# 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

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.

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

(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
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

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