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.