Proceedings VCM 2012 114 xây dựng hệ điều khiển véc tơ cho động cơ tự nâng kiểu mới

This paper will introduce a salient permanent magnet type axial-gap self-bearing motor ASBM, which is an electrical combination of an axial thrust bearing and an axial-flux motor, as wel

Development of Vector Control System for a Novel Self-Bearing Motor

Xây dựng hệ điều khiển véc tơ cho động cơ tự nâng kiểu mới

Nguyen Quang Dich and Nguyen Huy Phuong

Hanoi University of Science and Technology e-Mail: dichnq@mail.hut.edu.vn

Abstract:

Magnetic bearing motors have many advantages such as no friction loss, no abrasion, no lubrication and so forth However, they are not widely used due to their high cost, complex control and large size In order to solve these problems, a self-bearing motor is a reasonable trend in current researches This paper will introduce

a salient permanent magnet type axial-gap self-bearing motor (ASBM), which is an electrical combination of

an axial thrust bearing and an axial-flux motor, as well as the method of controlling axial position and rotating speed of the ASBM First, the axial force and the motoring torque are analyzed theoretically and then the control method is derived In order to confirm the proposed technique, an ASBM has been made and tested The experimental results confirm that the ASBM works stably with the proposed vector control Moreover, the rotating torque and the axial force can be controlled independently as well

Tóm tắt:

Các động cơ sử dụng ổ từ thường có các ưu điểm như là không có tổn hao do ma sát, không có hao mòn, không cần bôi trơn Tuy nhiên động cơ dùng ổ từ lại thường không được sử dụng phổ biến hiện nay do chúng thường có kích thước lớn, hệ điều khiển phức tạp và giá thành cao Để giải quyết những vấn đề này, động cơ tự nâng –động cơ điện có tích hợp chức năng của ổ từ - đang được nhiều nhà nghiên cứu quan tâm Bài báo này

sẽ giới thiệu một loại động cơ tự nâng kích thích vĩnh cửu loại từ trường dọc trục (ASBM) cũng như phương pháp điều khiển vị trí dọc trục và tốc độ quay của nó Đầu tiên, lực nâng và mô men quay được phân tích về mặt lý thuyết, sau đó phương pháp điều khiển được giới thiệu Để minh chứng cho phương pháp điều khiển được giới thiệu ở trên, động cơ ASBM được chế tạo và thử nghiệm Kết quả thực nghiệm chỉ ra rằng ASBM hoạt động ổn định với phương pháp điều khiển vector được giới thiệu Hơn nữa, mô men quay và lực nâng dọc

trục có thể được điều khiển một cách độc lập với nhau

Nomenclature

displacement

point

inductances of stator

inductances of stator and rotor

stator

currents

Acronyms

1 Introduction

Recently, magnetic bearing motors have been designed to overcome the deficiencies of conventional mechanical bearing motors They show the abilities to work in vacuum with no lubrication and no contamination, or to run at high speed, and to shape novel rotor dynamics Therefore, they are very valuable machines with a number of novel features, and with a vast range of diverse applications [1]

The conventional magnetic bearing motor usually has structures like a rotary motor installed between two radial magnetic bearings or mechanical combination of rotary motor and radial magnetic bearing as shown in Figs 1 and 2, in

which, two radial magnetic bearings create radial

levitation forces for rotor, whilst an axial magnetic

bearing produces a thrust force to keep the rotor in

right axial position to the stator However, these

types of magnetic bearing motor are large size,

heavy weight and complex control, which cause

problems in some applications that have limit

space [2],[3] For this reason, simpler and smaller

construction and less complex control system are

desirable

The Earnshaw’s theorem shows that a rotor can

be supported stably by static magnetic field when

being controlled by one axis actively Therefore, if

a stator has capabilities of producing a rotating

torque and controlling one axis actively, the

non-contact levitation can be realized in small and

simple structure Based on this feature, an

axial-gap self- bearing motor (ASBM) has been

introduced as in Fig 3 It is an electrical

combination of an axial flux motor and an axial

magnetic bearing, which is simpler in structure

and control than the conventional magnetic

bearing motor since hardware components can be

reduced [4],[5],[6] This type of motor can be

realized as induction (IM) [5], or permanent

magnet (PM) motor [6],[7],[8] The PM type

motor is specially paid attention, due to its high

power factor, high efficiency and simplicity in

production

In this paper, the salient 2-pole ASBM with

double stators is introduced The closed-loop

vector control method for the axial position and

the speed is developed in the way of eliminating the influence of each other Moreover, the compensational method for reference currents based on the difference between d and q axis inductances is also recommended In order to confirm the presented technique, an experimental setup has been made and tested

2 Modeling and Control

Fig 4 illustrates the principle structure of the proposed axial gap self-bearing motor The radial

motions x, y, θ x , θ y of the rotor are constrained by radial magnetic bearings such as the repulsive bearing Only rotational motion and translation of

rotor along z axis are considered The motor has

two degrees of freedom

The rotor is a flat disc with permanent magnet (PM) inserted on two faces of disc to create a salient-pole rotor Two stators, one in each side of the rotor, have three-phase windings to generate the rotating magnetic flux in the air gap that

produces the motoring torque T 1 and T 2 to the rotor and generates the attractive force between the rotor

and the stators F 1 and F 2 The total motoring

torque T is sum of those torques and the axial force F is different between two attractive forces

To get mathematical model of the ASBM, first,

the axial force F s and motoring torque T s are calculated for one stator Similar to the conventional permanent magnet motor, the mathematical model of the ASBM is also presented in rotor field oriented reference frame or

Fig 4 The principle structure of the axial gap self

bearing motor

u -v

Rotor

Stator

Fig.5 Coordinates

Fig 1 Structure of conventional magnetic bearing motor

Fig.2 Structure of radial combined magnetic bearing

motor

Fig.3 Structure of axial gap self bearing motor

so-called d, q coordinates as indicated in Fig 5,

where the d axis is aligned with the center lines of

permanent magnets and the q axis between the

magnets The axes u, v and w indicate the

direction of the flux produced by corresponding

phase windings The power invariant principle is

used for transforming between coordinates The

phase difference between the u axis and d axis is

an angular position θ of the rotor or the rotor flux

vector

Since the permanent magnet with unity

permeability is used, the rotor is salient type,

hence the self phase inductance of the stator is

dependent on the rotor angular position, which

means d axis inductance is different from q axis

inductance is a function of the air gap g between

rotor and stator Normally, the self phase

inductance is inversely proportional to the air gap,

so the d and q axis phase inductance of the stator

windings may be approximated by

0

0

3

2

3

2

sd

sq

L

g

L

g















in whichL sd0,L sq0 are effective inductances per unit

gap in d and q axis, and L sl is leakage inductance

Then, the stator voltage and flux of the ASBM

in the d,q coordinates can be expressed in the

following equations:

sd

sq

sd sd sd m

sq sq sq

di

dt di

dt

L i

L i





















with m is the flux linkage caused by rotor

magnetic field For simplicity, the permanent

magnet of the rotor is replaced by an equivalent

winding with current i f and inductance of rotor

winding L f It can be expressed only in d axis as

follows

f fd i L f f L i m sd

2

sd

L

g



and mutual inductance L m 3L sd 0/ 2g

(5)

From (1) to (3), the magnetic energy in the air

gap is calculated as

( f f sd sd sq sq) / 2

Therefore, the attractive force of a stator is received by derivative of magnetic energy with air gap

0

3 3

sq sd

L L

W







and motoring torque of a stator is derived by using Fleming left hand rule

0

3

s sd sq sq sd

sd sq sd

PL



with P is number of pole pairs

From (8) we can see that output torque is a combination of excitation torque and reluctance torque That means, in every operation mode, the motor has to produce an additional torque to compensate the reluctance torque In the non-salient pole rotor, this reluctance torque can be ignored to make control system become more simply But in the salient pole rotor when the reluctance torque can reach the relative high amplitude, the neglect of this torque component will reduce the quality of system, especially in

operation mode with axial load (i d ≠ 0)

From (7) and (8) F1 and T1 are calculated by substituting gg0z, i sd i d1 and i sqi q1, and F2

and T2 are calculated by substituting gg0z,

2

sd d

i i and i sqi q2 Thus, the total axial force F and torque T are given by:

1 2

(10) here, g0 is the axial gap at the equilibrium point

and z is the displacement

For linearization at the equilibrium point (z = 0)

we expand (9) and (10) into Mac Laurin series and take the first order term, the result is:

0

1 1 2 2 2 2 1 1

0

z

g

z

g

(11)

(12)

in which 2 2

force factors, K T  3PL i sd0 f / 2g0 and

To increase the total moment twice the

component moment created by one stator, the

moment-generated current must be same direction

and value In order to keep the rotor in right

position between two stators, the forces acting on

rotor from both sides must be same value but

inverse, i.e under the effect of axial load, if the

force-generated current of one side increases then

that current of other side has to decrease the same

amount, correspondingly The rotating torque can

be controlled effectively by using q-axis current,

and the axial force can be controlled by changing

the d-axis current We suppose that









(13)

with i d0 is an offset current, and the value can be

zero or a small value around zero, then by

inserting (13) into (11) and (12), we receive

0

T q R d q R d q

eff rl rlz

0 0

Fd d d f Fd f d Fq q

Fd f d d

z

g



From (14), the total torque consists of three

components:

The first component T eff 2K i T q is the efficient

torque, this is main component of the output torque

The second one T rl02K i i R d0q is the reluctance

torque caused by bias current i d0 Therefore, if we can assure that i d1 i d2   i.e i d i d00then this reluctance torque is eliminated

The last one T rlz 2K i i z g R d q / 0 is reluctance

torque caused by current i d under the effect of the

displacement z When the displacement is well

controlled to be zero, or very small in comparison

with air gap at the equilibrium point g 0, the influence of this component can be neglected Then the total torque becomes as follows

2 T q

By using above control law, we also receive the axial force as follows

4 Fd f d

Obviously, the effect of the inductance difference to axial force is also vanished

From (16) and (17), it is easy to see that the total torque can be controlled with the quadrate axis current and axial force can be controlled with the direct axis current And in combination with (1) the mathematic model of the ASBM is totally constructed with voltage, force and torque equations It is supposed that they are simple linear equations, so the control system can be easily implemented with the conventional controllers For simplicity, it is assumed that the radial motion of the rotor is restricted by ideal radial bearings Therefore, the axial motion of the rotor

is independent from radial motion The dynamic equation of the axial motion of the rotor is

Fig 6 The control scheme of the axial gap self bearing motor

Fmz (18)

where m is mass of moving part, and F is the axial

force shown in (15) Then by substituting (15) into

(18), we receive

0

4 Fd f d 4 Fd(d f) 4 Fq q z

g

or summarized as

with K z  4K Fd(i d2i2f)4K i Fq q2 is stiffness of

the ASBM and K m 4K i Fd f is force gain It is

easy to realize that K z is negative, which means

this system is unstable To stabilize the system, the

controller with derivative component must be

used Assuming that, the proportional derivative

controller (PD) is used, the output of the controller

will represent the direct axis reference current, i.e

with K p and K d are proportional and derivative

constant of the axial position controller By

substituting (21) into (20), we get

The necessary condition for the system

becomes stable only when all constant coefficients

of the polynomial function are the same sign

Therefore, if K d > 0, the proportional constant

must satisfy the condition

z

p

K

K

to ensure that the system is stable

Actually, there has steady-state error when only

PD controller is used, hence to remove the

steady-state error, the PID controller should be used

As stated above, the motoring torque of the

ASBM can be controlled by q-axis current (i q),

while the axial force can be controlled by d-axis

proposed for the ASBM drive is shown in Fig 6

The axial displacement from the equilibrium

point along the z-axis, z, can be detected by the gap

sensor The detected axial position is compared

with the axial position command z ref, then the error

is inserted in the axial position controller Rz The

output of the axial position controller is used for

compensation procedure from (15) Position

command z ref is always set to zero to make sure the

rotor is right in the midpoint between the two

stators The d-axis reference currents for the two

stator windings i d1ref and i d2ref can be generated by

using the offset current i d0 subtracting and adding

i dref respectively In this paper, the value of the offset current is zero

The rotor speed detected from encoder is compared to the reference speed, then, the difference is input of the speed controller Rω The output of the speed controller is used for calculating the q-axis reference current by using (14), the q-axis reference currents for the two stator windings are same with this current

The motor currents in the two-phase stator reference frame α,β are calculated by the measurement of two actual phase currents Therefore, the d,q components are obtained using the rotor position from encoder The quadrate components are controlled to the reference value which is given by the speed controller, while the direct components are controlled to the reference value which is given by the axial position controller The outputs of the current controllers, representing the voltage references, are afterward directed to the motor through inverters using the Pulse Width Modulation (PWM) technique, once

an inverse transformation from the rotating to the three phase stator referent frame has been performed All controllers are standard PI controllers except axial position one (PID)

3 Implementation and Results 3.1 Hardware

In order to confirm the proposed control method for the PM type ASBM, an experimental setup was set up which is shown schematically in Fig 7 The rotor disc has a diameter of 50 mm and two neodymium iron magnets with the thickness of 1mm for each side are inserted into its surfaces to create one pole pair For experimental simplicity, the rotor is supported by two radial ball bearings in order to restrict the radial motion of the rotor The stator has a diameter of core 50 mm and six concentrated wound poles, each with 200 coil turns The stators can slide on linear guide to ensure the same desired air gap between rotor and two stators A DC generator (Sanyo T402) is installed to give the load torque In order to measure the rotor angle and the axial position, a rotary encoder (Copal RE30D) and an

eddy-Fig 8 Picture of the experiment setup

current-type displacement sensor (Sentec

HA-101S) are installed, respectively

The control hardware of the ASBM drive is

based on a dSpace1104 board dedicated to control

of electrical drives, which includes PWM units,

general purpose input/output units (8 ADC and 8

DAC) and encoder interface The DSP reads the

displacement signal from the displacement sensor

via an A/D converter, and the rotor angle position

and speed from the encoder via an encoder

interface Two motor phase currents are sensed,

rescaled, and converted to digital values via an

A/D converter Then, the dSpace1104 calculates

reference currents using the rotation control and

axial position control algorithms and send its

commands to three-phase inverter board The

ASBM is supplied by two three-phase PWM

inverters with switching frequency of 40 kHz

The image of the experimental setup is

presented in Fig 8 and the parameters of the

ASBM is shown in table 1

Table 1 Parameters of the ASBM

resistor

Rs = 2.6Ω

Stator phase

per unit air gap

6 8.2 10 Hm

sd0

L   

Stator phase

per unit air gap

6 9.6 10 Hm

sq0

Leakage

inductance

3

6 10 H

sl

 

equilibrium point

0 1.7

Rotor flux

3.2 Experimental Results

Fig 9 shows the response of axial displacement and speed when the ASBM starts

Figure 7 Overview of control hardware of the ASBM

Fig 9 Response of displacement and speed at start

Fig 10 Response of displacement when speed

changed

to work First, the displacement error is 0.32mm

When the controllers is on, the displacement

jumps immediately to zero and the rotor speed

reaches 1500 rpm after 0.5s without influence of

each other

In the second experiment, the influence of rotor speed to the displacement is conducted by changing speed from 1500rpm to 1000 rpm and vice versa The result is shown in Fig 10 Obviously, the displacement controller and speed controller work independently with each other

4 Conclusion

The axial gap self bearing motor was fabricated

with salient PM type rotor and the vector control

was implemented The results confirm that the

motor can perform both functions of motor and

axial bearing without any additional windings

Furthermore, by using this proposed control

method, the axial displacement and speed are

advantages, the ASBM can be used for many kind

of applications, which require small size, high

speed and levitation force such as liquid pumps,

compressors and machine tools

Tài liệu tham khảo

[1] M Dussaux, “The industrial application of the

active magnetic bearing technology,” in Proc

2nd Int Symp Magnetic Bearings, Tokyo,

Japan, July 12–14, 1990

[2] A Chiba, T Deido, T Fukao and M A

Rahman “An analysis of bearingless AC

motors”, IEEE Trans Energy Conversion, vol

9, pp 61-67, Mar 1994

[3] Y Okada, K Dejima and T Ohishi, “Analysis

and comparison of PM synchronous motor and

induction motor type magnetic bearing”, IEEE

Trans Industry Applications, vol 32, pp

1047-1053, Sept./Oct 1995

[4] Y Okada, S Ueno, T Ohishi, T Yamane and

C C Tan, “Axial type self bearing motor for

axial flow blood pump”, Int Society for

Artificial Organs vol 27, pp 887-891, 2003

[5] S Ueno and Y Okada, “Vector control of an

induction type axial gap combined

motor-bearing”, in Proc of the IEEE Int Conf on

Advanced Intelligent Mechatronics, Sept

19-23, 1999, Atlanta, USA, pp 794-799

[6] S Ueno and Y Okada, “Characteristics and

control of a bidirectional axial gap combined

Mechatronics, Vol 5, No 3, Sept 2000, pp

310-318

[7] D Q Nguyen and S Ueno “A study on axial

gap self bearing motor drives”, Proc of the

Int Symposium on Micro/Nano system

technology, CD Rom, Dec 2008

[8] D Q Nguyen and S Ueno “Sensorless speed

control of a permanent magnet type axial gap

self bearing motor”, Journal of System Design and Dynamics, Vol 3, No 4, July 2009, pp 494-505

[9] A E Fitzgerald, C Kingsley Jr., and S D Uman, Electric Machinery, 5th edition, McGraw-Hill, New York,1992

[10] A Chiba, et al., Magnetic Bearings and Bearingless Drives, 1st edition, Elsevier, Great Britain, 2005

Quang Dich Nguyen was

born in Bac Ninh, Viet Nam

He received the B.S degree

in electrical engineering in

1997 from Hanoi University

of Technology, Ha Noi, Viet

2003 from Dresden University of Technology,

Mechatronics at Ritsumeikan University, Shiga, Japan

From 2000 he joined the Department of Industrial Automation, Hanoi University of Technology His main interests include magnetic bearings, self-bearing motor, sensorless motor control

Huy Phuong Nguyen

Vietnam He received the

(1997) and Ph.D (2000)

Industry from Moscow

Federation

From 2002 he joined the Department of Industrial Automation, Hanoi University of Science and Technology

His main interests include automatic control and process control in power plant