speed sensor less control of im using sliding mode observer with variable boundary layer

8/14/2019 Speed Sensor Less Control of IM Using Sliding Mode Observer With Variable Boundary Layer

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Speed Sensorless Control of Induction Motor Using Sliding Mode Observerwith Variable Boundary Layer

Min Yeong Jang, Bong Su Jang, Jun Ik Jeong, Yong Hun Park, and Young Ahn Kwon

School of Electrical Engineering, Pusan National University, Busan, Korea(Tel : +82-51-510-2372; E-mail: [email protected])

Abstract: The vector control in the speed and torque controlled ac drive is typically implemented through measuringthe rotor speed or position. However, speed and position sensors require the additional mounting space, reduce thereliability in harsh environments and increase the cost of a motor. Therefore, many studies have been performed for theelimination of speed and position sensors. This paper investigates an improved sliding mode observer for the speedsensorless control of an induction motor. The proposed control strategy is the sliding mode observer with a variable

boundary layer for a low-chattering and fast-response control. mulation and experimentation have been performed toverify the proposed control algorithm.

Keywords: induction motor, sensorless control, sliding mode observer

1. INTRODUCTION

The vector control in the speed and torque controlledac drive is widely used for a high performanceapplication. The vector control of an induction motor istypically implemented through measuring the rotor speed or position. However, speed and position sensorsrequire the additional mounting space, reduce thereliability in harsh environments and increase the cost of a motor. Various control algorithms for the eliminationof speed and position sensors have been proposed[1-5]:algorithms using state equations, model referenceadaptive systems (MRASs), Luenberger or Kalman-filter observers, saliency effects, sliding mode controls,

artificial intelligences, direct controls of torque and flux,and the current error correction. Most sensorlessalgorithms are based on the flux and speed estimationswhich are obtained from the voltage equations, and sothey are sensitive to the electrical and mechanical

parameters. This paper investigates an improved slidingmode observer for the speed sensorless control of aninduction motor. The sliding mode control is typicallyrobust to the plant parameter variation and systemdisturbance[6,7]. However, a sliding mode control has achattering problem due to the control discontinuity andswitching action. The proposed sliding mode control inthis paper is using the sliding mode observer with a

variable boundary layer for a low-chattering andfast-response control. The proposed algorithm isverified through the simulation and experimentation.

2. MATHEMATICAL MODELING OFINDUCTION MOTOR

Fig. 1 shows the real, stationary and synchronouslyrotating axes of a 3-phase symmetrical induction motor.The voltage and flux equations in the real axes may beexpressed as

+

+

=

abcr

abcs

r r sr

sr s s

abcr

abcs

i

i

LR L

LLR

v

v

p p

p pT )( (1)

as

ar

bs

cs

dsqs

r

r

s

s

e

sl

e

Fig. 1 The real, stationary and synchronously rotating

reference axes

=

abcr

abcs

r sr

sr s

abcr

abcs

i

i

LL

LL

T )((2)

where [ ]cs bs as T f f f =)( abcsf ,

[ ]cr br ar T f f f =)( abcr f ,[ ]s s s RRRdiag= sR ,[ ]r r r RRRdiag=r R ,

+

+

+

=

mslsmsms

msmslsms

msmsmsls

LLLL

LLLL

LLLL

sL ,

+

+

+

=

mslr msms

msmslr ms

msmsmslr

LLLL

LLLL

LLLL

r L ,

SICE Annual Conference 2008August 20-22, 2008, The University Electro-Communications, Japan

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+

+

+

=

r r r

r r r

r r r

sr

cos)3

2(cos)

32

(cos

)3

2(coscos)

32

(cos

)3

2(cos)

32

(coscos

ms LL

From (1) - (2), - and - axis voltage and fluxequations in the stationary reference frame fixed to thestator may be expressed as

s s s sv p+= iR (3)

s s s s v p+= iR (4)

r r r r r ++= piR0 (5)

r r r r r += piR0 (6)

r m s s r s m s ls s iLiLiiLiL +=++= )( (7)

r m s s r s m s ls s iLiLiiLiL +=++= )( (8)

s m r r r s m r lr r iLiLiiLiL +=++= )( (9)

s m r r r s m r lr r iLiLiiLiL +=++= )( (10)

where msm LL 23

= ,dt

d r r

= .

From (1) - (2), d - and q - axis voltage equations inthe reference frame with the synchronously rotating

speed of e may be expressed as

qsedsds sdsv += piR (11)

ds e ds qs s qs v ++= piR (12)

qr r e dr dr r )(0 += piR (13)

dr r e qr qr r )(0 ++= piR (14)

dr m ds s dr ds m ds ls ds iLiLiiLiL +=++= )( (15)

qr m qs s qr qs m qs ls qs iLiLiiLiL +=++= )( (17)

ds m dr r dr ds m dr lr dr iLiLiiLiL +=++= )( (18)

qs m qr r qr qs m qr lr qr iLiLiiLiL +=++= )( (19)

The electromagnetic torque in the synchronouslyrotating speed reference frame may be expressed as

)( dsqr qsdr r

me

L P T ii

L =

223

(20)

where P is the number of poles.

The mechanical equation of a motor may be expressedas

Lmm T Dt d

d J T ++=

(21)

where J is the inertia coefficient and D is the frictioncoefficient, m is the mechanical speed of the rotor,and LT is the load torque.

3. IMPROVED SLIDING MODE OBSERVER

FOR SENSORLESS INDUCTION MOTOR

This paper proposes a novel sensorless controlalgorithm based on the sliding mode observer. Ingeneral the sliding mode observer for a motor control isimplemented through the error between the measuredand estimated currents[8-10]. In an induction motor, theerror between the measured and estimated currents isused to construct sliding mode surfaces so that after sliding mode happens, the estimated fluxes are driven to

converge to real ones exponentially.From (3) - (10), the state equations of the slidingmode observer in the stationary reference frame may beexpressed as

)(

si

siuK

svBxA

x++=

t d d

(22)

xCs

i = (23)

xDr

= (24)

where ^ means the estimated value, K is the switchinggain, u is switching function, and

=

r

si

x , = si si

si , =

r

r

r

, = s

s

v

v

sv ,

=

22A

21A

12A

11A

A ,

+=

1001

r s

s

T

LR

11A ,

=

r r

r r

r s

m

T T

/1/1

LL

L

12A , =

10

01

r

m

T L

21A ,

=

r r

r r

T

T

/1

/1

22A ,

r s

2m

LL

L= 1 ,

r

r r

R

LT = ,

=

2B

1B

B , =10011

s L 1

B , =0000

2B ,

=

00100001

C , =10000100

D .

The proposed sliding mode control in this paper isusing the sliding mode observer with a variable

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boundary layer for a low-chattering and fast-responsecontrol. Fig. 2 shows the variable boundary layer of the

proposed sliding mode observer.

s

VariableBoundary

layer

50rpm

u 50rpm

u 200rpm u

200rpm

Fig. 2 Control input with a variable boundary layer

The rotor speed is estimated from the currents andfluxes obtained in (22) as follows:

+=

dt iiii K

iiii K

r s sr s si

r s sr s s p

))sgn()sgn(

))sgn()sgn(

21

21

k(k

k(kr (25)

The overall system of the proposed sensorless controlalgorithm is shown in Fig. 3.

PI

PI

PI

SpaceVectorPWMiqs*

iqs

ids

ProposedSMO

VectorRotation

IM

V dc

VectorRotation

e

ids*

r

* r

ds qs

s

s

i s

i s

Fig. 3 Configuration of the overall system

4. SIMULATION

The simulation has been performed to verify the proposed control algorithm applied to a sensorlessinduction motor. Table 1 shows the specification of theinduction motor used in the simulation andexperimentation.

Table 1 Motor specification

Rated Power 3 hp r R 1.5

Rated Voltage 220 V s L 245 mH

Pole Numbers 4 r L 247 mH

s R 2.7 m L 236 mH

Fig. 4 (a), (b) and (c) show the speed responses in thespeed commands of 20rpm, 50rpm and 800rpm and inthe no load.

0 1 2 3 4 50

10

20

300 1 2 3 4 5

0

10

20

30

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(a)

0 1 2 3 4 50

25

50

0 1 2 3 4 50

25

50

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(b)

0 1 2 3 4 50

400

800

0 1 2 3 4 50

400

800

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(c)

Fig. 4 Speed responses in the speed command of (a) 20 rpm (b) 50 rpm (c) 800 rpm

As shown in Fig. 4, the proposed sensorless controlalgorithm has good speed responses in the low and highspeeds.

Fig. 5(a) and Fig. 5(b) are the simulation resultsobtained for the comparison with the sliding modecontrol algorithm without variable boundary layer incase of considering the parameter variation. Fig. 5(a)and Fig. 5(b) show the speed responses in case the rotor winding resistance is increased by 30% of the nominalvalue and the load torque of 6Nm is applied in themiddle of the operation of 200rpm. As shown in the



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figures the proposed sensorless control algorithm has animproved and robust performance.

4 6 8 10 12 14100

200

3004 6 8 10 12 14

100

200

300

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(a)

4 6 8 10 12 14100

200

3004 6 8 10 12 14

100

200

300

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(b)

Fig. 5 Speed response in the rotor resistance increased

by 30% with the load variation (200rpm, 0 6Nm)(a) without variable boundary layer

(b) with variable boundary layer

5. EXPERIMENTS AND DISCUSSIONS

The experimentation has been performed to verify the proposed algorithm applied to a sensorless inductionmotor. The Intel-Pentium microprocessor system is usedfor the digital processing of the proposed algorithm.

Fig. 6 (a), (b) and (c) show the experimental speedresponses in the speed commands of 20rpm, 50rpm and

800rpm and in the no load.

0 1 2 3 4 50

10

20

300 1 2 3 4 5

0

10

20

30

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(a)

0 1 2 3 4 50

25

50

0 1 2 3 4 5

0

25

50

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(b)

0 1 2 3 4 50

400

800

0 1 2 3 4 50

400

800

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(c)

Fig. 6 Experimental speed responses in the speedcommand of

(a)20 rpm (b) 50 rpm (c) 800 rpm

The proposed sensorless control algorithm has goodspeed responses in the low and high speeds same as thesimulation result.

Fig. 7 is the experimental result obtained for thecomparison with the sliding mode control withoutvariable boundary layer in case that the rotor resistanceis increased by 30% of the nominal value, and the loadtorque 6Nm is applied in the middle of the operation of the speed command 200rpm.As shown in the experimental results, the proposedsensorless control algorithm has an improved and robust

performance.

4 6 8 10 12 14100

200

3004 6 8 10 12 14

100

200

300

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(a)



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4 6 8 10 12 14100

200

300 4 6 8 10 12 14

100

200

300

S p e e

d [ r p m

]

Time [sec]

Estimated Speed

S p e e

d [ r p m

]

Real Speed

(b)

Fig. 7 Experimental speed response in the rotor resistance increased by 30% with the load variation

(200rpm, 0 6Nm)(a) without variable boundary layer

(b) with variable boundary layer

6. CONCLUSIONS

This paper proposed a novel speed sensorless controlalgorithm of an induction motor based on the slidingmode observer. The sliding mode observer isimplemented through the error between the measuredand estimated currents. The error between the measuredand estimated currents is used to construct sliding modesurfaces so that after sliding mode happens, theestimated fluxes are driven to converge to real ones

exponentially. The proposed sliding mode control in this paper is using the sliding mode observer with a variable boundary layer for a low-chattering and fast-responsecontrol.

The simulation and experimental results indicate thatthe proposed algorithm shows good speed responses inthe low and high speeds, and shows robust speedresponses in the rotor resistance variation. Especially,

the proposed algorithm shows a better performance inthe parameter variation compared to the conventionalalgorithm.

REFERENCES

[1] Edited by K. Rajashekara, A. Kawamura, and K.Matsuse, Sensorless Control of AC Motor Drives,IEEE Press, 1996.

[2] J. Holtz, " Sensorless control of induction motor drives," Proc. IEEE , vol.90, pp.13591394, Aug.2002.

[3] P. Vas, Sensorless Vector and Direct TorqueControl , Oxford Univ. Press, 1998.

[4] Y. A. Kwon and S. H. Kim, New scheme for speed-sensorless control of induction motor IEEE Trans. Ind. Electr. , vol.51, pp.545-550, June 2004.

[5] Z. Yan and V. Utkin, Sliding mode observers for electric machines- an overview, IEEE Proc IECON ,

pp.1842-1847, 2002.[6] J. J. Slotine, "Sliding Controller Design for

Nonlinear Systems," Int. J. Contr. , Vol. 40, No. 2, pp.421-434, 1984.

[7] V. Utkin, J. Guldner and J. Shi, Sliding ModeControl in Electromechanical Systems , Taylor andFrancis, 1999.

[8] Z. M. A. Peixoto, P. F. Seixas, B. R. Menezes, and P.C. Cortizo, "Speed control of permanent magnetmotors using sliding mode observers for inducedEMF position and speed estimation," IEEE Proc

IECON, pp.1023-1028, 1995.[9] F. Parasiliti, R. Petrella, and M. Tursini, Adaptive

sliding mode observer for speed sensorless controlof induction motors, IEEE IAS Annual Meeting, pp.2277-2283, 1999.

[10] J. Li, L. Xu, and Z. Zhang, An adaptive slidingmode observer for induction motor sensorless speedcontrol, IEEE IAS Annual Meeting , pp.1329-1334,2004.

speed sensor less control of im using sliding mode observer with variable boundary layer

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