CN109672380A - Permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller - Google Patents

Permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller Download PDF

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CN109672380A
CN109672380A CN201811379844.6A CN201811379844A CN109672380A CN 109672380 A CN109672380 A CN 109672380A CN 201811379844 A CN201811379844 A CN 201811379844A CN 109672380 A CN109672380 A CN 109672380A
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freedom
magnet synchronous
bearing
degrees
module
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CN109672380B (en
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朱熀秋
顾志伟
颜磊
孙玉坤
华逸舟
杨泽斌
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Beijing Jintai Yongxiang Technology Development Co.,Ltd.
Hefei Jiuzhou Longteng Scientific And Technological Achievement Transformation Co ltd
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Jiangsu University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/001—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using fuzzy control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0014—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using neural networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Artificial Intelligence (AREA)
  • Evolutionary Computation (AREA)
  • Automation & Control Theory (AREA)
  • Fuzzy Systems (AREA)
  • Magnetic Bearings And Hydrostatic Bearings (AREA)
  • Feedback Control In General (AREA)

Abstract

The present invention discloses a kind of permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller, suspending power subsystem line neural network is sequentially connected in series between composite controlled object against module and additional controller module, additional controller module is made of five sliding mode controllers, and the input of each sliding mode controller is a given displacement and an error amount of a corresponding real-time displacement；Suspending power subsystem line neural network is against module by nerve network system, on-line learning algorithm module and 10 integrator S‑1Composition, each Bit andits control amount, each Bit andits control amount are through an integrator S‑1The multiple integral and each Bit andits control amount obtained afterwards two integrator S through concatenating‑1The double integral obtained afterwards is all input to nerve network system；The input of on-line learning algorithm module is five errors of the double integral with corresponding real-time displacement of five Bit andits control amounts, exports as weight matrix adjusted, raising suspension control performance.

Description

Permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller
Technical field
The present invention relates to permanent-magnet synchronous motor with five degrees of freedom without bearing, five specially inverse based on line neural network freedom Bearing-free permanent magnet synchronous motor suspending power subsystem sliding mode decoupling controller is spent, the technology neck of electric drive control equipment is belonged to Domain.
Background technique
Bearing-free permanent magnet synchronous motor be integrated with magnetic suspension bearing without lubrication, without mechanical wear, noise is small and uses the longevity It orders the advantages that long, and is provided simultaneously with the excellent operation characteristic of permanent magnet synchronous motor.Small, efficiency is lost in bearing-free permanent magnet synchronous motor It is high, without exciting current, control loop is simple, has many advantages, such as High Power Factor, high revolving speed, high-precision, in aerospace, life The fields such as object medicine, semiconductors manufacture have broad application prospects.Permanent-magnet synchronous motor with five degrees of freedom without bearing is one again Non-linear, multivariable, the system of close coupling realize that the decoupling control between suspending power is the premise of motor stabilizing operation.If Using the method for decentralised control, ignores the coupling between five free each suspending powers of bearing-free permanent magnet synchronous motor, just can not Meet permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power and controls high-precision requirement.China Patent Publication No. is The document of CN102013870A discloses a kind of inverse system decoupling controller of five-degree-of-freedom bearingless synchronous reluctance motor, using inverse Systems approach carries out decoupling control to the suspending power subsystem of five degrees of freedom without bearing synchronous magnetic resistance motor, and this method needs to derive The mathematical models of controlled device out, and accurate mathematical model is often difficult acquisition and the system under the control of this method Robustness it is poor；China Patent Publication No. discloses five free bearing-free permanent magnets of one kind for the document of CN1737708 and synchronizes electricity It is outstanding to approach permanent-magnet synchronous motor with five degrees of freedom without bearing using neural network for machine neural network inverse decoupling controller building method Buoyancy subsystem inversion model, neural network has that convergence rate is slow, easily falls into local minimum point, and passes through acquisition number According to the inversion model that off-line training obtains, weight is once it is determined that can not just adjust, robustness is also relatively poor.
Summary of the invention
The purpose of the invention is to overcome existing permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem solution The deficiency of coupling control method proposes a kind of permanent-magnet synchronous motor with five degrees of freedom without bearing suspension inverse based on line neural network Power subsystem sliding mode decoupling controller makes five degrees of freedom without by the connection weight of algorithm for design on-line control neural network Bearing permanent magnet synchronous electric motor suspending power subsystem inversion model accuracy improves, and the pseudo- linear second-order radial direction position obtained respectively to decoupling Move xa, ya, xb, ybWith pseudo- linear second-order axial displacement zbSubsystem designs sliding mode controller (Sliding Model Controller, SMC), the decoupling control between permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power is effectively realized, is obtained Good dynamic and static characteristic, overcomes the perturbation of permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power parameter of any subsystem, and modeling misses The problem of difference and load variation bring control performance decline.
The technical solution that permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller of the present invention uses It is: includes that be sequentially connected in series suspending power subsystem between the composite controlled object of permanent-magnet synchronous motor with five degrees of freedom without bearing online Nerve network reverse module and additional controller module, the output of composite controlled object are real-time displacement xa(t), ya(t), xb(t), yb(t), zb(t), input is to constant currentIt is characterized in that: additional controller module is by five sliding formworks Controller composition, the input of each sliding mode controller are a given displacementsWith a corresponding reality Shi Weiyixa(t), ya(t), xb(t), yb(t), zb(t) an error amount eax(t), eay(t), ebx(t), eby(t), ebz(t)、 Output is corresponding Bit andits control amount v1, v2, v3, v4, v5；Suspending power subsystem line neural network is against module by nerve Network system, on-line learning algorithm module and 10 integrator S-1Composition, each Bit andits control amount v1, v2, v3, v4, v5, it is every A Bit andits control amount v1, v2, v3, v4, v5Through an integrator S-1The multiple integral obtained afterwards and each Bit andits control amount v1, v2, v3, v4, v5Two integrator S through concatenating-1The double integral obtained afterwardsAll It is input to nerve network system；The input of on-line learning algorithm module is five Bit andits control amount v1, v2, v3, v4, v5Double product Divide and corresponding real-time displacement xa(t), ya(t), xb(t), yb(t), zb(t) five error es1(t), e2(t), e3(t), e4 (t), e5(t), output is weight matrix W adjusted0(t+1), weight matrix W0(t+1) nerve network system is also inputted.
The present invention has the advantages that
1. the present invention for this multivariable of permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem, it is non-linear, The object of close coupling recognizes the inverse of permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem using line neural network Model avoids the complex process that inversion model is solved using traditional mathematical method, while compared to traditional offline nerve net The inversion model that network obtains has higher accuracy, has stronger robustness.
2. permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power inverse based on line neural network that the present invention designs System sliding mode decoupling controller, using the sliding mode controller of new Reaching Law as additional closed loop controller.Sliding mode controller has both The advantage that fast response time, external interference resistance are strong and robustness is good, while being easily achieved in engineering, improve five degree of freedom The suspension control performance of bearing-free permanent magnet synchronous motor.
3. the on-line study neural network structure that the present invention uses is different from the structure that traditional Neural Network Online learns, The error of output and neural network input according to composite controlled object is that objective function carrys out online design learning algorithm, is simplified The structure of on-line study neural network.
Detailed description of the invention
Fig. 1 is permanent-magnet synchronous motor with five degrees of freedom without bearing structural schematic diagram；
Fig. 2 is the knot of permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller of the present invention Structure block diagram；
Fig. 3 is the structural block diagram of composite controlled object 1 in Fig. 1；
Fig. 4 is that the puppet that suspending power subsystem line neural network is formed against module 2 and composite controlled object 1 in Fig. 1 is linear System schematic and its isoboles；
Fig. 5 is the determination flow chart of variable element k in sliding mode controller in Fig. 1 (SMC)；
In figure: 1. composite controlled objects；2. suspending power subsystem line neural network is against module；3. additional controller mould Block；4. two degrees of freedom bearing-free permanent magnet synchronous motor levitation force winding current control module；5. Three Degree Of Freedom alternating current-direct current mixing magnetic Shaft current control module；11. bearing-free permanent magnet synchronous motor；12. displacement sensor；13. photoelectric encoder；14. goniometer Calculate module；21. on-line learning algorithm module；22. nerve network system；31,32,33,34,35.SMC (sliding mode controller)；41, 42.PI adjuster；43.IPARK converter；44.SVPWM；45. voltage source inverter；46. current sensor；47.CLARK becomes Parallel operation；48.PARK converter；51,52.PI adjuster；53.SVPWM；54. voltage source inverter；55. current sensor； 56.CLARK converter；57. power amplifier；111. two degrees of freedom bearing-free permanent magnet synchronous motor；112. Three Degree Of Freedom is handed over straight Flow hybrid magnetic bearing.
Specific embodiment
As shown in Figure 1, permanent-magnet synchronous motor with five degrees of freedom without bearing 11 is by two degrees of freedom bearing-free permanent magnet synchronous motor 111 It is formed with Three Degree Of Freedom AC-DC hybrid magnetic bearing 112, two degrees of freedom bearing-free permanent magnet synchronous motor 111 controls rotor radial xa, yaDisplacement, Three Degree Of Freedom AC-DC hybrid magnetic bearing 112 control rotor radial xb, ybAnd axial direction zbDisplacement.
As shown in FIG. 2 and 3, it is hanged by bearing-free permanent magnet synchronous motor 11, two degrees of freedom bearing-free permanent magnet synchronous motor Buoyancy winding current control module 4, Three Degree Of Freedom AC-DC hybrid magnetic bearing current control module 5, displacement sensor 12, photoelectricity Encoder 13 and angle calculation module 14 form composite controlled object 1.
Suspending power subsystem line neural network is sequentially connected in series between composite controlled object 1 against module 2 and additional control Device module 3, suspending power subsystem line neural network connect the input of composite controlled object 1, suspending power against the output of module 2 The output and the input of composite controlled object 1 of system line neural network against module 2 are to constant current The output of composite controlled object 1 is real-time displacement xa(t), ya(t), xb(t), yb(t), zb(t), i.e., four real-time radial displacement xa (t), ya(t), xb(t), yb(t) and a real-time axial displacement zb(t)。
Additional controller module 3 is by the first sliding mode controller 31 (SMC31), the second sliding mode controller 32 (SMC32), third Sliding mode controller 33 (SMC33), the 4th sliding mode controller 34 (SMC34) and the 5th sliding mode controller 35 (SMC35) this five Sliding mode controller composition.The input of additional controller module 3 is given displacementEach cunning therein The input of mould controller is a given displacementWith corresponding real-time displacement xa(t), ya(t), xb(t), yb(t), zb(t) difference eax(t), eay(t), ebx(t), eby(t), ebz(t), that output is corresponding Bit andits control amount v1, v2, v3, v4, v5.Namely: the input of the first sliding mode controller 31 is a given displacementWith real-time displacement xa(t) difference eax (t), that output is Bit andits control amount v1；The input of second sliding mode controller 32 is given displacementWith real-time displacement ya(t) difference Value eay(t), that output is Bit andits control amount v2；The input of third sliding mode controller 33 is given displacementWith real-time displacement xb (t) difference ebx(t), that output is Bit andits control amount v3；The input of 4th sliding mode controller 34 is given displacementWith it is real-time It is displaced yb(t) difference eby(t), that output is Bit andits control amount v4；The input of 5th sliding mode controller 35 is given displacementWith Real-time displacement zb(t) difference ebz(t), that output is Bit andits control amount v5。
Suspending power subsystem line neural network against module 2 by nerve network system 22, on-line learning algorithm module 21 with And 10 integrator S-1Composition, the input of the output Connection Neural Network system 22 of on-line learning algorithm module 21, five sliding formworks The integrated device S of the output of controller-1The input of Connection Neural Network system 22.The input of on-line learning algorithm module 21 is five Five Bit andits control amount v of sliding mode controller output1, v2, v3, v4, v5Double integral Respectively with corresponding real-time displacement xa(t), ya(t), xb(t), yb(t), zb(t) error e1(t), e2(t), e3 (t), e4(t), e5(t), the output of on-line learning algorithm module 21 is weight matrix W adjusted0(t+1), weight matrix W0 It (t+1) is one of nerve network system 22 input.Specifically:
Nerve network system 22 shares 16 inputs, the displacement control that each sliding mode controller 31,32,33,34,35 exports Amount v processed1, v2, v3, v4, v5All input nerve network system 22, the displacement control that each sliding mode controller 31,32,33,34,35 exports Amount v processed1, v2, v3, v4, v5Through an integrator S-1The multiple integral obtained afterwards all inputs nerve network system 22, each cunning The Bit andits control amount v that mould controller 31,32,33,34,35 exports1, v2, v3, v4, v5Two integrator S through concatenating-1Afterwards The double integral arrivedNerve network system 22 is all inputted, along with on-line study is calculated The weight matrix W of the input nerve network system 22 of method module 210(t+1), therefore totally ten six inputs.On-line learning algorithm module 21 altogether there are five input, wherein first input be the first sliding mode controller 31 output Bit andits control amount v1Through concatenating One, second integrator S-1The double integral obtained afterwardsWith real-time displacement xa(t) error e1(t), second input be The Bit andits control amount v of second sliding mode controller 32 output2Third, the 4th integrator S through concatenating-1The double integral obtained afterwardsWith real-time displacement ya(t) error e2(t), third input is the Bit andits control amount v that third sliding mode controller 33 exports3 The the 5th, the 6th integrator S through concatenating-1The double integral obtained afterwardsWith real-time displacement xb(t) error e3(t), the 4th A input is the Bit andits control amount v of the 4th sliding mode controller 34 output4The the 7th, the 8th integrator S through concatenating-1It obtains afterwards Double integralWith real-time displacement yb(t) error e4(t), the 5th input is the displacement of the 5th sliding mode controller 35 output Control amount v5The the 9th, the tenth integrator S through concatenating-1The double integral obtained afterwardsWith real-time displacement zb(t) error e5 (t)。
As shown in figure 3, composite controlled object 1 is shaftless come real-time detection two degrees of freedom using 5 eddy current displacement sensors The radial displacement x of bearing permanent magnet synchronous electric motor 111a(t), ya(t), the radial displacement x of Three Degree Of Freedom AC-DC hybrid magnetic bearing 112b (t), yb(t) and axial displacement zb(t)。
Two degrees of freedom bearing-free permanent magnet synchronous motor levitation force winding current control module 4 is adjusted by pi regulator 41, PI Device 42, IPARK converter 43, SVPWM44, voltage source inverter 45, current sensor 46, CLARK converter 47 and PARK Converter 48 forms；Current sensor 46 detects the levitation force winding electric current of two degrees of freedom bearing-free permanent magnet synchronous motor 111 iBa, iBb, iBc, the input terminal of the output end connection CLARK converter 47 of current sensor 46, through the generation of CLARK converter 47 α- Electric current i under β coordinate systemBα, iBβ, the input terminal of the output end connection PARK converter 48 of CLARK converter 47, angle calculation Module 14 obtains angle, θ, calculation formula according to the rotational speed omega that photoelectric encoder 13 measures are as follows: θ=ω t, PARK converter 48 according to Electric current i under d-q coordinate system is generated according to the counted θ of angle calculation module 14Bd, iBq, this electric current is that two degrees of freedom bearing-free permanent magnet is same The feedback current for walking motor levitation force winding is exported against module 2 to constant current with suspending power subsystem line neural network After obtain difference, difference obtains the given voltage signal under d-q coordinate system after modulating again through pi regulator 41,42The output end of pi regulator 41,42 is connected with the input terminal of IPARK converter 43, the foundation again of IPARK converter 43 The counted θ of angle calculation module 15 generates the voltage under alpha-beta coordinate systemVoltageIt is generated through SVPWM44 The switching signal S of voltage source inverter 45A(A=1,2,3,4,5,6), switching signal S of the voltage source inverter 45 according to offerA (A=1,2,3,4,5,6) 111 levitation force winding of two degrees of freedom bearing-free permanent magnet synchronous motor is controlled.
Three Degree Of Freedom AC-DC hybrid magnetic bearing current control module 5 by pi regulator 51, pi regulator 52, SVPWM53, Voltage source inverter 54, current sensor 55 and CLARK converter 56 form.Current sensor 55 detects that Three Degree Of Freedom is handed over The radial displacement of direct current hybrid magnetic bearing 112 controls electric power ia, ib, ic, the output end connection CLARK transformation of current sensor 55 The input terminal of device 56 generates radial displacement under alpha-beta coordinate system through CLARK converter 56 and controls electric current ix, iy, with suspending power subsystem Line neural network of uniting is exported against module 2 to constant currentAfter obtain difference, difference is adjusted through pi regulator 51,52 again The given voltage signal under alpha-beta coordinate system is obtained after systemVoltageVoltage source inverter 54 is generated through SVPWM53 Switching signal SH(H=1,2,3,4,5,6), switching signal S of the voltage source inverter 54 according to offerH(H=1,2,3,4,5, 6) 112 radial displacement electric current of Three Degree Of Freedom AC-DC hybrid magnetic bearing is controlled；Three Degree Of Freedom AC-DC hybrid magnetic bearing 112 axial displacement controls electric current izThe given current signal exported by suspending power subsystem line neural network against module 2Through Power amplifier 57 obtains.
For composite controlled object 1, five degree of freedom is established to the working principle of five free bearing-free permanent magnet synchronous motors 11 Bearing-free permanent magnet synchronous motor suspending power subsystem mathematical model carries out 11 rotor of permanent-magnet synchronous motor with five degrees of freedom without bearing Mechanical analysis considers the coupling influence between the gyroscopic effect and each freedom degree of magnetic suspension bearing system, establishes the equation of motion, And it choosesMake For the state variable of composite controlled object 1, U=[u1,u2,u3,u4,u5]T=[iBd *,iBq *,ix *,iy *,iz *]TAs composite quilt Control the input variable of object 1, Y=[y1,y2,y3,y4,y5]T=[xa(t),ya(t),xb(t),yb(t),zb(t)]TAs compound The output variable of controlled device 1 establishes the state equation of composite controlled object 1, derivation is carried out to output variable Y, until each The aobvious U containing input variable of a component, obtains opposite order α=(α of composite controlled object 11,α2,α2,α4,α5)=(2,2,2,2, 2) reversibility Analysis, is carried out to composite controlled object 1 and knows that composite controlled object 1 is reversible.
Using random current signal [iBd *,iBq *,ix *,iy *,iz *] motivated, obtain the output of composite controlled object 1 [xa(t),ya(t),xb(t),yb(t),zb(t)], displacement x is acquired using five point value derivative algorithmsa(t), ya(t), xb(t), yb (t), zb(t) single order, second dervative constitute the input sample collection of neural networkWith desired output sample Collect [iBd *,iBq *,ix *,iy *,iz *], then data are normalized.
The present invention uses structure for 15 × 32 × 5 BP neural network, and the excitation function of hidden layer neuron is chosen for70% in 5000 groups of samples that sampling is obtained is used as training sample, and remaining 30% is used as test specimens This.Network is trained using LM learning algorithm, after the training of 1200 steps, error precision reaches 0.001, obtains trained Nerve network system 22 saves its structure and parameter, with 10 integrators and instruction known to the opposite order of composite controlled object 1 The nerve network system 22 perfected can construct the offline Neural Network Inverse System of composite controlled object 1.
Trained neural network input/output relation can be expressed asWherein u is output vector, and z is Input variable, the connection weight matrix of input layer to hidden layer are V0, the connection weight matrix of hidden layer to output layer is W0= [w1,w2,w3,w4,w5]T∈R32×5, in formula, w1, w2, w3, w4, w5Indicate the matrix of 1 row 32 column；T is transposition；R32×5Table Show any one 32 row, 5 column matrix；wq=[w1q,w2q,…,w11q,w32q], w1q,w2q,…,w11q,w32qFor connection weight, q= 1,2,3,4,5；σ () is general hidden layer excitation function.
Initial time initializes suspending power subsystem line neural network against module 2, and off-line training is obtained The connection weight matrix W of nerve network system 220And V0Initial weight as on-line study neural network.Based on basic function Thought, only to the W being affected to neural network approximation properties0It is adjusted.T moment, according to the defeated of each sliding mode controller The error e of each output valve of integrated value Yu composite controlled object 1 of signal outi(t), i=1,2,3,4,5, wherein Calculate the connection weight matrix w for obtaining t momentij(t) correction amount wij(t):
In formula, Δ wijIt (t) is connection weight matrix wij(t) correction amount；eiIt (t) is each sliding mode controller output signal The error of differential value and 1 output valve of composite controlled object；For error ei(t) to connection weight wij(t) local derviation；μj>0 For adjustable parameter；I=1,2,3,4,5；J=1,2 ..., 32.
Set error threshold { ε1,ε2,ε3,ε4,ε5, wherein εiFor lesser constant, i=1,2,3,4,5.When | ei(t)| < εiWhen, connection weight wij(t) it does not adjust, still there is W0 (t+1)=W0 (t), when | ei(t) | > εiWhen, obtain the company at t+1 moment Meet weight matrix wij(t+1).Its calculation method is obtained by following formula:
In formula, Δ wijIt (t) is connection weight wij(t) correction amount；eiIt (t) is the differential of each sliding mode controller output signal The error of value and 1 output valve of composite controlled object；For error ei(t) to connection weight matrix wij(t) local derviation；μj>0 For adjustable parameter；I=1,2,3,4,5；J=1,2 ..., 32, to obtain the connection weight square for updating the t+1 moment adjusted Battle array W0(t+1)。
The parameter of on-line tuning nerve network system 22, until ei(t)=0, i=1,2,3,4,5.Suspending power subsystem exists Line nerve network reverse module 2 is connected with compound controlled system 1 may make up the second order puppet of 5 single-input single-outputs as shown in Figure 4 Linear displacement subsystem.
Additional controller module 3 is to make system closed-loop control to the sliding mode controller of pseudo-linear system construction.It is compound controlled Object 1 obtains 5 pseudo-linear systems, respectively second order radial displacement x after decouplinga, ya, xb, ybSubsystem and second order axial displacement zbSubsystem.
In order to eliminate the intrinsic buffeting problem of Sliding mode variable structure control, the present invention on the basis of conventional exponentially approaching rule, It is proposed a kind of novel exponentially approaching rule, expression are as follows:Wherein, s is sliding-mode surface, and C is to be System and has state variableL >=0, ε > 0, k > 0 are system design parameters.
The steady-state error and rapidity of consideration system, k here are the nonlinear function of Error Absolute Value, and Fig. 5 is to become ginseng Number k flow chart, if e is the system given value for inputting SMC and the error of real-time detection value, i.e. e is eax(t), eay(t), ebx(t), eby(t), ebz(t), znFor given fiducial value, there is z1< z2< ... < zn, mnFor the selective value of k after comparison, there is m0< m1< ... mn.Will | e | with z1Compare, if | e |≤z1, select k=m0, second step is otherwise executed, second step is incited somebody to action | e | with z2Compare, if | e |≤ z2, select k=m1, third step is otherwise executed, and so on, compared k and obtains optimal value mn, value mnI.e. optimal k value.
First sliding mode controller 31 is for second order radial displacement xaSubsystem design, take system state equation expression formula Are as follows:r1For system state variables and have For state variable r1Derivative and be denoted asChoosing Take the sliding-mode surface of system are as follows: s1=c1r1+r2, solvec1For sliding-mode surface coefficient,For sliding-mode surface s1Lead Number, the novel Reaching Law that the first sliding mode controller 31 uses may be expressed as:Then the first sliding formwork control The output v of device 311It is obtained by following calculation formula:Wherein, l1>=0, ε1> 0, k1>0 It is system design parameters.Construct Lyapunov function:According to Lyapunov Theory of Stability it is found that sliding mode Accessibility condition are as follows:By can be calculated:It can Know radial displacement xaSubsystem can reach sliding-mode surface by free position in finite time.
Similarly, the second sliding mode controller 32 is for second order radial displacement yaSubsystem design, take system mode side Journey expression formula are as follows:r3For system state variables and have For state variable r3Derivative and be denoted asThe sliding-mode surface of selecting system are as follows: s2=c2r3+r4, solvec2For sliding-mode surface coefficient,For sliding formwork Face s2Derivative, the second sliding mode controller 32 use novel Reaching Law may be expressed as:Then second The output v of sliding mode controller 322It is obtained by following calculation formula:Wherein, l2>=0, ε2> 0, k2> 0 is system design parameters.Construct Lyapunov function:According to Lyapunov Theory of Stability it is found that The accessibility condition of sliding mode are as follows:By can be calculated:Know radial displacement yaSubsystem can be by appointing in finite time Meaning state reaches sliding-mode surface.
Similarly, third sliding mode controller 33 is for second order radial displacement xbSubsystem design, take system mode side Journey expression formula are as follows:r5For system state variables and have For state variable r5Derivative and be denoted asThe sliding-mode surface of selecting system are as follows: s3=c3r5+r6, solvec3For sliding-mode surface coefficient,For sliding-mode surface s3Derivative, third sliding mode controller 33 use novel Reaching Law may be expressed as:Then third is sliding The output v of mould controller 333It is obtained by following calculation formula:Wherein, l3>=0, ε3 > 0, k3> 0 is system design parameters.Construct Lyapunov function:It is according to Lyapunov Theory of Stability it is found that sliding The accessibility condition of dynamic model state are as follows:By can be calculated:Know radial displacement xbSubsystem can be by any in finite time State reaches sliding-mode surface.
Similarly, the 4th sliding mode controller 34 is for second order radial displacement ybSubsystem design, take system mode side Journey expression formula are as follows:r7For system state variables and have For state variable r7Derivative and be denoted asThe sliding-mode surface of selecting system are as follows: s4=c4r7+r8, solvec4For sliding-mode surface coefficient,For sliding formwork Face s4Derivative, the 4th sliding mode controller 34 use novel Reaching Law may be expressed as:Then the 4th is sliding The output v of mould controller 344It is obtained by following calculation formula:Wherein, l4>=0, ε4> 0, k4> 0 is system design parameters.Construct Lyapunov function:According to Lyapunov Theory of Stability it is found that sliding The accessibility condition of mode are as follows:By can be calculated: Know radial displacement ybSubsystem can reach sliding-mode surface by free position in finite time.
Similarly, the 5th sliding mode controller 35 is for second order radial displacement zbSubsystem design, take system mode side Journey expression formula are as follows:r9For system state variables and have For state variable r9Derivative and be denoted asThe sliding-mode surface of selecting system are as follows: s5=c5r9+r10, solvec5For sliding-mode surface coefficient,For sliding formwork Face s5Derivative, the 5th sliding mode controller 35 use novel Reaching Law may be expressed as:Then the 5th The output v of sliding mode controller 355It is obtained by following calculation formula:Wherein, r9To be System and has state variablel5>=0, ε5> 0, k5> 0 is system design parameters.Construct Lyapunov function:According to Lyapunov Theory of Stability it is found that the accessibility condition of sliding mode are as follows:It can by calculating :Know axial displacement zbSubsystem can in finite time Sliding-mode surface is reached by free position.

Claims (7)

1. a kind of permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller, includes five degrees of freedom without Suspending power subsystem line neural network is sequentially connected in series between the composite controlled object of bearing permanent magnet synchronous electric motor against module (2) and attached Add controller module (3), the output of composite controlled object is real-time displacement xa(t), ya(t), xb(t), yb(t), zb(t), it inputs It is to constant currentIt is characterized in that: additional controller module (3) is made of five sliding mode controllers, often The input of a sliding mode controller is a given displacementWith a corresponding real-time displacement xa(t), ya(t), xb(t), yb(t), zb(t) an error amount eax(t), eay(t), ebx(t), eby(t), ebz(t), output is corresponding A Bit andits control amount v1, v2, v3, v4, v5；Suspending power subsystem line neural network is against module (2) by nerve network system (22), on-line learning algorithm module (21) and 10 integrator S-1Composition, each Bit andits control amount v1, v2, v3, v4, v5, it is every A Bit andits control amount v1, v2, v3, v4, v5Through an integrator S-1The multiple integral obtained afterwards and each Bit andits control amount v1, v2, v3, v4, v5Two integrator S through concatenating-1The double integral obtained afterwards It is all defeated Enter to nerve network system (22)；The input of on-line learning algorithm module (21) is five Bit andits control amount v1, v2, v3, v4, v5's Double integral and corresponding real-time displacement xa(t), ya(t), xb(t), yb(t), zb(t) five error es1(t), e2(t), e3 (t), e4(t), e5(t), output is weight matrix W adjusted0(t+1), weight matrix W0(t+1) neural network is also inputted System (22).
2. permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller according to claim 1, Be characterized in: nerve network system (22) uses structure for 15 × 32 × 5 BP neural network, and trained neural network inputs defeated Relationship is outU is output vector, and z is input variable, and the connection weight matrix of input layer to hidden layer is V0, Connection weight matrix W of the hidden layer to output layer0=[w1,w2,w3,w4,w5]T∈R32×5, w1, w2, w3, w4, w5Indicate one 1 The matrix that row 32 arranges；T is transposition；R32×5Indicate any one 32 row, 5 column matrix；wq=[w1q,w2q,…,w11q,w32q], w1q, w2q,…,w11q,w32qFor connection weight, q=1,2,3,4,5；σ () is general hidden layer excitation function.
3. permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller according to claim 2, Be characterized in: on-line learning algorithm module (21) is according to formulaWhen calculating acquisition t The connection weight matrix w at quarterij(t) correction amount wij(t)；Set error threshold { ε1,ε2,ε3,ε4,ε5, when | ei(t) | < εi When, connection weight matrix wij(t) it does not adjust, when | ei(t) | > εiWhen, obtain the connection weight matrix w at t+1 momentij(t+1), Obtain the weight matrix W at t+1 moment adjusted0(t+1)；I=1,2,3,4,5,For error ei(t) to connection weight square Battle array wij(t) local derviation；μj> 0 is adjustable parameter；J=1,2 ..., 32.
4. permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller according to claim 1, It is characterized in: the exponentially approaching rule of the sliding mode controllerS is sliding-mode surface, and C is system state variables And haveL >=0, ε > 0, k > 0 are system design parameters.
5. permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller according to claim 4, Be characterized in: parameter k is nonlinear function, if e is error amount eax(t), eay(t), ebx(t), eby(t), ebz(t), znFor what is given Fiducial value has z1< z2< ... < zn, mnFor the selective value of k after comparison, there is m0< m1< ... mn, will | e | with z1Compare, if | e |≤ z1, select k=m0, otherwise incite somebody to action | e | with z2Compare, if | e |≤z2, select k=m1, and so on ground compare k and obtain optimal value mn, value mnIt is optimal k value.
6. permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller according to claim 1, It is characterized in: the Bit andits control amount For r1's Derivative,For r3Derivative,For r5Derivative,For r7Derivative,For r9Derivative；s1=c1r1+r2, s2=c2r3+r4, s3 =c3r5+r6, s4=c4r7+r8；c1、c2、c3、c4、c5For sliding-mode surface coefficient；l1、l2、l3、l4、l5>=0, ε1、ε2、ε3、ε4、ε5>0； k1、k2、k3、k4、k5> 0 is system design parameters.
7. permanent-magnet synchronous motor with five degrees of freedom without bearing suspending power subsystem decoupled controller according to claim 1, Be characterized in: composite controlled object is by bearing-free permanent magnet synchronous motor, two degrees of freedom bearing-free permanent magnet synchronous motor levitation force winding Current control module (4), Three Degree Of Freedom AC-DC hybrid magnetic bearing current control module (5), displacement sensor (12), photoelectricity are compiled Code device (13) and angle calculation module (14) composition.
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