is j omega is as follows: | Gc(jΩ)|。
The controller used in the present invention is a PID controller, and its transfer function is as follows:
k in formula (12)pIs a proportional element gain, KIFor integral element gain, KDAnd KFThe parameters of the incomplete differential link.
The gain of the PID controller increases with increasing rotation speed in the medium and high rotation speed range as shown in fig. 2, so that the parallel synchronous reference coordinate transformation has not only higher notch depth but also step-changing effect relative to the series synchronous reference coordinate transformation under the condition of the same parameters.
As shown in fig. 3, the amplitude-frequency characteristic curve of the closed-loop system corresponding to the rotor rotation speed of 100Hz and 400Hz, the light blue curve is the amplitude-frequency characteristic curve of the original magnetic bearing control system, the red line is the amplitude-frequency characteristic curve of the closed-loop transfer function of the magnetic bearing control system with two-channel series synchronous reference coordinate transformation, and the dark blue line is the amplitude-frequency characteristic curve of the closed-loop transfer function of the magnetic bearing control system with two-channel variable-step synchronous reference coordinate transformation, wherein the channel switching is performed, and it can be seen from the figure that the amplitude of the magnetic bearing system under the series synchronous reference coordinate transformation is attenuated by 40dB at 100Hz, and the amplitude of the magnetic bearing system under the parallel synchronous reference coordinate transformation is attenuated by 53 dB; when the frequency of the magnetic bearing system is 400Hz, the amplitude of the magnetic bearing system under the transformation of the series synchronous reference coordinate is attenuated by 36dB, and the amplitude of the magnetic bearing system under the transformation of the parallel synchronous reference coordinate is attenuated by 57dB, so that the attenuation capacity of the series synchronous reference coordinate on the same frequency signal is reduced along with the increase of the rotating speed, the attenuation capacity of the parallel synchronous reference coordinate on the same frequency signal is improved, and the attenuation capacity of the parallel synchronous reference coordinate on the same frequency signal is better than that of the series synchronous reference coordinate.
A higher notch depth represents a higher response speed, as shown in fig. 4, the red curve is a convergence diagram of the unbalance amount under the series type synchronous coordinate transformation, the series type synchronous reference coordinate transformation is turned on at 0.724s, the steady state value is converged at 0.76s, the blue curve with the convergence time of 36ms is a convergence diagram of the unbalance amount under the parallel type synchronous coordinate transformation, the parallel type synchronous reference coordinate transformation is turned on at 1.853s, the steady state value is converged at 1.873s, and the convergence time is 20 ms.
The double-steering variable-step-size vibration suppression method for the magnetic bearing control system can be switched between a clockwise rotation mode and a counterclockwise rotation mode without re-setting parameters, and the trap depth can be increased along with the increase of the rotating speed in a medium-high speed range by adopting a structure connected with the controller in parallel, so that the effect of variable step size is achieved, and the response speed of the unbalanced vibration suppression method at high rotating speed is increased.
The invention relates to a double-steering variable-step-length vibration suppression method for a magnetic bearing control system, which is characterized by realizing the suppression of unbalanced vibration of magnetic suspension molecular pumps of different steering blade rotors, respectively realizing the extraction and suppression of double-channel same-frequency vibration of clockwise steering and anticlockwise steering through channel switching, and realizing the deepening of a trapped wave depth along with the increase of rotating speed by using the amplitude-frequency characteristic of a controller through a structure connected with the controller in parallel, thereby having the effect of variable step length. The invention has the advantages of being suitable for the vane rotors based on different steering, achieving higher response speed by vibration suppression at high rotating speed, simultaneously realizing suppression of double-channel same-frequency signals, and having less calculation amount, and can improve the control precision of the rotors based on the unbalanced vibration control of the different steering vane rotors of the magnetic suspension molecular pump system while realizing higher response speed.
Claims (7)
1. A double-steering variable-step-length vibration suppression method of a magnetic suspension molecular pump is characterized by comprising the following steps of:
acquiring an adjustable phase angle of a rotor of a magnetic suspension molecular pump, and the rotor rotating speed and a same-frequency signal in an unbalanced vibration state, and constructing a state space equation of the rotor of the magnetic suspension molecular pump in the unbalanced vibration state;
the state space equation is:
wherein in the formula
、
In order to input the signal, the signal is,
and
in order to be a state variable, the state variable,
and
in order to output the signal(s),
is the rotational speed of the rotor and is,
is the cut-off frequency of the low-pass filter,
in order to be the gain of the low-pass filter,
is an adjustable phase angle;
based on the state space equation, constructing a transfer function model for inhibiting the unbalanced vibration state according to an unbalanced quantity matrix of the magnetic suspension molecular pump rotor in the unbalanced vibration state, wherein the transfer function model is used for inhibiting the same-frequency signals of the magnetic suspension molecular pump rotor in the unbalanced vibration state;
in the process of constructing the transfer function model, the unbalance amount matrix comprises a first unbalance amount matrix used for representing the corresponding situation when the rotor rotates anticlockwise and a second unbalance amount matrix used for representing the corresponding situation when the rotor rotates clockwise;
the matrix expression of the first unbalance amount matrix is as follows:
the matrix expression of the second unbalance amount matrix is as follows:
wherein,
is the magnitude of the amount of unbalance,
phase angle, which is the amount of unbalance;
based on the state space equation, the first unbalance amount matrix and the second unbalance amount matrix according to a formula
Respectively constructing a first open-loop transfer function corresponding to the counterclockwise rotation of the rotor and a second open-loop transfer function corresponding to the clockwise rotation of the rotor, wherein,
the functional expression of the first open-loop transfer function is:
a functional expression of the second open-loop transfer function:
wherein,
，
2. the method for suppressing the dual-steering variable-step-size vibration of the magnetic molecular pump as claimed in claim 1, wherein:
in the process of constructing the state space equation, the method further comprises the following steps:
taking the same-frequency signals as input signals of the state space equation, collecting state variables of the same-frequency signals, and acquiring output signals of the state space equation;
and acquiring the cut-off frequency and the gain of a low-pass filter for processing the same-frequency signals, and constructing the state space equation according to the cut-off frequency, the gain of the low-pass filter, the input signal, the state variable, the adjustable phase angle and the rotor rotating speed.
3. The method for suppressing the dual-steering variable-step-size vibration of the magnetic molecular pump as claimed in claim 1, wherein:
based on the first open-loop transfer function and the second open-loop transfer function, obtaining a first closed-loop transfer function corresponding to the first open-loop transfer function and a second closed-loop transfer function corresponding to the second open-loop transfer function according to the fact that a pole of the open-loop transfer function is a zero point of the closed-loop transfer function, and constructing a transfer function model, wherein the same-frequency signal is suppressed by adjusting the value of s of the transfer function model;
in pair when
And then, the first closed-loop transfer function and the second closed-loop transfer function are approximately equal to 0 and are used for realizing the suppression of the same-frequency signals.
4. The system of the double-steering variable-step-size vibration suppression method of the magnetic molecular pump according to claim 1, characterized by comprising:
the first sensor is used for acquiring a first signal of a rotor of the magnetic suspension molecular pump in an unbalanced vibration state;
the second sensor is used for acquiring a second signal of the rotor of the magnetic suspension molecular pump in the unbalanced vibration state;
the signal suppression module is used for suppressing the first signal and the second signal and acquiring a third signal and a fourth signal after suppression;
the first controller is used for sending a first control signal to a rotor system of the magnetic suspension molecular pump rotor through a first power amplifier according to the third signal;
and the second controller is used for sending a second control signal to the rotor system through a second power amplifier according to the fourth signal.
5. The system for the dual-steering variable-step-size vibration suppression method of the magnetic levitation molecular pump as recited in claim 4, wherein:
the signal suppression module comprises a signal suppression module and a signal suppression module,
a signal suppression unit for implementing the dual steering step-variable vibration suppression method according to any one of claims 1 to 3;
the rotor steering simulation unit is used for respectively arranging coefficient switching units at a signal input end and a signal output end of the signal suppression unit, and realizing the simulation of the steering of the magnetic suspension molecular pump rotor by adjusting the coefficient switching units, wherein the steering comprises clockwise rotation and anticlockwise rotation;
the coefficient switching unit includes a switching coefficient
And
；
when the rotor of the magnetic suspension molecular pump rotates clockwise
；
When the rotor of the magnetic suspension molecular pump rotates anticlockwise
。
6. The system of the double-steering variable-step-size vibration suppression method of the magnetic molecular pump as claimed in claim 5, wherein:
the coefficient switching unit comprises a first coefficient switching unit, a second coefficient switching unit, a third coefficient switching unit and a fourth coefficient switching unit;
the coefficient switching unit is composed of
A coefficient subunit and
a coefficient subunit;
the first controller is respectively connected with the first coefficient switching unit and the third coefficient switching unit;
the second controller is respectively connected with the second coefficient switching unit and the fourth coefficient switching unit;
of the first coefficient switching unit
Coefficient sub-unit, and of said second coefficient switching unit
A coefficient subunit constituting a first signal input channel of the signal suppression unit;
of the second coefficient switching unit
Coefficient subunit, and the first systemOf number switching units
A coefficient subunit constituting a second signal input channel of the signal suppression unit;
the first signal input channel and the second signal input channel constitute the signal input terminal of the signal suppression unit;
of the third coefficient switching unit
Coefficient sub-unit, and of the fourth coefficient switching unit
A coefficient subunit constituting a first signal output channel of the signal suppression unit;
of said fourth coefficient switching unit
Coefficient subunit and the third coefficient switching unit
A coefficient subunit constituting a second signal output channel of the signal suppression unit;
the first signal output channel and the second signal output channel constitute the signal output terminal of the signal suppressing unit.
7. The system of the double-steering variable-step-size vibration suppression method of the magnetic molecular pump as claimed in claim 6, wherein:
the signal suppression unit is respectively connected with the first controller and the second controller in parallel;
the functional expression of the closed loop transfer function of the signal suppression unit is as follows:
the transfer function expression of the first controller or the second controller is:
wherein,
is the output of the rotor of the magnetic suspension molecular pump,
is the input of the rotor of the magnetic suspension molecular pump,
as a function of the coefficients of the sensors,
is an analog-to-digital conversion coefficient;
the first controller and the second controller are PID controllers, and transfer functions of the PID controllers are as follows:
in the formula
In order to gain in the proportional link,
in order to integrate the gain of the element,
and
the parameters are parameters of incomplete differential links.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102425562A (en) * | 2011-12-05 | 2012-04-25 | 北京中科科仪技术发展有限责任公司 | Dynamic balance method for magnetic suspension molecular pump |
| CN102425561A (en) * | 2011-12-05 | 2012-04-25 | 北京中科科仪技术发展有限责任公司 | Dynamic balance method for magnetic suspension molecular pump |
| CN107870568A (en) * | 2017-12-21 | 2018-04-03 | 北京航空航天大学 | A kind of magnetic suspension rotor method for inhibiting harmonic current based on second order bimodulus Repetitive controller |
| CN108716471A (en) * | 2018-04-03 | 2018-10-30 | 北京航空航天大学 | A kind of rotor of magnetic suspension molecular pump infinitesimal displacement Active Control Method |
| CN109062274A (en) * | 2018-09-03 | 2018-12-21 | 河南工业大学 | A kind of magnetic bearing oscillatory torque suppressing method based on complex variable finite-dimensional repetitive control |
-
2021
- 2021-11-25 CN CN202111411653.5A patent/CN114109887B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102425562A (en) * | 2011-12-05 | 2012-04-25 | 北京中科科仪技术发展有限责任公司 | Dynamic balance method for magnetic suspension molecular pump |
| CN102425561A (en) * | 2011-12-05 | 2012-04-25 | 北京中科科仪技术发展有限责任公司 | Dynamic balance method for magnetic suspension molecular pump |
| WO2013082999A1 (en) * | 2011-12-05 | 2013-06-13 | 北京中科科仪股份有限公司 | Method of dynamic balance for magnetic levitation molecular pump (4) |
| GB201411235D0 (en) * | 2011-12-05 | 2014-08-06 | Kyky Technology Co Ltd And Tsinghua University | Method of dynamic balance for magnetic levitation molecular pump |
| CN107870568A (en) * | 2017-12-21 | 2018-04-03 | 北京航空航天大学 | A kind of magnetic suspension rotor method for inhibiting harmonic current based on second order bimodulus Repetitive controller |
| CN108716471A (en) * | 2018-04-03 | 2018-10-30 | 北京航空航天大学 | A kind of rotor of magnetic suspension molecular pump infinitesimal displacement Active Control Method |
| CN109062274A (en) * | 2018-09-03 | 2018-12-21 | 河南工业大学 | A kind of magnetic bearing oscillatory torque suppressing method based on complex variable finite-dimensional repetitive control |
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