indico.cern.ch

indico.cern.ch

Rotor Displacement Self-sensing Method for Six-pole Radial Hybrid Magnetic Bearing Using Mixed-kernel Fuzzy
Support Vector Machine
26th International Conference on Magnet Technology
Tiantian Liu, Huangqiu Zhu, Mengyao Wu, and Weiyu Zhang

Poster ID :Mon-Mo-Po1.09-10(Poster Session)

School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, Jiangsu, China

Background

Simulations
100
80

Operation Principle

S

Permanent
magnet
Stator

40

40

20

Radial
control coils

B1

c1
A1

a1

Rotor
Control flux
N

S

C1

N

k 1

Bias flux

Radial control coils on the corresponding two magnetic poles are
connected in series and the winding directions are opposite, so that
the six control coils can be driven by a three-phase inverter.
The magnetic flux consists of bias flux and control flux, which are
generated by the permanent magnet and the electrification of the
control coils, respectively.

Kernel fuzzy clustering (KFC) algorithm is used to blur the input training
samples. And the objective function expression of KFC algorithm in high
dimensional space is as follows:
N

Mathematical Model

A1
a1
B1
b1
C1
c1
m

GA1

A2

Ga1

a2

GB1

B2

Gb1

b2

GC1

C2

Gc1

c2

1
NiA
4
1
NiA
4
1
NiB
4
1
NiB
4
1
NiC
4
1
NiC
4

GA2
Ga2
GB2
Gb2
GC2
Gc2

m

To simplify the calculation, the
influence of magnetic resistance and
eddy current can be neglected.

Radial suspension forces can be
expressed as follows:

The equation of motion is
shown as
Fx

mx

my Fy mg

In the vicinity of the equilibrium position, the suspension forces in the xand y-direction of the six-pole radial HMB are only linearly related to
the control current and displacement.

0.2

0

Sample sequence (mm)

0.4

0.6

0

-0.4

-0.6

-0.2

0

0.2

Sample sequence (mm)

*
PID Fx

0.6

0.4

ya *

ey

PID

(a) Radial basis kernel function

(b) Polynomial kernel function

Fitting error
Prediction error

80
60
40

0
-0.6

-0.4

-0.2

0

0.2

Sample sequence (mm)

0.4

0.6

(c) Mixed-kernel function

ya

The mixed-kernel function
FSVM method combines the
advantages of polynomial
kernel function and radial
basis kernel function, and
can effectively improve the
prediction accuracy and
fitting ability of the model.

xa

Fy*

ix *
iy*

ia *

ib*
ic*

Current
hysteresis
three-phase
power
inverter

ia

0.1

ib

0

ic

-0.1

-0.2

Six-pole
Radial HMB

0

0.1 0.2

0.3

t/s

0.4

0.5 0.6 0.7

0.3

Mixed-kernel function FSVM
Displacement Prediction Module

Predicted values
Actual values

0.2
0.1

Mixed-kernel function FSVM
Displacement Prediction Module

0
-0.1
-0.2
-0.3

In the floating period, the predicted
values is closer to the actual values.
So the prediction performance of the method proposed
in this paper is good .
-0.4

0

0.1

0.2

0.3

t/s

0.4

0.5 0.6 0.7

Experiments

J m I , U ,V jk m dis 2 ik , v j
j 1 k 1

Mixed-kernel Function

where Kl is the radial basis kernel function, Kl=exp(-||x-xi||/2s2), Kg is the
polynomial kernel function, Kg=((x,xi)+1)3, is the mixing coefficient, 0<<1. 2 3 0 S r m N 30 S r m ix x Fx 2 3 2 r 2 r 3 0 S r m N 30 S r m 2 i y y 2 3 Fy 2 r 2 r -0.2 ex N K m K l (1 ) K g 1 NiA 4 1 NiA 4 1 NiB 4 1 NiB 4 1 NiC 4 1 NiC 4 -0.4 20 y ( x ) k K xk , x b b1 xa* 20 100 According to KTT condition and the Mercer condition, the prediction model of the SVM can be expressed as follows: Predicted values Actual values 0.2 Displacement Prediction Model FSVM 0.3 60 F o cr -e uc rr ne t rt na s of r m ta oi n The six-pole radial hybrid magnetic bearing is mainly composed of a permanent magnet, two pieces of stator, radial control coils and rotor. N The initial displacements of magnetic bearing rotor is x=0.3mm, y=-0.4mm. Fitting error Prediction error 80 60 0 -0.6 Six-pole radial Hybrid Magnetic Bearing 100 Fitting error Prediction error C al kr rt na fs eo m a it no The rotor of a magnetic bearing is suspended in the air gap by using permanent magnet or currents in the coils to generate magnetic force, which has the advantages of no friction, long life, high speed and high precision and so on. So magnetic bearings have been widely used in aerospace, medical instruments, rail transit and other fields. In traditional magnetic bearings, displacement sensors are often used to detect rotor displacements, which provide some problems such as high price, occupying space and increasing system structural complexity. To solve above problems, the self-sensing method is proposed to predict rotor displacements. Self-sensing Modeling When the system is in a stable state, a 50 N disturbance force is added to the rotor. Main paramenters of six-pole radial HMB: Parameters Air gap length d0 Saturation induction density Bs Radial magnetic pole area Sr Maximum ampere-turns of a radial coil (Nrir)max Magnetomotive force of permanent magnet m Width of magnetic poles WHrP Axial width of permanent magnet Wm Magnetic bearing length Values 0.5 mm 0.8 T 260 mm2 160 At 320 At 16 mm 3 mm 25 mm 200 200 100ms 0 0 -200 70ms 0 0.2 0.4 0.6 Time (s) 0.8 1.0 1.2 -200 0 0.2 0.4 0.6 Time (s) 0.8 1.0 1.2 The rotor can quickly return to the equilibrium position, and the system has good anti-interference performance, which verifies the feasibility of the method proposed in this paper. 1) Acquisition and preprocessing of sample data for input and output variables. 2) Initialize parameters. 3) Determine if the particles meet the requirements. 4) Produce the next generation population. 5) Retrain and test the FSVM model. 6) Output the predicted values. Conclusions A self-sensing method using the mixed-kernel function FSVM is proposed to establish the rotor displacement prediction model of six-pole radial HMB. The prediction model between the currents of the control coil and the displacement of the rotor is established, which realizes the self-sensing control of the rotor. The predicted values are nearly equal to the actual values, which proves that the method can accurately detect the displacements of the rotor and realize the stable suspension of the magnetic bearing system.

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