CN105071729A - Bearing-free asynchronous motor stator magnetic flux linkage orientated reverse decoupling method taking current dynamics into consideration - Google Patents
Bearing-free asynchronous motor stator magnetic flux linkage orientated reverse decoupling method taking current dynamics into consideration Download PDFInfo
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Abstract
The invention discloses a bearing-free asynchronous motor stator magnetic flux linkage orientated reverse decoupling method taking current dynamics into consideration. A torque winding current dynamic differential equation is introduced, the influence of single-side electromagnetic tension influence of rotor imbalance is taken into consideration, dynamic mathematic models of a stator magnetic flux linkage orientated original system and a stator magnetic flux linkage orientated reverse system of a bearing-free asynchronous motor are established, through a reverse system decoupling method, and before the reverse system is connected in series with the original system, the system is dynamically decoupled into four linear subsystems: an alpha radial displacement two-order linear subsystem and a beta radial displacement two-order linear subsystem, a stator magnetic flux linage one-order linear subsystem and a rotation speed two-order linear subsystem. According to the invention, on the basis that the current dynamic influence of a torque winding stator is taken into consideration, stator magnetic flux linkage orientated reverse system dynamic decoupling is carried out on the bearing-free asynchronous motor, such that the influence exerted by rotor parameters on decoupling performance can be effectively avoided, the stator current closed-loop link of the original system and the load torque identification link of the reverse system are omitted, the system structure is simplified, and the system decoupling performance is improved.
Description
Technical field
The present invention relates to extraordinary alternating current machine Drive Control Technique field, is a kind of accurate induction-type bearingless motor Inverse Decoupling method, is particularly useful for structure induction-type bearingless motor high-performance magnetism suspension operation control system.
Background technology
Bearing-free motor is the similitude based on magnetic bearing and alternating-current motor stator structure, the New-type electric machine that what development in recent years was got up be suitable for runs up, and is with a wide range of applications in fields such as Aero-Space, material sealing transmission, advanced manufactures.Induction-type bearingless motor is the complex control object of a multivariable, non-linear, close coupling, realize its high-performance suspension operation and control, and must realize motor speed, dynamic decoupling between magnetic linkage and two rotor radial displacement components; And method of inverse is the effective means of carrying out Linearized Decoupling for multivariable, non linear system, thus can be applied to the dynamic Decoupling Control of Load Torque of bearing-free motor.
Though the Inverse Decoupling method of prior art to induction-type bearingless motor has some to study, and be all based on rotor flux-oriented control, and in motor operation course, the identification precision of rotor flux can be subject to the impact of rotor parameter unavoidably.Although the impact of rotor parameter can be suppressed to a certain extent by external regulator filter, cannot eradicate.Compare with rotor flux, the estimated accuracy of stator magnetic linkage only depends on stator resistance, substantially not by the impact of rotor parameter, thus has stronger robustness.If on the basis of torque system Stator flux oriented control, the inverse kinematics decoupling zero of total system can be carried out to bearing-free motor, not only can Guarantee control system performance, and can effectively avoid rotor parameter on the impact of motor flux estimate algorithm precision.At present, about the stator magnetic linkage oriented overall Inverse Decoupling method of bearing-free motor, no matter whether considering winding dynamic characteristic, have no applicable design always and completed by development, is the target that current industry is badly in need of improving.
Summary of the invention
Main purpose of the present invention is that open one considers the stator magnetic linkage oriented reversed decoupling method of the dynamic induction-type bearingless motor of electric current, Stator flux oriented control is adopted to replace traditional torque system rotor flux-oriented control, the technical problem solved is four linear subsystems by induction-type bearingless motor system decoupling, improves rotor magnetic suspension control performance and dynamic antijamming capability.
The present invention specifically by the following technical solutions and technical measures to realize.
The present invention proposes a kind of stator magnetic linkage oriented reversed decoupling method of consideration dynamic induction-type bearingless motor of electric current, at consideration torque winding current dynamic differential equation, on the basis of the monolateral electromagnet pull of unbalanced rotor, set up the dynamic mathematical models considering the stator magnetic linkage oriented original system of the dynamic induction-type bearingless motor of stator current and stator magnetic linkage oriented inverse system, before stator magnetic linkage oriented inverse system is serially connected in stator magnetic linkage oriented original system, induction-type bearingless motor system dynamic decoupling is made to be the second-order linearity subsystem of four linear subsystem: α and β, two radial displacements, a stator magnetic linkage
first-order linear subsystem, a rotating speed
ωsecond-order linearity subsystem, the output variable of stator magnetic linkage oriented original system comprises radial displacement α and β, stator magnetic linkage
, and rotating speed
ω, the second dervative of radial displacement α and β
with
, stator magnetic linkage first derivative
, and the second dervative of rotating speed
as the input variable of stator magnetic linkage oriented inverse system, the output variable of stator magnetic linkage oriented inverse system, as the input variable of stator magnetic linkage oriented original system, is respectively the d shaft current component of suspending windings
with q shaft current component
, torque winding d shaft voltage component
with q shaft voltage component
, wherein,
The dynamic mathematical models of described stator magnetic linkage oriented original system are:
，
In formula, the input variable of definition original system is
, system state variables is
, system output variables is
,
,
be respectively torque wound stator electric current
d,
qaxle component,
,
be respectively suspending windings stator current
d,
qaxle component,
for torque system stator magnetic linkage,
ωfor rotor anglec of rotation frequency,
be the magnetic suspension force coefficient determined by electric machine structure, m is rotor quality,
,
be respectively the stator and rotor leakage inductance of torque system in dq coordinate system,
for the radial displacement stiffness coefficient that electric machine structure determines,
,
,
,
for torque wound stator resistance,
for torque wound rotor resistance,
for
dqthe self-induction of the equivalent two-phase torque winding in coordinate system,
for
dqequivalent two-phase rotor windings self-inductance in coordinate system,
for the magnetic pole logarithm of torque winding,
jfor moment of inertia,
for load torque;
The dynamic mathematical models of described stator magnetic linkage oriented inverse system are:
，
In formula, the input variable of getting inverse system is
.
Preferably, the stator magnetic linkage oriented reversed decoupling method of the dynamic induction-type bearingless motor of aforementioned consideration electric current, the Mathematical Modeling of wherein said stator magnetic linkage oriented original system obtains by the following method:
(1) define that α β is static two-phase symmetrical coordinates system, dq is torque system stator magnetic linkage oriented synchronous rotary two-phase symmetrical coordinates systems,
(2) according to the static and dynamic Status constraints of motor internal stator current dynamic differential equation and Stator flux oriented control, can consider that the dynamic stator magnetic linkage oriented torque system dynamic mathematical models of stator current are:
，
(3) according to the operation principle of induction-type bearingless motor, the controllable radial electromagnetic force model of two pole magnetic suspension systems is obtained:
，
,
be respectively static α, β reference axis to controllable radial suspending power component,
,
be respectively edge
d,
qreference axis to air gap flux linkage component, its expression formula is:
，
(4) according to principle of dynamics, structure rotor radial suspended motion equation is:
，
In formula,
mfor the quality of rotor,
,
produce at motor internal when being respectively rotor generation radial disbalance
α, βto the monolateral electromagnet pull of unbalanced rotor,
,
,
it is the radial displacement stiffness coefficient determined by electric machine structure and motor-field intensity;
(5) choosing four pole torque winding voltages is input variable, and input variable u, state variable x, the output variable y of definition original system are respectively:
，
，
，
The formula of integrating step (2) to (4) can draw the dynamic mathematical models taking into account the stator magnetic linkage oriented original system of induction-type bearingless motor considering the impact of unbalanced rotor monolateral electromagnet pull and torque system stator current dynamic characteristic:
。
Preferably, the stator magnetic linkage oriented reversed decoupling method of the dynamic induction-type bearingless motor of aforementioned consideration electric current, the Mathematical Modeling of wherein said stator magnetic linkage oriented inverse system obtains by the following method:
Known by Interactor Algorithm Analysis, described stator magnetic linkage oriented original system is reversible, to output variable
successively to time differentiate, obtain:
，
Getting inverse system input variable is
, then consider that the dynamic mathematical models of the stator magnetic linkage oriented inverse system of induction-type bearingless motor of stator current dynamic characteristic are:
。
Compared with prior art, the present invention at least has following advantages and beneficial effect:
1, the present invention is on the basis considering stator current dynamic effects, propose the stator magnetic linkage oriented Inverse Decoupling method of induction-type bearingless motor, control to replace traditional rotor flux linkage orientation Inverse Decoupling with stator magnetic linkage oriented Inverse Decoupling, rotor parameter effectively can be avoided the impact of motor magnetic linkage control performance, improve rotor magnetic suspension control performance;
2, the present invention is α and β two radial displacement subsystems, stator magnetic linkage subsystem and motor speed subsystem four linear subsystems having non-linear, multivariable, strong coupling induction-type bearingless motor system decoupling, for structure reversed decoupling closed-loop system provides the foundation with the reliable uneoupled control realized between two radial displacement components, stator magnetic linkage, motor speed, method of the present invention eliminates the torque wound stator current closed-loop in stator magnetic linkage oriented original system and the load torque in inverse system
t lidentification link, system configuration is simplified, and improves the dynamic antijamming capability of system.
Accompanying drawing explanation
Fig. 1 is that the present invention considers the dynamic induction-type bearingless motor of electric current stator magnetic linkage oriented reversed decoupling Method And Principle figure.
Embodiment
For making content of the present invention become apparent, below in conjunction with specific embodiment, describe the present invention.
Core concept of the present invention is:
1) induction-type bearingless motor is the complex object of a multivariable, non-linear, close coupling, wherein there is complicated nonlinear electromagnetic coupled relation; And inverse system method is applicable to effective dynamic decoupling method of multivariable, Complex Nonlinear System just.
2) stator magnetic linkage of induction-type bearingless motor torque system, can calculate in real time according to its stator voltage, electric current and stator resistance parameters etc., and not by the impact of variable rotor resistance parameter.Therefore, adopt Stator flux oriented control, rotor parameter effectively can be avoided the impact of motor flux linkage calculation precision, thus avoid rotor parameter on the impact of Electric Machine Control performance.
3) when setting up system mathematic model, choosing stator voltage is torque original system input control amount, its stator current dynamic differential equation can be considered into induction-type bearingless motor original system and inverse system dynamic mathematical models, thus the original cross-couplings of d, q between centers of torque original system obtains decoupling zero naturally by method of inverse, the stator current closed-loop control link in former Field Oriented Control System can be dispensed, system configuration is simplified.
4) considering that stator current dynamic characteristic is on the basis of torque system Stator flux oriented control, no longer containing the load variation being difficult to predict in the induction-type bearingless motor entire system inverse system model derived, load torque on-line identification link when inverse system realizes can be dispensed, further simplied system structure.
5) by Inverse Decoupling, can be four linear subsystems such as rotating speed, magnetic linkage, two radial displacement components non-linear, close coupling, multivariable induction-type bearingless motor system dynamic decoupling.If be the closed-loop adjustment controller that each subsystem configures is suitable more on this basis, the high-performance that can realize self-bearings motors runs control.
Based on above-mentioned theory basis, the dynamic induction-type bearingless motor of the consideration electric current stator magnetic linkage oriented reversed decoupling method of the present invention's design comprises: consider the stator magnetic linkage oriented original system of the dynamic induction-type bearingless motor of stator current (hereinafter referred to as original system), consider the stator magnetic linkage oriented inverse system of the dynamic induction-type bearingless motor of stator current (hereinafter referred to as inverse system); Before described inverse system is serially connected in original system, the induction-type bearingless motor system making inverse system and original system composition is four linear subsystem: α and β, two second order radial displacement linear subsystems, a single order stator magnetic linkage by dynamic decoupling
ψ s1linear subsystem, a second order rotating speed
ωlinear subsystem, not containing the load torque variable being difficult to predict in this inverse system model. and the present invention specifically comprises the steps:
step one,set up and consider the dynamic stator magnetic linkage oriented bearing-free motor system mathematic model of stator current
(1) define that α β is static two-phase symmetrical coordinates system, dq is torque system stator magnetic linkage oriented synchronous rotary two-phase symmetrical coordinates systems.Ignore the impact of two pole suspension magnetics on four pole torque field, consider motor internal stator current dynamic differential equation, in conjunction with the static and dynamic Status constraints of Stator flux oriented control, can obtain considering that the dynamic stator magnetic linkage oriented torque system dynamic mathematical models of stator current are:
(1)
The synchronous angular velocity of motor can be expressed as:
(2)
In formula (1), (2),
,
for torque wound stator electric current
d,
qaxle component,
for torque system stator magnetic linkage,
ωfor rotor anglec of rotation frequency,
synchro angle frequency,
for
dqthe magnetizing inductance of equivalent two-phase torque winding in coordinate system,
for
dqthe self-induction of the equivalent two-phase torque winding in coordinate system,
;
for
dqequivalent two-phase rotor windings self-inductance in coordinate system,
,
,
be respectively torque system to exist
dqstator and rotor leakage inductance in coordinate system,
for torque wound stator resistance,
for torque wound rotor resistance,
for load torque,
for the magnetic pole logarithm of torque winding,
jfor moment of inertia, parameter
,
,
.
(2) in suspend control Current Decoupling computational process, the air gap flux linkage information of torque system be used.Along d, q reference axis to two air gap flux linkage components obtain by the relation real-time identification between torque system air gap flux linkage and stator magnetic linkage:
，
(3)
Meanwhile, ignore the Mutual Inductance Coupling impact between double winding that rotor eccentricity causes, according to the operation principle of induction-type bearingless motor, the controllable radial electromagnetic force model of two pole magnetic suspension systems can be derived:
(4)
In formula,
,
be respectively edge
d,
qreference axis to air gap flux linkage component;
,
be respectively edge
d,
qthe suspending windings stator current components of axial coordinate axis;
be the magnetic suspension force coefficient determined by electric machine structure, its expression formula is:
(5)
In formula,
for air-gap permeance,
,
be respectively stator core length and stator inside radius;
for the single-phase magnetizing inductance of three-phase symmetrical suspending windings;
,
being respectively the whole square of three-phase and quadrupole concentrates the extremely whole square of torque winding, three-phase two to concentrate every effective turns-in-series mutually of suspending windings.
(3) according to principle of dynamics, can obtain rotor radial suspended motion equation is:
(6)
In formula,
mfor the quality of rotor;
,
for the monolateral electromagnet pull component of imbalance, its numerical value changes with rotor displacement amount, and its calculation expression is:
、
，
Wherein,
it is the radial displacement stiffness coefficient determined by electric machine structure and motor-field intensity.
It should be noted that, formula of the present invention and letter more, be outstanding emphasis of the present invention, the alphabetical implication not lexical or textual analysis one by one of formula of the present invention, the letter of non-lexical or textual analysis all has fixing meaning of parameters, is that those skilled in the art know.
step 2,set up the state space dynamic mathematical models considering the stator magnetic linkage oriented original system of the dynamic induction-type bearingless motor of stator current
(1) input variable choosing original system four pole torque system is:
，
State variable is:
,
Output variable is:
,
(2) combine (1) formula and (4) formula, and consider the impact that the monolateral electromagnet pull component of unbalanced rotor changes with radial displacement, arrange and obtain considering the stator magnetic linkage oriented original system state space equation of the dynamic induction-type bearingless motor of stator current:
(7)
step 3,set up the state space dynamic mathematical models considering the stator magnetic linkage oriented inverse system of the dynamic induction-type bearingless motor of stator current
(1) be reversible by system described in Interactor Algorithm Analysis (7) formula
To output variable
successively to time differentiate, until aobvious containing input variable in output variable order derivative, differentiate result is:
(8)
(9)
(10)
(11)
Order:
(12)
According to (8) ~ (12) formula, the Jacobi matrix of induction-type bearingless motor system can be obtained:
(13)
In formula,
be four pole torque systems
daxle rotor flux.In normal operation, along stator magnetic linkage oriented
dthe torque system air gap flux linkage component of change in coordinate axis direction
, rotor flux component
all be not equal to zero, therefore have
.Therefore, Jacobi matrix is full rank.The Relative order of system is
, and have:
.According to inverse system theorem, the original system described by (7) formula is reversible.
(2) the state space dynamic mathematical models of inverse system are set up
Getting inverse system input variable is
, and substitute into (8) ~ (11) formula, arrangement can consider the stator magnetic linkage oriented inverse system state space equation of the dynamic induction-type bearingless motor of stator current:
(14)
The feature of the inverse system dynamic model that formula (14) provides is: wherein no longer containing the load torque variable being difficult to predict
, thus provide convenience for simplifying induction-type bearingless motor decoupling and controlling system structure.
step 4,by method of inverse, dynamic decoupling is carried out to the dynamic stator magnetic linkage oriented induction-type bearingless motor system of consideration stator current
As shown in Figure 1, be consider the dynamic induction-type bearingless motor of electric current stator magnetic linkage oriented reversed decoupling Method And Principle figure.By connected mode shown in Fig. 1, before the inverse system constructed based on (14) formula is serially connected in the original system described in (7) formula, having multivariable, the induction-type bearingless motor decoupling zero of non-linear, strong coupling is four linear subsystem: α and β, two radial displacement second-order linearity integration subsystems, stator magnetic linkage first-order linear integration subsystem, a rotating speed second-order linearity integration subsystem.Need be only the appropriate closed-loop regulator of each subsystem configures according to linear system control theory, just can realize induction-type bearingless motor α and β two radial displacements, dynamic Decoupling Control of Load Torque between stator magnetic linkage and rotating speed.
Consider in the stator magnetic linkage oriented reversed decoupling method of the dynamic induction-type bearingless motor of electric current, consider that the input variable of the stator magnetic linkage oriented inverse system of the dynamic induction-type bearingless motor of stator current is respectively the second dervative of radial displacement α and β
with
, stator magnetic linkage first derivative
, rotating speed second dervative
, the output variable of inverse system, as the control inputs amount of original system, is respectively the d axle component of suspending windings stator current
with q axle component
, torque winding d shaft voltage component
with q shaft voltage component
.
The present invention is on the basis considering the impact of stator current dynamic characteristic, traditional rotor flux linkage orientation Inverse Decoupling is replaced with stator magnetic linkage oriented Inverse Decoupling, rotor parameter effectively can be avoided the impact of motor magnetic linkage control performance, the stator current closed loop in original system and the Load Torque Identification link in inverse system can be saved.
Except describing above, the present invention can also be widely used in other embodiments, and protection scope of the present invention is not by the restriction of embodiment, and it is as the criterion with the protection range of claim.Any those skilled in the art, according to the simple modification of technical spirit of the present invention to above embodiment, still belong to the protection range of technical solution of the present invention.
Claims (3)
1. consider the stator magnetic linkage oriented reversed decoupling method of the dynamic induction-type bearingless motor of electric current for one kind, it is characterized in that, this reversed decoupling method be stator magnetic linkage oriented inverse system is serially connected in stator magnetic linkage oriented original system before, make induction-type bearingless motor system dynamic decoupling be second-order linearity subsystem, a stator magnetic linkage of four linear subsystem: α and β, two radial displacements
first-order linear subsystem, a rotating speed
ωsecond-order linearity subsystem, the output variable of stator magnetic linkage oriented original system comprises radial displacement α and β, stator magnetic linkage
, and rotating speed
ω, the second dervative of radial displacement α and β
with
, stator magnetic linkage first derivative
, and the second dervative of rotating speed
as the input variable of stator magnetic linkage oriented inverse system, the output variable of stator magnetic linkage oriented inverse system, as the input variable of stator magnetic linkage oriented original system, is respectively the d shaft current component of suspending windings
with q shaft current component
, torque winding d shaft voltage component
with q shaft voltage component
, wherein,
The dynamic mathematical models of described stator magnetic linkage oriented original system are:
，
In formula, the input variable of definition original system is
, system state variables is
, system output variables is
,
,
be respectively torque wound stator electric current
d,
qaxle component,
,
be respectively suspending windings stator current
d,
qaxle component,
for torque system stator magnetic linkage,
ωfor rotor anglec of rotation frequency,
be the magnetic suspension force coefficient determined by electric machine structure, m is rotor quality,
,
be respectively the stator and rotor leakage inductance of torque system in dq coordinate system,
for the radial displacement stiffness coefficient that electric machine structure determines,
,
,
,
for torque wound stator resistance,
for torque wound rotor resistance,
for
dqthe self-induction of the equivalent two-phase torque winding in coordinate system,
for
dqequivalent two-phase rotor windings self-inductance in coordinate system,
for the magnetic pole logarithm of torque winding,
jfor moment of inertia,
for load torque;
The dynamic mathematical models of described stator magnetic linkage oriented inverse system are:
，
In formula, the input variable of getting inverse system is
.
2. consider the stator magnetic linkage oriented reversed decoupling method of the dynamic induction-type bearingless motor of electric current according to claim 1, it is characterized in that, the Mathematical Modeling of wherein said stator magnetic linkage oriented original system obtains by the following method:
(1) define that α β is static two-phase symmetrical coordinates system, dq is torque system stator magnetic linkage oriented synchronous rotary two-phase symmetrical coordinates systems,
(2) according to the static and dynamic Status constraints of motor internal stator current dynamic differential equation and Stator flux oriented control, can consider that the dynamic stator magnetic linkage oriented torque system dynamic mathematical models of stator current are:
，
(3) according to the operation principle of induction-type bearingless motor, the controllable radial electromagnetic force model of two pole magnetic suspension systems is obtained:
，
,
be respectively static α, β reference axis to controllable radial suspending power component,
,
be respectively edge
d,
qreference axis to air gap flux linkage component, its expression formula is:
，
(4) according to principle of dynamics, structure rotor radial suspended motion equation is:
，
In formula,
mfor the quality of rotor,
,
produce at motor internal when being respectively rotor generation radial disbalance
α, βto the monolateral electromagnet pull of unbalanced rotor,
,
,
it is the radial displacement stiffness coefficient determined by electric machine structure and motor-field intensity;
(5) choosing four pole torque winding voltages is input variable, and input variable u, state variable x, the output variable y of definition original system are respectively:
，
，
，
The formula of integrating step (2) to (4) can draw the dynamic mathematical models taking into account the stator magnetic linkage oriented original system of induction-type bearingless motor considering the impact of unbalanced rotor monolateral electromagnet pull and torque system stator current dynamic characteristic:
。
3. consider the stator magnetic linkage oriented reversed decoupling method of the dynamic induction-type bearingless motor of electric current according to claim 1, it is characterized in that, the Mathematical Modeling of wherein said stator magnetic linkage oriented inverse system obtains by the following method:
Known by Interactor Algorithm Analysis, described stator magnetic linkage oriented original system is reversible, to output variable
successively to time differentiate, obtain:
，
Getting inverse system input variable is
, then consider that the dynamic mathematical models of the stator magnetic linkage oriented inverse system of induction-type bearingless motor of stator current dynamic characteristic are:
。
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Cited By (4)
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Application publication date: 20151118 |