CN105301964B - Modal decoupling decentralized control method for magnetic bearing - Google Patents
Modal decoupling decentralized control method for magnetic bearing Download PDFInfo
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Abstract
The invention provides a modal decoupling decentralized control method for a magnetic bearing, which comprises the following steps: step 1, decoupling a gyro coupling term of a magnetic bearing; step 2, respectively carrying out reverse diagonal term compensation on a differential link, a proportional link and an integral link; and 3, respectively compensating positive angle terms introduced by the differential coupling compensation controller, the proportional coupling compensation controller and the integral coupling compensation controller. Compared with the traditional PID control method, cross feedback control and Linear Quadratic (LQR), the modal decoupling decentralized control method is not influenced by the rotating speed of the magnetic bearing rotor and has good decoupling effect on the gyroscopic effect existing in the system.
Description
Technical field
It is used for the scattered control of magnetic bearings control method, especially a kind of Modes Decoupling for magnetic bearing the present invention relates to one kind
Method processed.
Background technology
Limitation and the demand of practical application due to manufacturing process, generally dimensionally magnetic bearing system on rotor matter
The heart is asymmetric.If it is symmetrical on rotor centroid in physical dimension to design magnetic axis bearing rotor system, this is on stricti jurise
System can not be referred to as parameter balanced system.The same symmetry for including bearing rigidity of symmetric parameter system condition is met, due to
The relating to parameters such as system stiffness and air-gap permeance, umber of turn, equalization point gas length, and by thermal expansion, equalization point
The uncertain influence waited of gas length, therefore, accomplish magnetic bearing rigidity on four-degree-of-freedom it is always consistent be extremely difficult
's.So, magnetic bearing is usually asymmetry parameter system in actual application system.
Analyzed from cross-feedback control, for the symmetrical magnetic bearing system of parameter, application speed cross feedback can
Make system full decoupled so that the zero pole point of system does not change with the change of rotating speed.But for the system of parameter unbalance,
Because the determination to interaction coefficent does not have preferable scheme, the need for the gain of cross aisle can not meet decoupling, therefore, tradition
Scattered cross-feedback control can not carry out effective suppression to the coupling of gyro present in parameter unbalance system.Using LQR
The centralized Control methods such as control preferably can be controlled to parameter unbalance system, but the LQR in the case where changing rotating speed
The drawbacks of control shows it, i.e. the determination problem of Q parameters.
The content of the invention
The technical problem to be solved in the present invention is that the scattered cross-feedback control of existing magnetic bearing can not be to parameter unbalance
The coupling of gyro present in system is effectively suppressed.
In order to solve the above-mentioned technical problem, the invention provides a kind of Modes Decoupling decentralised control side for magnetic bearing
Method, is provided with differentiation element, proportional component and integral element in the PID controller of magnetic bearing, for respectively to magnetic bearing
Four frees degree carry out decentralised control, and Modes Decoupling decentralized control method comprises the following steps：
Step 1, the gyro coupling terms to magnetic bearing are decoupled, and are concretely comprised the following steps：
Step 1.1, a derivative controller being in parallel with differentiation element is designed, for eliminating in differentiation element by difference
The coupled interference that the intrinsic differential gain is brought；
Step 1.2, a speed cross-feedback control device is designed, corresponds to magnetic for being drawn in the rear end of derivative controller
The four-legs intersection passage of bearing four-degree-of-freedom control, is decoupled with the gyro coupling terms for realizing magnetic bearing；
Step 1.3, a displacement cross-feedback control device is designed, for what is introduced in release rate cross-feedback control device
Ratio coupling terms；
Step 2, differentiation element, proportional component and integral element are carried out respectively opposing that angle is compensated, concretely comprised the following steps：
Step 2.1, a differential coupling compensating controller is designed, for opposing to the differential coupling included in differentiation element
Angle is eliminated；
Step 2.2, a ratio compensating for coupling controller is designed, for differentiation element, proportional component and integral element
The ratio coupling of introducing opposes that angle is eliminated；
Step 2.3, an integration compensating for coupling controller is designed, angle is opposed in the integration coupling for being introduced to integral element
Item is eliminated；
Step 3, respectively to differential coupling compensating controller, ratio compensating for coupling controller and integration compensating for coupling controller
The just diagonal item introduced is compensated, and is concretely comprised the following steps：
Step 3.1, one is designed just to angle compensation differentiation element, the just diagonal item introduced to differential coupling compensating controller
Compensate；
Step 3.2, a just diagonal compensating proportion link, the just diagonal item that comparative example compensating for coupling controller is introduced are designed
Compensate；
Step 3.3, one is designed just to angle compensation integral element, the just diagonal item introduced to integration compensating for coupling controller
Compensate.
Drawn using speed cross-feedback control device in the rear end of derivative controller and correspond to the control of magnetic bearing four-degree-of-freedom
Four-legs intersection passage, with realize the gyro coupling terms in parameter unbalance system decouple, be easy to suppress rotor gyro effect
System mode coupling is compensated while answering, realizes and the mode amount of magnetic bearing rotor is controlled, the steady of system is improved
It is qualitative；The ratio coupling terms that can be introduced using displacement cross-feedback control device in release rate cross-feedback control device；Using
Differential coupling compensating controller, ratio compensating for coupling controller and integration compensating for coupling controller are opposed to differential coupling respectively
Angle, ratio coupling oppose that angle and integration coupling oppose that angle is eliminated, and differential coupling opposes angle, ratio coupling
Oppose that angle and integration coupling oppose that angle is not influenceed by magnetic bearing rotor speed so that decoupling function effect is good；Using just
To angle compensation differentiation element, just diagonal compensating proportion link and just to angle compensation integral element to differential coupling compensate control
The just diagonal item that device, ratio compensating for coupling controller and integration compensating for coupling controller are introduced is compensated, so as to eliminate pair
The just diagonal item introduced when oppose angle compensation, because the just diagonal item added can change ratio, integration and differential ginseng
Number, so as to change system design rigidity and damping, even results in system unstability.
As the further limits scheme of the present invention, in step 1.1, the transmission function of derivative controller is：
In formula, βnFor differential coefficient, s is pull-type operator, TfβnFor inertial element coefficient, TfβnParameter values it is smaller, neglect
Slightly disregard, n represents the differentiator on different magnetic bearings, and x is corresponded respectively to from 1 to 4l、xr、yl、yrDirection magnetic bearing.
It is used as the further limits scheme of the present invention, in step 1.2, the transfer function matrix of speed cross-feedback control device
For：
In formula, τ1、τ2、τ3And τ4It is intrinsic differential coefficient,WithFor speed cross-feedback control device
Carry out the speed cross aisle coefficient that the decoupling of gyro coupling terms is obtained.
It is used as the further limits scheme of the present invention, in step 1.3, the transfer function matrix of displacement cross-feedback control device
For：
In formula,WithAcquisition is eliminated to carry out ratio coupling terms to speed cross-feedback control device
Displacement cross aisle coefficient.
It is used as the further limits scheme of the present invention, in step 2.1, the transfer function matrix of differential coupling compensating controller
For：
In formula, kcA、kcB、kcCAnd kcDFor differential uneoupled control channel parameters.
It is used as the further limits scheme of the present invention, in step 2.2, the transfer function matrix of ratio compensating for coupling controller
For：
In formula, kcsA、kcsB、kcsC、kcsDFor ratio uneoupled control channel parameters.
As the further limits scheme of the present invention, in step 2.3, the transfer function matrix of compensating for coupling controller is integrated
For：
In formula, kciA、kciB、kciC、kciDFor integration decoupling control passage parameter, Ti1、Ti2、Ti3And Ti4It is intrinsic for integrator
Integral coefficient.
It is used as the further limits scheme of the present invention, in step 3.1, the transfer function matrix just to angle compensation differentiation element
For：
In formula, cv1To cv8It is the gain of the extraction channel after the differentiation element of PID controller, cv9To cv16For differential control
The gain of extraction channel after device.
It is used as the further limits scheme of the present invention, in step 3.2, the transfer function matrix of just diagonal compensating proportion link
For：
In formula, Cs1、Cs2、Cs3、Cs4、Cs5、Cs6、Cs7And Cs8For the increasing of ratio compensating for coupling controller front end extraction channel
Benefit.
It is used as the further limits scheme of the present invention, in step 3.3, the transfer function matrix just to angle compensation integral element
For：
In formula, Ci1、Ci2、Ci3、Ci4、Ci5、Ci6、Ci7And Ci8For the increasing of integration compensating for coupling controller rear end extraction channel
Benefit.
The beneficial effects of the present invention are：(1) drawn using speed cross-feedback control device in the rear end of derivative controller
The four-legs intersection passage controlled corresponding to magnetic bearing four-degree-of-freedom, to realize the gyro coupling terms solution in parameter unbalance system
Coupling, is easy to compensate system mode coupling while rotor gyro effect is suppressed, realizes the mode to magnetic bearing rotor
Amount is controlled, and improves the stability of system；(2) being capable of release rate cross-feedback control using displacement cross-feedback control device
The ratio coupling terms introduced in device；(3) using differential coupling compensating controller, ratio compensating for coupling controller and integration coupling
Compensating controller opposes that angle, ratio coupling oppose that angle and integration coupling oppose that angle disappears to differential coupling respectively
Remove, and differential coupling opposes that angle, ratio coupling oppose that angle and integration coupling oppose angle not by magnetic bearing rotor speed
Influence so that decoupling function effect is good；(4) using just to angle compensation differentiation element, just diagonal compensating proportion link and just right
Angle compensation integral element is drawn to differential coupling compensating controller, ratio compensating for coupling controller and integration compensating for coupling controller
The just diagonal item entered is compensated, so that the just diagonal item to being introduced when oppose angle compensation is eliminated, because add
Just diagonal item can change ratio, integration and differential parameter, so as to change system design rigidity and damping, even result in system mistake
Surely.
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is asymmetry parameter system decoupling control figure of the invention；
Fig. 3 is magnetic bearing Model control zero pole plot of the invention.
Embodiment
For the ease of the understanding of the Modes Decoupling decentralized control method provided by the present invention for magnetic bearing, basis first turns
Subdynamical theory can obtain magnetic bearing system mathematical modeling：
In formula, m is magnetic bearing rotor quality, JxAnd JyFor equator moment of inertia, JzFor polar moment of inertia, a and b are left and right
Two ends magnetic bearing is to the distance of barycenter, and ω is the rotating speed of rotor, vectorial qc=[x y- θxθy]TSat for the barycenter of magnetic bearing system
Mark, vectorial i=[ilx irx ily iry]TFor control electric current, current stiffness coefficient matrix KiWith displacement rigidity coefficient matrix KsRespectively
For：
Ki=diag (kiLx,kiRx,kiLy,kiRy)
Ks=diag (ksLx,ksRx,ksLy,ksRy)
In magnetic bearing system mathematical modeling as described by formula (1-1), four frees degree the control method of magnetic bearing according to
PID control so is used, because can be according to the design rigidity of system with damping regulation controller parameter；If operating speed intersects anti-
Feedback control, then need to draw cross aisle in the rear end of differentiation element；And for actual control system, particularly by mould
Intend the controller of circuit composition, it is impossible to accomplish the control of complete differential, there may be in differentiation element intrinsic non-adjustable
Gain, differential coefficient, inertial element of section etc.；For different controllers, the intrinsic differential coefficient of differentiation element is also differed；
Equally, the integral coefficient of integral element is also possible to unequal.
The transmission function for making the differentiation element of PID controller in four frees degree is：
In formula, s is pull-type operator, and proportion differential link and inertial element, τ are included in differentiation elementnFor intrinsic differential system
Number, TfnFor inertial element coefficient, n represents the differentiator on different magnetic bearings, x is corresponded respectively to from 1 to 4l、xr、yl、yrSide
To magnetic bearing；Inertial element coefficient T in differentiatorfnSmaller, the influence to control effect is also smaller, can ignore；Therefore, it is micro-
Point link can be considered the proportion differential link in formula (1-2).
The transmission function of integral element in PID controller is：
In formula, TinFor the intrinsic integral coefficient of integrator.
The transmission function of proportional component in PID controller is：
kPn, n=1 ... 4
The transfer function matrix of PID controller is：
Gt(s)=Pt(s)+Dt(s)+It(s) (1-4)
Pt(s)=diag (kP1,kP2,kP3,kP4) (1-5)
Dt(s)=diag (kD1×(τ1s+1),kD2×(τ2s+1),kD3×(τ3s+1),kD4×(τ4s+1)) (1-6)
System transter matrix equation can be released to formula (1-7) by formula (1-1) and formula (1-4), is shown below：
From formula (1-4), the transfer function matrix G of PID controllert(s) as the P shown in formula (1-5) to formula (1-7)t
(s)、Dt(s)、It(s) constitute, the G substituted into formula (1-8)t(s) item, the product that obtained each matrix is calculated respectively is as follows
Shown in formula：
Stiffness coefficient matrix K is carried in systemsPartial matrix product is shown below：
From formula (1-9) to formula (1-12), the opposition angle in each matrix in the case that parameter is symmetry equivalent is zero,
It is not introduced into the coupling amount unrelated with rotating speed.Systematic parameter can introduce anti-diagonal matrix when asymmetric in the sytem matrix differential equation,
The coupling for causing each state variable to be offset on parameter.Meanwhile, equally deposited in the gyro matrix G on the left of formula (1-8)
In nondiagonal term, gyro is caused to couple.Coupling in system transter matrix equation (1-8), gyro matrix G
Item is related to rotating speed, and other non-diagonal coupling terms present in system are unrelated with rotating speed.This explanation gyro, which is coupled, is probably
Cause the main cause of system unstability, but actually this saying is not exclusively accurate.Physically accurately explain it is unstability
The Mode variation as caused by gyroscopic effect, misaligned characteristic, system feedback gain and phase angle are jointly caused.Therefore, Modal Solution
The design of coupling controller can consider the compensation pair the diagonal coupling terms of the anon-normal unrelated with rotating speed emphatically.
As illustrated in fig. 1 and 2, provided by the present invention for the Modes Decoupling decentralized control method of magnetic bearing, including following step
Suddenly：
Step 1, the gyro coupling terms to magnetic bearing are decoupled, and are concretely comprised the following steps：
Step 1.1, a derivative controller being in parallel with differentiation element is designed, for eliminating in differentiation element by difference
The coupled interference that the intrinsic differential gain is brought, it is contemplated that the intrinsic differential gain is different in differentiation element, the differential control of setting
Device is in parallel with controller differentiation element, eliminates the coupling influence that the intrinsic differential gain of the difference in differentiation element is brought, it is passed
Delivery function is shown below：
In formula, βnFor differential coefficient, s is pull-type operator, TfβnFor inertial element coefficient, TfβnParameter values it is smaller, neglect
Slightly disregard, n represents the differentiator on different magnetic bearings, and x is corresponded respectively to from 1 to 4l、xr、yl、yrDirection magnetic bearing.
Step 1.2, a speed cross-feedback control device is designed, corresponds to magnetic for being drawn in the rear end of derivative controller
The four-legs intersection passage of bearing four-degree-of-freedom control, is decoupled with the gyro coupling terms for realizing magnetic bearing, with traditional cross feedback
Control design case method is different, four cross aisle coefficients is separately designed in the present system, to meet during parameter unbalance to gyro
The requirement of decoupling, the transfer function matrix of speed cross-feedback control device is：
In formula, τ1、τ2、τ3And τ4It is intrinsic differential coefficient,WithFor speed cross-feedback control device
Carry out the speed cross aisle coefficient that the decoupling of gyro coupling terms is obtained；
If derivative controller meets following parameters relationship：
Then derive that each speed cross aisle coefficient is shown below：
Step 1.3, a displacement cross-feedback control device is designed, for what is introduced in release rate cross-feedback control device
, there is proportional in ratio coupling terms, usable displacement cross-feedback control device is eliminated to it in formula (1-14), and displacement intersects anti-
Feedback controller transfer function matrix be：
In formula,WithAcquisition is eliminated to carry out ratio coupling terms to speed cross-feedback control device
Displacement cross aisle coefficient, everybody transfer fork channel factor value be shown below：
Step 2, differentiation element, proportional component and integral element are carried out respectively opposing that angle is compensated, concretely comprised the following steps：
Step 2.1, a differential coupling compensating controller is designed, for opposing to the differential coupling included in differentiation element
Angle is eliminated, and the transfer function matrix of differential coupling compensating controller is：
In formula, kcA、kcB、kcCAnd kcDIt is anti-using the differential in the transfer function matrix for differential uneoupled control channel parameters
Diagonal item can oppose angle with the differential coupling in subtractive (1-10), and the corresponding parameter being derived by is shown below：
Step 2.2, a ratio compensating for coupling controller is designed, for differentiation element, proportional component and integral element
The ratio coupling of introducing opposes that angle is eliminated, and from formula (1-25), can be introduced during using differential coupling compensating controller
Proportional, can be with design proportion compensating for coupling controller in the proportional and formula (1-9), formula (1-10) and formula (1-12)
Ratio coupling opposes that angle is compensated, and the transfer function matrix of ratio compensating for coupling controller is：
In formula, kcsA、kcsB、kcsC、kcsDFor ratio uneoupled control channel parameters.The coupling of ratio present in cancellation system is anti-
Diagonal item, then be derived by corresponding parameter and be shown below：
X1'=X1-akiLxkD1+bkiRxkD2 (1-35)
X'2=X2-akiLykD3+bkiRykD4 (1-36)
X1=aksLx-bksRx-akiLxkP1+bkiRxkP2 (1-37)
X2=aksLy-bksRy-akiLykP3+bkiRykP4 (1-38)
Step 2.3, an integration compensating for coupling controller is designed, angle is opposed in the integration coupling for being introduced to integral element
Item is eliminated, and the transfer function matrix of integration compensating for coupling controller is：
In formula, kciA、kciB、kciC、kciDFor integration decoupling control passage parameter, Ti1、Ti2、Ti3And Ti4It is intrinsic for integrator
Angle is opposed in integral coefficient, the integration coupling shown in subtractive (1-11), each integration decoupling control passage ginseng being derived by
Number is shown below：
Step 3, respectively to differential coupling compensating controller, ratio compensating for coupling controller and integration compensating for coupling controller
The just diagonal item introduced is compensated, and can be introduced when with the compensating for coupling controller in step 2 to opposing that angle item is compensated
Just diagonal item, therefore, Modes Decoupling of the additional just diagonal item in this part to system is considered as when designing final controller
Whether have an impact, it is generally the case that the selection of magnetic bearing system PID controller parameter is the design rigidity and damping according to system
Determine, if adding the just diagonal term coefficient in the part in systems, ratio can be changed when converting to decentralized controller control passage
Example, integration, differential parameter, so as to change system design rigidity and damping, even result in system unstability, accordingly, it would be desirable to by upper
The just diagonal item that formula is produced is compensated, and is concretely comprised the following steps：
Step 3.1, one is designed just to angle compensation differentiation element, the just diagonal item introduced to differential coupling compensating controller
Compensate, due in differentiator include proportion differential link, it may be considered that using addition just to angle compensation differentiation element to by
The just diagonal item that differential coupling compensating controller shown in formula (1-25) is produced implements compensation, if the pass of the parameter in differentiation element
It is for τ1=β2、τ2=β1、τ3=β4、τ4=β3, then what is be derived by is just to the transfer function matrix of angle compensation differentiation element：
In formula, cv1To cv8It is the gain of the extraction channel after the differentiation element of PID controller, cv9To cv16For differential control
The gain of extraction channel after device.Relevant parameter is derived by be shown below：
Step 3.2, a just diagonal compensating proportion link, the just diagonal item that comparative example compensating for coupling controller is introduced are designed
Compensate, the just diagonal item that the ratio compensating for coupling controller shown in formula (1-30) is introduced is compensated, is derived by
The transfer function matrix of just diagonal compensating proportion link is：
In formula, Cs1、Cs2、Cs3、Cs4、Cs5、Cs6、Cs7And Cs8For the increasing of ratio compensating for coupling controller front end extraction channel
Benefit, the value for being derived by each parameter is shown below：
Step 3.3, one is designed just to angle compensation integral element, the just diagonal item introduced to integration compensating for coupling controller
Compensate, the just diagonal item that the integration compensating for coupling controller shown in formula (1-39) is introduced is compensated, is derived by just
It is to the transfer function matrix of angle compensation integral element：
In formula, Ci1、Ci2、Ci3、Ci4、Ci5、Ci6、Ci7And Ci8For the increasing of integration compensating for coupling controller rear end extraction channel
Benefit.The value for being derived by each parameter is shown below：
As shown in figure 3, for the Modes Decoupling cross-feedback control method designed using the present invention, magnetic bearing rotor speed exists
The zero pole plot of system during 0~1000Hz, changes from the figure 3, it may be seen that the change of rotor speed does not result in system zero pole point,
Modes Decoupling cross-feedback control has good decoupling function to gyroscopic effect present in system.Except in complex frequency domain coordinate
Exist at axle origin outside a pair of zero pole points, the limit of remaining in system is respectively positioned on the negative semiaxis of real axis, meet stable condition.
The beneficial effect of the present invention compared with prior art is：
1) to due to systematic parameter and the asymmetric caused modal coupling problem design uneoupled control of PID controller parameter
Structure, is coupled to system mode while rotor gyro effect is suppressed using the Modes Decoupling decentralized control method of design and carried out
Compensation, realizes and the mode amount of rotor is controlled, and improves the stability of system.
2) compared with traditional PID control method, cross-feedback control, Linear-Quadratic Problem (LQR), the method in the present invention is not
Influenceed by magnetic bearing rotor speed, there is good decoupling function to gyroscopic effect present in system.
Claims (10)
1. a kind of Modes Decoupling decentralized control method for magnetic bearing, differential ring is provided with the PID controller of magnetic bearing
Section, proportional component and integral element, carry out decentralised control, it is characterised in that mould for four frees degree respectively to magnetic bearing
State decoupled-decentralized control method comprises the following steps：
Step 1, the gyro coupling terms to magnetic bearing are decoupled, and are concretely comprised the following steps：
Step 1.1, a derivative controller being in parallel with differentiation element is designed, for eliminating in differentiation element by different intrinsic
The coupled interference that the differential gain is brought；
Step 1.2, a speed cross-feedback control device is designed, corresponds to magnetic bearing for being drawn in the rear end of derivative controller
The four-legs intersection passage of four-degree-of-freedom control, is decoupled with the gyro coupling terms for realizing magnetic bearing；
Step 1.3, a displacement cross-feedback control device is designed, for the ratio introduced in release rate cross-feedback control device
Coupling terms；
Step 2, differentiation element, proportional component and integral element are carried out respectively opposing that angle is compensated, concretely comprised the following steps：
Step 2.1, a differential coupling compensating controller is designed, for opposing angle to the differential coupling included in differentiation element
Eliminated；
Step 2.2, a ratio compensating for coupling controller is designed, for being introduced to differentiation element, proportional component and integral element
Ratio coupling oppose that angle is eliminated；
Step 2.3, an integration compensating for coupling controller is designed, the integration coupling for being introduced to integral element opposes that angle is entered
Row is eliminated；
Step 3, differential coupling compensating controller, ratio compensating for coupling controller and integration compensating for coupling controller are introduced respectively
Just diagonal item compensate, concretely comprise the following steps：
Step 3.1, one is designed just to angle compensation differentiation element, and the just diagonal item that differential coupling compensating controller is introduced is carried out
Compensation；
Step 3.2, a just diagonal compensating proportion link is designed, the just diagonal item that comparative example compensating for coupling controller is introduced is carried out
Compensation；
Step 3.3, one is designed just to angle compensation integral element, and the just diagonal item that integration compensating for coupling controller is introduced is carried out
Compensation.
2. the Modes Decoupling decentralized control method according to claim 1 for magnetic bearing, it is characterised in that：Step 1.1
In, the transmission function of derivative controller is：
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In formula, βnFor differential coefficient, s is pull-type operator, TfβnFor inertial element coefficient, TfβnParameter values it is smaller, ignore not
Meter, n represents the differentiator on different magnetic bearings, x is corresponded respectively to from 1 to 4l、xr、yl、yrDirection magnetic bearing.
3. the Modes Decoupling decentralized control method according to claim 1 for magnetic bearing, it is characterised in that：Step 1.2
In, the transfer function matrix of speed cross-feedback control device is：
In formula, τ1、τ2、τ3And τ4It is intrinsic differential coefficient,WithTop is carried out for speed cross-feedback control device
The speed cross aisle coefficient that the decoupling of spiral shell coupling terms is obtained.
4. the Modes Decoupling decentralized control method according to claim 1 for magnetic bearing, it is characterised in that：Step 1.3
In, the transfer function matrix of displacement cross-feedback control device is：
In formula,WithThe position obtained is eliminated to carry out ratio coupling terms to speed cross-feedback control device
Transfer fork channel factor.
5. the Modes Decoupling decentralized control method according to claim 1 for magnetic bearing, it is characterised in that：Step 2.1
In, the transfer function matrix of differential coupling compensating controller is：
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<mn>1</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mrow>
<mi>c</mi>
<mi>C</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>4</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mrow>
<mi>c</mi>
<mi>D</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>3</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>25</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, kcA、kcB、kcCAnd kcDFor differential uneoupled control channel parameters.
6. the Modes Decoupling decentralized control method according to claim 1 for magnetic bearing, it is characterised in that：Step 2.2
In, the transfer function matrix of ratio compensating for coupling controller is：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>k</mi>
<mrow>
<mi>c</mi>
<mi>s</mi>
<mi>A</mi>
</mrow>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>k</mi>
<mrow>
<mi>c</mi>
<mi>s</mi>
<mi>B</mi>
</mrow>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>k</mi>
<mrow>
<mi>cs</mi>
<mi>C</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>k</mi>
<mrow>
<mi>c</mi>
<mi>s</mi>
<mi>D</mi>
</mrow>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>30</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, kcsA、kcsB、kcsC、kcsDFor ratio uneoupled control channel parameters.
7. the Modes Decoupling decentralized control method according to claim 1 for magnetic bearing, it is characterised in that：Step 2.3
In, the transfer function matrix of integration compensating for coupling controller is：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mfrac>
<msub>
<mi>k</mi>
<mrow>
<mi>c</mi>
<mi>i</mi>
<mi>A</mi>
</mrow>
</msub>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mfrac>
<msub>
<mi>k</mi>
<mrow>
<mi>c</mi>
<mi>i</mi>
<mi>B</mi>
</mrow>
</msub>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mfrac>
<msub>
<mi>k</mi>
<mrow>
<mi>c</mi>
<mi>i</mi>
<mi>C</mi>
</mrow>
</msub>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mfrac>
<msub>
<mi>k</mi>
<mrow>
<mi>c</mi>
<mi>i</mi>
<mi>D</mi>
</mrow>
</msub>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>39</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, kciA、kciB、kciC、kciDFor integration decoupling control passage parameter, Ti1、Ti2、Ti3And Ti4Inherently integrated for integrator
Coefficient.
8. the Modes Decoupling decentralized control method according to claim 1 for magnetic bearing, it is characterised in that：Step 3.1
In, just it is to the transfer function matrix of angle compensation differentiation element：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>1</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>2</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>2</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>3</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>1</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>4</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>2</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>5</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>3</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>6</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>4</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>7</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>3</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>8</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>4</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>+</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>9</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>1</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>10</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>2</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>11</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>1</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>12</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>2</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>13</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>3</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>14</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>4</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>15</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>3</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>v</mi>
<mn>16</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>4</mn>
</msub>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>44</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, cv1To cv8It is the gain of the extraction channel after the differentiation element of PID controller, cv9To cv16After derivative controller
The gain of extraction channel.
9. the Modes Decoupling decentralized control method according to claim 1 for magnetic bearing, it is characterised in that：Step 3.2
In, the transfer function matrix of just diagonal compensating proportion link is：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>c</mi>
<mrow>
<mi>s</mi>
<mn>1</mn>
</mrow>
</msub>
</mtd>
<mtd>
<msub>
<mi>c</mi>
<mrow>
<mi>s</mi>
<mn>2</mn>
</mrow>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>c</mi>
<mrow>
<mi>s</mi>
<mn>3</mn>
</mrow>
</msub>
</mtd>
<mtd>
<msub>
<mi>c</mi>
<mrow>
<mi>s</mi>
<mn>4</mn>
</mrow>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>c</mi>
<mrow>
<mi>s</mi>
<mn>5</mn>
</mrow>
</msub>
</mtd>
<mtd>
<msub>
<mi>c</mi>
<mrow>
<mi>s</mi>
<mn>6</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>c</mi>
<mrow>
<mi>s</mi>
<mn>7</mn>
</mrow>
</msub>
</mtd>
<mtd>
<msub>
<mi>c</mi>
<mrow>
<mi>s</mi>
<mn>8</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>53</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, cs1、cs2、cs3、cs4、cs5、cs6、cs7And cs8For the gain of ratio compensating for coupling controller front end extraction channel.
10. the Modes Decoupling decentralized control method according to claim 1 for magnetic bearing, it is characterised in that：Step 3.3
In, just it is to the transfer function matrix of angle compensation integral element：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mn>5</mn>
</mrow>
</msub>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mn>6</mn>
</mrow>
</msub>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mn>7</mn>
</mrow>
</msub>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>3</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mn>8</mn>
</mrow>
</msub>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mn>4</mn>
</mrow>
</msub>
<mi>s</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>58</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, ci1、ci2、ci3、ci4、ci5、ci6、ci7And ci8For the gain of integration compensating for coupling controller rear end extraction channel.
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