CN110131312A - Five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller and building method - Google Patents
Five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller and building method Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
- F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
- F16C32/0406—Magnetic bearings
- F16C32/044—Active magnetic bearings
- F16C32/0444—Details of devices to control the actuation of the electromagnets
- F16C32/0451—Details of controllers, i.e. the units determining the power to be supplied, e.g. comparing elements, feedback arrangements with P.I.D. control
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
- F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
- F16C32/0406—Magnetic bearings
- F16C32/044—Active magnetic bearings
- F16C32/0474—Active magnetic bearings for rotary movement
- F16C32/0489—Active magnetic bearings for rotary movement with active support of five degrees of freedom, e.g. two radial magnetic bearings combined with an axial bearing
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2300/00—Application independent of particular apparatuses
- F16C2300/20—Application independent of particular apparatuses related to type of movement
- F16C2300/22—High-speed rotation
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2322/00—Apparatus used in shaping articles
- F16C2322/39—General buildup of machine tools, e.g. spindles, slides, actuators
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- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2326/00—Articles relating to transporting
- F16C2326/47—Cosmonautic vehicles, i.e. bearings adapted for use in outer-space
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- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2361/00—Apparatus or articles in engineering in general
- F16C2361/55—Flywheel systems
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Abstract
The present invention discloses a kind of five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller and building method, it is formed by being serially connected in the identical five adaptive automatic disturbance rejection controllers of internal structure before composite controlled object, single-degree-of-freedom controlled device is controlled respectively, each adaptive automatic disturbance rejection controller is by Nonlinear Tracking Differentiator, nonlinear state error Feedback Control Laws, adaptive extended state observer, BP neural network, first compensation factor and the second compensation factor composition, by the adaptive extended state observer for constructing system, it can compensate inside controlled device automatically, external disturbance, and adoption status error Feedback Control Laws realize the excellent control performance of system, key parameter is adjusted using the property of neural network Nonlinear Function Approximation, realize the online self-tuning of active disturbance rejection decoupling controller key parameter, it improves certainly The control performance of anti-interference decoupling controller.
Description
Technical field
The invention belongs to high speed and ultrahigh speed Electrified Transmission fields, are a kind of control of five-degree-of-freedom alternating active magnetic bearings
Device provides condition for efficient, the accurate bearing of high speed rotating shaft, is suitable for high-speed machine tool, flywheel energy storage, space flight and aviation and nuclear energy
Deng.
Background technique
Magnetic bearing by electromagnetic force by rotor suspension in aerial, make between stator and rotor there is no any Mechanical Contact,
Therefore have without friction, without wearing, being not necessarily to outstanding advantages of lubrication, service life length, high-precision and high speed, especially in high speed machine
In bed axis system, the supporting way of main shaft be largely fixed the attainable cutting speed of lathe institute, machining accuracy and
Magnetic bearing is applied in the support of high-speed machine tool main shaft by application range, is that the raising of high-speed machine tool spindle technology level is created
Advantage.
Five-degree-of-freedom alternating active magnetic axle system is a close coupling, nonlinear multi-input multi-output system, Yao Shixian
The high-speed, high precision stable operation of magnetic bearing needs to carry out Linearized Decoupling control to system.Common Linearized Decoupling control
Method has: approximate linearization method, differential geometry method, parsing inverse system method etc..Wherein approximate linearization method can only carry out system
Static decoupling, critical speed, system parameter change and the factors such as interference can reduce its control performance.Differential geometry method, which uses, to be compared
Abstract mathematical tool calculates complexity, is unfavorable for promoting and applying.Method of inverse is parsed to require specific system parameter and be controlled
The mathematical model of object it is known that but often extremely difficult analytic solutions for finding out inversion model in practical engineering applications, and be difficult to definitely retouch
State the nonlinear characteristic of system.
Currently, automatic disturbance rejection controller has the advantages that not depending on controlled device mathematical models is widely used in complexity
Control system in, such as Chinese Patent Application No. is 201310491326.4, a kind of entitled " the axial magnetic axis of flywheel energy storage
Hold the building method of automatic disturbance rejection controller " document in propose to control axial magnetic bearing using automatic disturbance rejection controller, but
It only controls axial magnetic bearing with automatic disturbance rejection controller, and automatic disturbance rejection controller does not have to the decoupling of magnetic bearing simultaneously
Can, and Self-tuning System only is carried out to a parameter of automatic disturbance rejection controller.
Summary of the invention
The purpose of the present invention is to overcome the shortcomings of existing five-degree-of-freedom alternating active magnet bearing systems decoupling control technology,
A kind of adaptive active disturbance rejection decoupling controller of five-degree-of-freedom alternating active magnetic bearings and its building method are provided, can both realize five from
By the decoupling control between the radial and axial five freedom degree offset variables of degree exchange active magnet bearing systems, and system can be made to obtain
Good dynamic and static performance is obtained, the control performance of whole system is effectively improved.
The present invention use five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller the technical solution adopted is that: by going here and there
The identical five adaptive automatic disturbance rejection controller compositions of the internal structure before composite controlled object are connect, control single-degree-of-freedom respectively
Controlled device, the input of the first adaptive automatic disturbance rejection controller therein are radial displacement xaWith the desired value x of radial displacementa *、
Output is control current expected value iax *, the input of the second adaptive automatic disturbance rejection controller is radial displacement yaWith radial displacement
Desired value ya*, output is control current expected value iay *, the input of the adaptive automatic disturbance rejection controller of third is radial displacement xbAnd diameter
To the desired value x of displacementb *, output for control current expected value ibx *, the input of the 4th adaptive automatic disturbance rejection controller is radial position
Move ybWith the desired value y of radial displacementb *, output be current expected value iby *, the input of the 5th adaptive automatic disturbance rejection controller is axis
To the desired value z of displacement z and axial displacement*, output for control current expected value iz *；Each adaptive automatic disturbance rejection controller by
Nonlinear Tracking Differentiator, nonlinear state error Feedback Control Laws, adaptive extended state observer, BP neural network, the first compensation
The factor and the second compensation factor composition, the input of five Nonlinear Tracking Differentiators is the desired value x of radial displacement respectivelya *、ya*、xb *、
yb *With the desired value z of axial displacement*, the output of first Nonlinear Tracking Differentiator therein is corresponding tracking signal x1Believe with differential
Number x2, the input of first adaptive extended state observer is the output displacement x of composite controlled objecta, three parameter betas01、β02
And β03, control amount u, output be x1、x2Estimated value z1、z2The estimated value z always disturbed3, first nonlinear state error be anti-
The input for presenting control law is error e1=x1-z1And e2=x2-z2, output be control amount u0, the input of first BP neural network
For error e1、e2, displacement xaIt is three parameter betas with bias 1, output01、β02And β03, the input of first the first compensation factor
For error u0-z3, output for single-degree-of-freedom controlled device electric current ia *, the input of first the second compensation factor is electric current
ia *, output is to the control amount u of adaptive extended state observer.
The technical solution that the building method of the five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller uses
It is to include the following steps:
Step A: constructing first Nonlinear Tracking Differentiator using following formula, obtains tracking signal x1With differential signal x2:
It is comprehensive for steepest
Close function, h0For integration step；r0For velocity factor；H is the sampling period；xa *It (k) is radial displacement xa *In the value at k moment；x1
It (k) is x1In the value at k moment；x1It (k+1) is x1In the value at k+1 moment；x2It (k) is x2In the value at k moment；x2It (k+1) is x2In k
The value at+1 moment.
Step B: constructing first adaptive extended state observer using following formula, obtains it and exports z1、z2And z3:
U (k) is that disturbance compensation forms control amount u (k)=(u0(k)-z3(k))/b0, u0It (k) is control amount u0At the k moment
Value；Fal is nonlinear function, expression formula:z1(k)、z2(k)、z3(k)
Respectively z1、z2、z3In the value at k moment, z1(k+1)、z2(k+1)、z3It (k+1) is respectively z1、z2、z3In the value at k+1 moment, xa
It (k) is xaIn the value at k moment, e is error, and h is sampling period, b0For the estimated value of the first compensation factor, b be the second compensation because
The value of son, b=1/b0；α1Take 0.5, α2Take 0.25, δ1> 0 is 5~10 times of sampling period.
Step C: formula u is used0=β1fal(e1,α3,δ2)+β2fal(e2,α4,δ2) first nonlinear state error of construction
Feedback Control Laws obtain control amount u0；Fal is nonlinear function, error e1=x1-z1, e2=x2-z2, α3Take 0.5, α4It takes
0.25, δ2> 0 takes 5~10 times of sampling period；
Step D: three parameter betas are adjusted using first BP nerve net01、β02And β03。
The present invention has the advantages that
1, before the adaptive active disturbance rejection decoupling controller in the present invention is series at composite controlled object, thus having strong coupling
Conjunction, the five-degree-of-freedom alternating active magnet bearing systems decoupling of nonlinear characteristic are no coupled linear system, pass through construction system
Adaptive extended state observer can compensate automatically inside controlled device, external disturbance, and adoption status error feedback control
Restrain the excellent control performance of realization system.
2, the parameter of the adjusting as needed for standard automatic disturbance rejection controller is more, there is also influencing each other between some parameters,
Therefore parameter tuning is very difficult.And the disturbance that five-degree-of-freedom alternating active magnetic bearings are subject to is often unfixed, therefore
The parameter of a set of fixation is difficult to meet the control requirement of system, and active disturbance rejection decoupling controller proposed by the present invention utilizes nerve net
The property of network Nonlinear Function Approximation adjusts key parameter, realizes the online of active disturbance rejection decoupling controller key parameter
Self-tuning System improves the control performance of active disturbance rejection decoupling controller.
Detailed description of the invention
Fig. 1 is five-degree-of-freedom alternating active magnetic bearings structural schematic diagram；
Fig. 2 is the structural schematic diagram of composite controlled object 4；
Fig. 3 is the overall frame of the adaptive active disturbance rejection decoupling controller of five-degree-of-freedom alternating active magnetic bearings of the present invention
Figure；
Fig. 4 is the structure chart of the adaptive automatic disturbance rejection controller of one of them in Fig. 1；
In figure: a, b. radial direction active magnetic bearings；C. axial active magnetic bearings；D. high-speed motor；F1, f2. radial displacement pass
Sensor；F3. shaft position sensor；G1, g2. auxiliary bearing；H1, h2. end cap；I. sleeve；M. shaft；1. five-degree-of-freedom alternating
Active magnetic bearings；2. analog line driver；3. coordinate transform；4. composite controlled object；5. automatic disturbance rejection controller；21,22. electric currents with
Track inverter；23. switch power amplifier；31,32.Clark inverse transformation；51,52,53,54,55. adaptive Active Disturbance Rejection Control
Device；511. Nonlinear Tracking Differentiator；512. nonlinearity erron state feedback control laws；513. adaptive extended state observers；
514.BP neural network；515. first compensation factors；516. second compensation factors；517. single-degree-of-freedom controlled devices.
Specific embodiment
Such as Fig. 1, five-degree-of-freedom alternating active magnetic bearings 1 are by two radial active magnetic bearings a, b, an axial active magnetic axis
C and high-speed motor d is held to constitute；Two radial active magnetic bearings a, b, an axial direction active magnetic bearings c and high-speed motor d are coaxial
Heart shares the same shaft m in sleeve i, and the axial ends of shaft m is supported by auxiliary bearing g1, g2 respectively, auxiliary
Bearing g1, g2 are separately fixed on corresponding end cap h1, h2.Two radial displacement transducers f1, f2 are separately fixed at corresponding
The two sides of radial active magnetic bearings a, b, measurement rotor radial displacement.Shaft position sensor f3 is fixed on end cap h2, and is located
In on the axial line of shaft m, rotor axial displacement is measured.
As shown in Fig. 2, composite controlled object 4 is by coordinate transformation module 3, analog line driver 2 and five-degree-of-freedom alternating active
Magnetic bearing 1 is sequentially connected in series composition.Power drive is made of two current tracking inverters 21,22 and a switch power amplifier 23
Dynamic device 2, and before being serially connected with five-degree-of-freedom alternating active magnetic bearings 1, become by two Clark inverse transform modules 31,32 as coordinates
Block 3 is changed the mold, coordinate transformation module 3 is serially connected with before analog line driver 2, wherein the first Clark inverse transform module 31 is serially connected with the
Before one current tracking inverter 21, before the 2nd Clark inverse transform module 32 is serially connected with the second current tracking inverter 22, coordinate becomes
Mold changing block 3, analog line driver 2 and five-degree-of-freedom alternating active magnetic bearings 1 collectively form composite controlled object 4.Radial active magnetic
The radial equivalent control current expected value i of bearing aax *、iay *Three-phase current expectation is transformed to through the first Clark inverse transform module 31
Value iau *、iav *、iaw *, the radial equivalent control current expected value i of radial active magnetic bearings bbx*、iby* through the 2nd Clark inversion
Mold changing block 32 is transformed to three-phase current desired value ibu *、ibv *、ibw *.First current tracking inverter 21 tracks three-phase current expectation
Value, the driving current i of outputting radial active magnetic bearings aau、iav、iaw.Second current tracking inverter 22 tracks the three-phase current phase
Prestige value, the driving current i of outputting radial active magnetic bearings bbu、ibv、ibw.Axial control current expected value iz *It is input to switch function
Rate amplifier 23, switch power amplifier 23 control current expected value i according to axialz *Export axial driving current iz.Composite quilt
The input for controlling object 4 is equivalent control current expected value iax *、iay *、iz *、ibx *、iby *, export as the position on five directions shaft m
Move xa、ya、z、xb、yb.Displacement x on five directions shaft ma、ya、z、xb、ybIt is measured respectively by displacement sensor f1, f2, f3,
The desired value i of control electric current can be obtained according to the displacement on five directions shaft max *、iay *、iz *、ibx *、iby *。
As shown in figure 3, five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller of the present invention is adaptive by five
Answer automatic disturbance rejection controller to form, be first, second, third, fourth respectively, the 5th adaptive automatic disturbance rejection controller 51,52,53,
54、55。
Every single-degree-of-freedom of five-degree-of-freedom alternating active magnetic bearings all by the adaptive automatic disturbance rejection controller of a second order into
Row control.The radial two-freedom of first, second 51,52 pairs of adaptive automatic disturbance rejection controller radial direction AC magnetism active bearings a into
Row control, the input of the first adaptive automatic disturbance rejection controller 51 are radial displacement xaWith the desired value x of radial displacementa *, export and be
The equivalent control current expected value i of composite controlled object 4ax *, the input of the second adaptive automatic disturbance rejection controller 52 is radial displacement
yaWith the desired value y of radial displacementa*, the equivalent control current expected value i for composite controlled object 4 is exporteday *；Third, four selfs
The radial two-freedom for adapting to 53,54 couples of radial AC active magnetic bearings b of automatic disturbance rejection controller controls, and third is adaptive certainly
The input of disturbance rejection control device 53 is radial displacement xbWith the desired value x of radial displacementb *, export as the equivalent of composite controlled object 4
Control current expected value ibx *, the input of the 4th adaptive automatic disturbance rejection controller 54 is radial displacement ybWith the expectation of radial displacement
Value yb *, export the equivalent control current expected value i for composite controlled object 4by *；5th 55 pairs of lists of adaptive automatic disturbance rejection controller
Axis-of-freedom is controlled to active magnetic bearings c, and the input of the 5th adaptive automatic disturbance rejection controller 55 is the axial displacement of shaft m
The desired value z of z and axial displacement*, export the equivalent control current expected value i for composite controlled object 4z *。
The structure of five adaptive automatic disturbance rejection controllers 51,52,53,54,55 is identical with algorithm, only adaptive with first below
It answers and is illustrated for automatic disturbance rejection controller 51.As shown in figure 4, the first adaptive automatic disturbance rejection controller 51 is by Nonlinear Tracking Differentiator
511, nonlinear state error Feedback Control Laws 512, adaptive extended state observer 513, BP neural network 514, first are mended
The factor 515, the second compensation factor 516 composition are repaid, single-degree-of-freedom controlled device 517 is controlled, single-degree-of-freedom quilt herein
Control object 517 refers to the radial one degree of freedom of the radial AC magnetic active bearings a in composite controlled object 4, i.e. control is radial
Displacement xa, correspond to the first adaptive automatic disturbance rejection controller 51, radial displacement x realized by the first adaptive automatic disturbance rejection controller 51a
Control.First adaptive automatic disturbance rejection controller 51 constructs according to the following steps:
1, Nonlinear Tracking Differentiator is constructed
By the desired value x of radial displacementa *As the input of Nonlinear Tracking Differentiator 511, Nonlinear Tracking Differentiator 511 is according to compound controlled
The demand for control of object 4, it is reasonable to extract tracking signal x1With differential signal x2.Nonlinear Tracking Differentiator are as follows:
In formula:For steepest comprehensive function, h0For integration step；r0For speed because
Son；H is the sampling period；xa *It (k) is radial displacement xa *In the value at k moment；x1It (k) is x1In the value at k moment；x1It (k+1) is x1?
The value at k+1 moment；x2It (k) is x2In the value at k moment；x2It (k+1) is x2In the value at k+1 moment.
2, adaptive extended state observer is constructed
The adaptive extended state observer 512 of input, output construction based on composite controlled object 4, wherein adaptive expand
The input for opening state observer 512 is the output displacement x of composite controlled object 4aAnd adaptive extended state observer 512
Three adjustable parameter β01、β02And β03；The output of adaptive extended state observer 512 is z1、z2And z3, z1、z2Respectively x1
And x2Estimated value, z3For the estimation always disturbed；Extended state observer uses following form:
Wherein u (k) is that disturbance compensation forms control amount u (k)=(u0(k)-z3(k))/b0, u0It (k) is control amount u0In k
The value at quarter；Fal is nonlinear function, expression formula:β01、β02、β03、α1、
α2、δ1、b、b0For the adjustable parameter of extended state observer；z1(k)、z2(k)、z3It (k) is respectively z1、z2、z3In the value at k moment,
z1(k+1)、z2(k+1)、z3It (k+1) is respectively z1、z2、z3In the value at k+1 moment, xaIt (k) is xaIn the value at k moment；E is error,
H is sampling period, b0For the estimated value of the first compensation factor 55, b is the value of the second compensation factor 516, b=1/b0；First compensation
The input of the factor 515 is difference u0-z3, export electric current ia *(k)=(u0-z3)/b0, the input of the second compensation factor 516 is electric current
ia *(k), output is control amount u=u0-z3, u0It is non-513 output control amount of linear state error feedback control rule.As 0 < α1、
α2When < 1, fal function has small error large gain, the characteristic of the big small gain of error, under normal conditions α1Take 0.5, α2Take 0.25；
δ1> 0,5~10 times of the general desirable sampling period；β01、β02、β03Value adjusted by BP nerve net 514, controlled pair of this basis
As 4 variation and disturbance and the parameter beta of adjust automatically extended state observer01、β02、β03, i.e., adaptive expansion state observation
Device.
3, nonlinear state error Feedback Control Laws are constructed
By two output x of Nonlinear Tracking Differentiator 5111And x2Two output z of extended state observer 512 are individually subtracted1With
z2, obtain systematic error e1=x1-z1And e2=x2-z2, the error is defeated as nonlinear state error Feedback Control Laws 513
Enter, nonlinear state error Feedback Control Laws 513 export control amount u0.For exchanging radial direction magnetic bearing system, nonlinear state
Error Feedback Control Laws 72 are as follows:
u0=β1fal(e1,α3,δ2)+β2fal(e2,α4,δ2),
In formula: β1And β2For two parameters of nonlinear state error Feedback Control Laws 513, fal is nonlinear function, is led to
α in normal situation3Take 0.5, α4Take 0.25, δ2> 0,5~10 times of the general desirable sampling period.
4, the adaptive extended state observer parameter tuning method based on BP neural network
BP neural network 514 uses three-decker, 4 nodes of input layer, 3 nodes of output layer, selection signal error e1、
Signal differentiation error e2, system export xa4 input nodes with bias 1 as BP neural network 514, in conjunction with compound controlled
Object 4 and process examination, which are gathered, selects 5 hidden layer nodes, and three nodes of output layer are adaptive extended state observer 513
Three parameter betas01、β02、β03.It is possible thereby to realize the online self-tuning of adaptive 512 parameter of extended state observer.
The input of 514 input layer of BP neural network isWherein in indicates that input layer, j indicate the four of input layer
A node, j=1,2,3,4；The input and output of hidden layer areWherein im indicates hidden layer,For the value at hidden layer weighting coefficient k moment, k indicates the k moment, and i indicates five nodes of hidden layer, i=1,2,3,4,
5；The input and output of output layer areWherein out indicates that output layer, k indicate the k moment,
For the value at hidden layer weighting coefficient k moment, l indicates three nodes of output layer, l=1,2,3.
BP neural network according to gradient descent method corrective networks weight coefficient, i.e., according to property target function E (k) to weighting be
Adjustment is searched in several negative gradient directions.Traditional BP algorithm is connected to the network the iterative relation weighedAdd momentum
The iterative relation of network connection power is afterWherein n indicates that the number of adjustment power, E are
Target function, w are weighting coefficient, and η is learning rate, and α is factor of momentum, 0 < α < 1；α Δ w (n-1) is exactly the momentum added
?.The improved method for adding multiple momentum term is exactly then to add a β on the basis of commonly addition momentum term α Δ w (n-1)
Δ w (n-2) and γ Δ w (n-3) item,
I.e.Namely adjust (n-2) and (n-3)
Weight variable quantity when secondary, β, γ are factor of momentum, 0 < β <, 1,0 < γ < 1.
The specific algorithm of the adaptive automatic disturbance rejection controller of BP neural network is as follows:
1) it determines the structure of BP neural network, that is, determines input layer number and node in hidden layer, select inertia coeffeicent
α, β, γ and learning rate η provide the initial value of each layer weighting coefficientWithThis season k=1；
2) sampling obtains the error e at k moment1(k) and e2(k)；
3) input, the output of each layer neuron of neural network are calculated, the output of output layer is adaptive expansion state
Three adjustable parameter β in observer01、β02And β03；
4) study for carrying out neural network, to weighting coefficientWithOn-line tuning is carried out, realizes ESO tri-
The β of adjustable parameter01、β02And β03Self-tuning System；
5) k=k+l is set, is recalculated back to step 3), until systematic error is met the requirements.
5, by Nonlinear Tracking Differentiator 511, nonlinear state error Feedback Control Laws 512, adaptive extended state observer
513, BP neural network 514, the first compensation factor 515, the second compensation factor 516 constitute first adaptively certainly as a whole
Disturbance rejection control device 51 controls single-degree-of-freedom controlled device 517.
The adaptive automatic disturbance rejection controller 51,52,53,54,55 of second, third, fourth, fifth can be similarly constructed, respectively
Corresponding single-degree-of-freedom controlled device is controlled, i.e., controls radial displacement y respectivelya、xb、ybWith axial displacement z.
Claims (6)
1. a kind of five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller, it is characterized in that: by being serially connected in compound controlled pair
As the identical five adaptive automatic disturbance rejection controller compositions of internal structure before (4), single-degree-of-freedom controlled device is controlled respectively,
In the first adaptive automatic disturbance rejection controller (51) input be radial displacement xaWith the desired value x of radial displacementa *, output for control
Current expected value i processedax *, the input of the second adaptive automatic disturbance rejection controller (52) is radial displacement yaWith the expectation of radial displacement
Value ya*, output is control current expected value iay *, the input of the adaptive automatic disturbance rejection controller of third (53) is radial displacement xbAnd diameter
To the desired value x of displacementb *, output for control current expected value ibx *, the input of the 4th adaptive automatic disturbance rejection controller (54) is diameter
To displacement ybWith the desired value y of radial displacementb *, output be current expected value iby *, the 5th adaptive automatic disturbance rejection controller (55)
Input is the desired value z of axial displacement z and axial displacement*, output for control current expected value iz *；Each adaptive active disturbance rejection control
Device processed all by Nonlinear Tracking Differentiator, nonlinear state error Feedback Control Laws, adaptive extended state observer, BP neural network,
First compensation factor and the second compensation factor composition, the input of five Nonlinear Tracking Differentiators is the desired value x of radial displacement respectivelya *、
ya*、xb *、yb *With the desired value z of axial displacement*, the output of first Nonlinear Tracking Differentiator (511) therein is corresponding tracking letter
Number x1With differential signal x2, the input of first adaptive extended state observer (512) is the output displacement of composite controlled object
xa, three parameter betas01、β02And β03, control amount u, output be x1、x2Estimated value z1、z2The estimated value z always disturbed3, first
The input of nonlinear state error Feedback Control Laws (513) is error e1=x1-z1And e2=x2-z2, output be control amount u0, the
The input of one BP neural network (514) is error e1、e2, displacement xaIt is three parameter betas with bias 1, output01、β02And β03,
The input of first the first compensation factor (515) is error u0-z3, output for single-degree-of-freedom controlled device electric current ia *, the
The input of one the second compensation factor (516) is electric current ia *, output is to the control amount of adaptive extended state observer (512)
u。
2. five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller according to claim 1, it is characterized in that: compound
Controlled device (4) is sequentially connected in series by coordinate transformation module (3), analog line driver (2) and five-degree-of-freedom alternating active magnetic bearings (1)
Composition, analog line driver (2) are made of two current tracking inverters (21,22) and a switch power amplifier (23), are sat
Mark conversion module (3) is made of two Clark inverse transform modules (31,32), and the first Clark inverse transform module (31) is serially connected with the
Before one current tracking inverter (21), before the 2nd Clark inverse transform module (32) is serially connected with the second current tracking inverter (22).
3. a kind of building method of five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller as described in claim 1,
It is characterized in that including the following steps:
Step A: constructing first Nonlinear Tracking Differentiator (511) using following formula, obtains tracking signal x1With differential signal x2:
For the comprehensive letter of steepest
Number, h0For integration step；r0For velocity factor；H is the sampling period；xa* (k) is radial displacement xa* in the value at k moment；x1(k) it is
x1In the value at k moment；x1It (k+1) is x1In the value at k+1 moment；x2It (k) is x2In the value at k moment；x2It (k+1) is x2In k+1
The value at quarter.
Step B: constructing first adaptive extended state observer (512) using following formula, obtains it and exports z1、z2And z3:
U (k) is that disturbance compensation forms control amount u (k)=(u0(k)-z3(k))/b0, u0It (k) is control amount u0In the value at k moment；
Fal is nonlinear function, expression formula:z1(k)、z2(k)、z3(k) respectively
For z1、z2、z3In the value at k moment, z1(k+1)、z2(k+1)、z3It (k+1) is respectively z1、z2、z3In the value at k+1 moment, xa(k) it is
xaIn the value at k moment, e is error, and h is sampling period, b0For the estimated value of the first compensation factor, b is the second compensation factor
Value, b=1/b0；α1Take 0.5, α2Take 0.25, δ1> 0 is 5~10 times of sampling period.
Step C: formula u is used0=β1fal(e1,α3,δ2)+β2fal(e2,α4,δ2) first nonlinear state error feedback of construction
Control law (513), obtains control amount u0；Fal is nonlinear function, error e1=x1-z1, e2=x2-z2, α3Take 0.5, α4It takes
0.25, δ2> 0 takes 5~10 times of sampling period；
Step D: three parameter betas are adjusted using first BP neural network (514)01、β02And β03。
4. the building method of five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller according to claim 3,
Be characterized in: in step D, first BP neural network (514) uses three-decker, and input layer is 4 nodes, and output layer is 3
Node.
5. the building method of five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller according to claim 4,
Be characterized in: the iterative relation of first BP neural network (514) connection weight isN indicates the number of adjustment power, and E is target function, w
For weighting coefficient, η is learning rate, and α, β, γ are factor of momentum.
6. the building method of five-degree-of-freedom alternating active magnetic bearings active disturbance rejection decoupling controller according to claim 5,
It is characterized in: provides the initial value of each layer weighting coefficient of BP neural networkWithK=1 is enabled, sampling obtains the k moment
Error e1(k) and e2(k), outputting and inputting for each layer neuron of neural network is calculated, output is three parameter betas01、β02
And β03；The study for carrying out neural network later, to weighting coefficientWithOn-line tuning；Most postposition k=k+l is carried out
It recalculates, until error is met the requirements.
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