Control system. Electrical engineering

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Abstract— This paper describes the design of feedback

linearization and fuzzy PI controllers for the maglev guiding

system of linear elevator. The controllers so designed based on

the nonlinear control techniques are applied to control the gap

of permanent magnet synchronous linear motor (PMLSM)

with the aim of improving the vertical thrust and control the

horizontal vibration and noise in the process of elevator

operation. Matlab modeling of this system is used in this paper.

The simulation result of the entire system are presented in this

paper.

Key words: Maglev Guiding System, Fuzzy PI Control,

Nonlinear control, Linear Elevator, Feedback Linearization

I. INTRODUCTION

ONIENTIONAL elevators consist of an elevator car in

a shaft operated by a rope, which is mounted on a

traction sheave. The mechanical guiding of such

elevators is well-known. Usually, slideways or roller guides

are used. However, compared with non-contact solutions,

the conventional lead frame has many disadvantages. Since

more and more high- rise buildings occur in world, the

efficiency of passenger transport become more important.

The higher the speed is, the more deteriorated the effect is.

Conventional rail require lubrication and regular

maintenance. The improved non-contact rail can get higher

comfort through subtractive the audible noise and

controlling the oriented stiffness[1][2].

The conventional elevator guide shoes prone to car

vibration when the elevator is running at high-speed. The

elevator vibration is one of the concerns in engineering

circles, it should be said that mechanical and electrical

reasons can be individually or jointly caused the vibration of

elevator system. Suspension technologies has brought the

technological innovations, the planform and stereogram of

placement for the maglev guiding device can been seen as in

Fig.1and Fig.2.

The elevator external disturbances and non-linear friction

for elevator guide shoes has a larger impact, such as, when

the elevator is running at low speed, such as leveling or

maintenance parking, a slow-fast phenomena will be occur

This work is supported by Liaoning Province Education Department Fund #L2010404.

Qing Hu is with the School of Electrical Engineering, Shenyang University of Technology, China (e-mail: [email protected]).

Mingliang Hao is with the School of Electrical Engineering, Shenyang

University of Technology, China (e-mail: [email protected]). Hao Liu is with the School of Electrical Engineering, Shenyang

University of Technology, China (e-mail: [email protected]).

sometimes, in severe cases, even a high-frequency vibration

and vibration noise will appear, this time it has led to

elevator car panels resonance in fact, which the comfort of

the elevator riding is seriously affected. Therefore, magnetic

levitation technology is applied to elevator guide shoes to

restrain the car disturbance and vibration problems. In the

elevator is running, the stability of air gap for liner motor is

particularly important, it can be affects the magnitude of the

propulsion force, using magnetic levitation guide shoes, by

controlling its current, the air gap of the magnetic levitation

(also called the air gap of linear motor) is controlled[3-6].

II. SYSTEM DESCRIPTION AND MODELING

According to Newton's second law, suppose the gravity

and the linear motor thrust balance with each other and

obtain the equations of motion:

( ) ( ) ( ) ( )tFiFtFtm DK , +−= δδ (1)

Fuzzy PI Control of Maglev Guiding System based on Feedback

Linearization

Qing Hu , Mingliang Hao , Hao Liu,

C

Fig. 1: Linear elevator with maglev guiding system

Fig. 2: Stereogram of linear elevator with maglev guiding system

1213978-1-4244-8738-7/11/$26.00 c©2011 IEEE

where , )(tδ , F(i, ), and FK(t)and FD(t) is the air gap

length, differential of air gap, electromagnetic force, another electromagnetic force, and external disturbance force,

respectively.

Due to the resistance in the electromagnet and the rail has

been ignored, the reluctance of magnetic circuit composed

of electromagnets and maglev rail focused on the air gap

between the two, the effective air-gap reluctance as follows:

A R

0μ

δ = (2)

where 0 and A is permeability of the vacuum and

cross-section of the air gap respectively.

The pulling force of the electromagnetic force is given by

( ) ( )

( )t tiAN

iF 2

22 0

4 ,

δ

μ δ −= (3)

which N and ( )ti is the number of winding turns and the current of single maglev device.

( ) ( ) ( )

( ) ( )

( ) ( )t

t

tiAN ti

t

AN tRitu δ

δ

μ

δ

μ 2

2 0

2 0

22 −+= (4)

Math model of a single electromagnetic device is obtained

as follow:

( ) ( ) ( ) ( )

( ) ( )

( )

( ) ( ) ( )

( ) ( )

( ) ( )−+=

−=

+−=

t t

tiAN ti

t

AN tRitu

t

tiAN iF

tFiFtFtm

δ δ

μ

δ

μ

δ

μ δ

δδ

2

2 0

2 0

2

22 0

DK

42

4 ,

,

(5)

where 4

2 0 AN

k μ

= and [ ]T321 xxx=x , the state

variable δ=1x , δ=2x ix =3 , and output of system

1xy == δ are chosen, then nonlinear state function is

obtained

( ) ( )

=

+++−=

1

KD

1

2

2

3

2

3

2

1

0

0

2

0

0

xy

m

tF

m

tF u

k

xx

x

m

k

x

x

x

x

(6)

where ( )

m

tFK can be seen as the disturbance as

( ) m

tFD .

III. CONTROLLER DESIGN

A. Feedback Linearization

State variable vector is chosen as follow,

[ ] T

1

3 21

T 321 −==

x

x

m

k xxzzzz (7)

then the state function of system can be derived[7]

[ ] ==

+=+=

Cz

BAzzz

001

1

0

0

000

100

010

y

vv (8)

Nonlinear voltage feedback control principle is given by

( ) ( ) v x

mx Rxvxxu

3

1 3 −=+= βα (9)

B. PI State feedback Controller Design

The definition of deviation e(t) is given by

( ) expyyte −= (10)

where y is the actual output of the system. From the state

space function (8), yexp is defined as expected output of the

system. By integration of the system deviation p can be

derived

( )= t

ttep 0

d . (11)

then derivative of p is obtained

( ) ( ) expytetp −== Cz (12)

By equation (8) and (12) together form the augmented

system, its open-loop state equation is derived

[ ]=

− ++=

p y

y v

p

z C

Bz

C

Az

0

0

000

0

exp (13)

1214 2011 Chinese Control and Decision Conference (CCDC)

where augmented system is controllable.

In order to achieve arbitrary pole placement, the following

state feedback control law is chosen as follow:

[ ]= p

Kv z

K I (14)

where the state feedback gain vector K is defined

[ ]210 KKK=K (15)

and KI is the integral coefficient is set as follow:

( )+++= t

tteKzKzKzKv 0

I322110 d (16)

C. Fuzzy PI Controller Design

After linearization in order to eliminate the ignored

factors, which impact on the system, this paper adopts the

fuzzy PI control method to design controller.

Fuzzy control principle and membership function is seen

as Tab.1 and Fig.3, respectively.

IV. SIMULATION

Reference maglev model and fuzzy PI control are

proposed, the entire system is comprised of the above two

parts. Matlab Simulink of system is seen as Fig.4 to Fig.6,

respectively.

The parameters of the magnetic levitation system for

single maglev device are: A = 0.50×0.50m2, N = 400 turns,

= 0.003m, FK = 5000N, M = 500kg. The simulation results

are shown in Fig.7, 8, 9, 10 and 11. Fig.7 is given and sensed

air gap of single maglev device without external

disturbance; the air gap error of maglev system can be

reduced rapidly.

TAB. 1: FUZZY CONTROL LAW

EC

E

NB NM NS ZO PS PM PB

NB

NM

NS

ZO

PS

PM

PB

PB

PB

PM

PM

PS

PS

ZO

PB

PB

PM

PM

PS

ZO

ZO

PM

PM

PM

PS

ZO

NS

NM

PM

PS

PS

ZO

NS

NM

NM

PS

PS

ZO

NS

NS

NM

NM

ZO

ZO

NS

NM

NM

NM

NB

ZO

NS

NS

NM

NM

NB

NB

Fig. 3: Membership function

Fig. 4: Maglev device model

Fig. 5: Fuzzy PI control model

Fig. 6: Single maglev system model

Fig. 7: The air gap of single maglev device (without external

disturbance)

2011 Chinese Control and Decision Conference (CCDC) 1215

Fig.8 and Fig.9 are external disturbance force and

response of the maglev force, respectively. The disturbance

force at 350N is added to the single maglev device started at

t = 0.45s, and ended at t = 0.5s, respectively. Fig.10 is the

acceleration of maglev device.Fig.11 is the air gap of single

maglev device added the external disturbance.

V. CONCLUSION

This paper deals with control design of the maglev

guiding system in linear elevator. Based on the control

requirements that is robustness and following behaviors of

maglev device.

Feedback linearization is used in maglev device.

Meanwhile, the fuzzy PI controller is designed. Simulation

results have shown that the built controller achieves good

performance with robustness.

REFERENCES

[1] Morishita M, Akashi M.Electromagnetic Non-contact Guide System

for Elevator Cars [C]. The Third International Symposium on Linear Drives for Industry Applications, Nagano, Japan, October 2001, pp.

416-419. [2] Inaba H, Shigeta M.,Ando T, ect. Attitude control system of a

super-high speed elevator car based on magnetic guides [J]. Industrial

Electronics, Control and Instrumentation, 1994, 2, pp. 1028 – 1033. [3] M. Miyatake, T. Koseki, S. Sone. Evaluation of Operational

Performance in Ropeless Elevator Systems[J].Journal of The Japan Society of Applied Electromagnetic and Mechanics, 1997,Vol. 5, No.

3, pp. 49-55.

[4] Benedikt Schmülling, Oliver Effing, Kay Hameyer. State Control of an Electromagnetic Guiding System for Ropeless Elevators [C].

Power Electronics and Applications, 2007 European Conference , 2007, pp. 1-10.

[5] Benedikt Schmulling, Rudiger Appunn, and Kay Hameyer.

Electromagnetic guiding of vertical transportation vehicles: state control of an over-determined system [C]. Proceeding of the 2008

International Conference on Electrical Machines, 2008, pp.1-6. [6] K. Yoshida, S. Moriyama, X. Zhang. Contactless Elevator Motion

Control in Ropeless Linear Elevator [J].2003 National Convention

Record, IEE Japan, 5-084, pp.130. [7] R. Appunn, B. Schmulling and K. Hameyer. Electromagnetic Guiding

of Vertical Transportation Vehicles: Experimental Evaluation [J]. IEEE Transactions on Industrial Electronics, 2009, pp.1109-1117.

Fig. 8: External disturbance force

Fig. 9: Response of maglev force

Fig. 10: Acceleration of maglev device

Fig. 11: The air gap of single maglev device (added the external disturbance)

1216 2011 Chinese Control and Decision Conference (CCDC)

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