A Novel Speed Sensor Less Field-Oriented Control Scheme of IM Using Extended Kalman Filter With Load...

8/14/2019 A Novel Speed Sensor Less Field-Oriented Control Scheme of IM Using Extended Kalman Filter With Load Torque O

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A Novel Speed Sensorless Field-Oriented ControlScheme of IM Using Extended Kalman Filter with

Load Torque ObserverWANG Chenchen, LI Yongdong

Department of Electrical EngineeringTsinghua University,

Beijing, 100084, P.R.China

Abstract The Extended kalman filter (EKF) has beenfound wide application in the sensorless control of inductionmotor (IM) because of its good steady and dynamic behaviour,disturbance resistance, and fast convergence. This paperpresents a novel speed sensorless field-oriented control schemeof Induction motor using extended kalman filter. As thequadrature axes rotor flux is equal to zero in the field-orientedcontrol, the observer based on the IM model in synchronousreference coordinate to estimate the flux and rotor speedsimultaneously is simpler. Compared to the traditional observerusing extended kalman filter, the orders of model and thematrixes are reduced, the complexity and the computationaltime are also decreased. The load torque is also observed byEKF and compensated to the system to reduce the ripple causedby a sudden change of the load torque. The speed and torqueripple in steady state also reduces when the load torque isincluded as a state variable. The simulation and experimentalresults show the validity and the feasibility of the presentedscheme.

Keywords induction motors; extended kalman filter; speedsensorless; field-oriented control; load torque observer.

I. INTRODUCTION

The sensorless field-oriented control of IM has beenresearched extensively over the last two decades. Goodperformance of the control lies on the accuracy of theestimated or observed flux and rotor angular speed of themotor. The flux and speed are calculated using the statorcurrent and voltage in the traditional approaches, with a largeerror especially in the low speed range. Recently, theextended kalman filter algorithm, in which the system(process) and measurement noise is considered, has beenwidely used in the sensorless control of IM[1-9]. With EKF,it is possible to estimate the states and identify theparameters in a relatively short time interval. According to

the stator current and reconstructed voltage, the flux andspeed of IM can be estimated simultaneously using the EKF.Since the good steady and dynamic behaviour, disturbanceresistance, and the fast convergence, the EKF is consideredto be a preferable method to estimate the motor speed[10-12].

This paper presents a novel speed sensorless field-orientedcontrol scheme of Induction motor using EKF. As thequadrature axes flux is equal to zero in the field-orientedcontrol, the elements related to the q axes flux could beomitted if the model of IM in a synchronous referencecoordinate is used. Then the orders of the model and iterative

matrices are reduced. Furthermore, the load torque isincluded as a state variable to improve the steady anddynamic performances. The observed load torque is alsocompensated to the system as a feedforward to reduce theripple caused by a sudden change of load torque. Thesimulation and experimental results show the validity andfeasibility of the presented scheme. The comparative study of

presented scheme with the one in stationary referencecoordinate is also carried out.The paper is organized as follows: after the introduction in

Section I, the models of motor and EKF algorithm isdiscussed in Section II; Section III presents the novel speedsensorless field-oriented control scheme based on the modelin synchronous coordinate, and then two methods are derived;The observation and compensation of load torque is studiedin Section IV; Section V and VI gives the simulation andexperimental results. Finally, the conclusion is given inSection VII.

II. MATHEMATICAL MODEL OF IM AND EKF ALGORITHM

A dynamic model for induction motor in an arbitraryreference coordinate rotating with a angular speed K , bychoosing the stator current and rotor flux as state variables, isas follows[13]:

d ( )( ) ( )

d x t

A x t B u t t

= + (1)

( ) ( ) y t C x t = (2)where

T ds qs dr qr x i i = ,

T

ds qs y i i

= ,T

ds qsu u u

= ,1 2 2

1 2 2

/

/

/ 0 1/

0 / 1/

K r r

K r r

m r r K r

m r r K r

a a a

a a a A

L

L

=

,

978-1-4244-1874-9/08/$25.00 2008 IEEE 1796

Authorized licensed use limited to: Reva Institute of Tehnology and Management. Downloaded on December 14, 2008 at 00:22 from IEEE Xplore. Restrictions apply.


2/7

10

10

0 0

0 0

L

B L

=

,1 0 0 0

0 1 0 0C

=

,

2 21 m s r m

s r s r

L L L L

L L L L

= = ,

2s r m

sr

L L L L L

L

= = , r r

r

L

R = ,

2

1 2( )s r m

r

R R La

L L L = + , 2

m

r

La

L L = .

Generally, we set 0K = , and add the angular speed of rotor as a state variable. Then a 5 order nonlinear model of IM is obtained and can be described as:

1 1( , , )k k k k x f x u w = , (3)

( , )k k k z h x v= , (4)where

T ds qs dr qr r x i i = .

Here w is the input noise (process noise) of the system,which stands for the error of the parameters; v is the outputnoise (measurement noise) which stands for the errors inmeasurement and sample. From the nonlinear model above,the rotor speed can be estimated by the following EKFalgorithm.

1. Prediction of the state variables:

1 ( , , 0)k k k x f x u

= . (5)

2. Estimation of the error covariance matrix:1 1

T k k k k k P P Q

= + , (6)where

k

k x

f x

=

, cov{ } { }T k k k k Q w E w w= = .

3. Kalman filter gain:

( )1T T k k k k k k k K P H H P H R = + . (7)

where

k

k x

h H

x

=

, cov{ } { }T k k k k R v E v v= = .

4. Estimation of the state variables: ( ( , 0))k k k k k x x K z h x

= + . (8)5. Update of the error covariance matrix:

( )k k h k P I K H P= . (9)

III. PROPOSED SCHEME IN THE SYNCHRONOUS REFERENCECOORIDNATE

If we select K s = , which is the synchronous angularspeed, the model in the synchronous reference coordinate is:

1 2 2

1 2 2

/

/

/ 0 1/

0 / 1/

s r r

s r r

m r r sl

m r sl r

a a a

a a a A

L

L

=

. (10)

Since the d axes is oriented towards the rotor flux in field-oriented control, the q axes rotor flux equals zero:

0rq =

. (11)The elements correlative with rq are omitted. Then the

state variables ( , , )sd sq rd x i i = ,

1 2

1 2

/

/ 0 1/

s r

s r

m r r

a a

A a a

L

=

. (12)

The dynamic model of IM can be given when the r isadded as a state variable (Method I):

2 21 1 4 2 3

3 2

24 1 1 2 2 3 4

3

1 3

( ) [ ( ), ( ), ]

1( )

1( )

1

0

msd

r

msq

r

m

r r

x t f x t u t t Q

L x aa x x x x u

x L

L x x x a x a x x u x L Q

L x x

= +

+ + + +

+ + +

= +

&

. (13)

according tom sq

s r sl r r rd

L i

= + = + ,

where ( , , , )sd sq rd r x i i = ,

1 2 3 4( , , , )Q diag q q q q= ,and

22 22

1 4 223 3

2 1 2 14 1 2 4 1 2 32

3 3 3

2

( )

10 0

0 0 0 0

k

m m

r r r

m m m

sr r r

m

r r

I L x L x a

a x x x x

L x L x L x x x a a x x a x

T x x x

L

= +

+

+ +

where sT is the period of the observer.It can be seen that, in the synchronous coordinate, the

order of the model and the correlative matrix decreases from5 to 4. The numerical complexity can be reduced in theiteration of matrix for the one order decrease. But it can alsobe seen that the elements of k in (13) are complex. If wechange the variable r by synchronous speed s , then thedynamic model can be given (Method II):

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21 1 4 2 3

24 1 2 2 4 3

1 3

( ) [ ( ), ( ), ]

1

1

1

0

sd r

r ssq

m

m

r r

x t f x t u t t Q

aa x x x x u

L

L R a x x x a x x u

L L Q

L x x

= +

+ + +

+

= +

&

, (14)

where ( , , , )sd sq rd s x i i = ,and

21 4 2

24 2 4 1 2 3

10 0

0 0 0 0

r

r s

mk s

m

r r

aa x x

a L R x a x x a x

L I T

L

= +

.

Obviously, the model and the iterative matrix are simplerby the alteration of the state variable. The diagram of theproposed speed sensorless field-oriented control method isshown in Fig. 1 in which s is selected to be the variable.The method in which r is selected to be the variable issimilar and will not be shown here.

IV. LOAD TORQUE OBSERVATION

As we know, the mechanical equation of the motor is:

m Lr

T T p

J

= & , (15)

where J : the inertia of motor; p : pairs of poles of motor;

mT : electromagnetic torque; LT : load torque, include friction and windage.

In the aforementioned discussion, the mechanical timeconstant is considered adequately larger than theelectromagnetic time constant, so it makes:

0r =& , (16)Actually, we can include the load torque as a state variable,

and (15) can be used in the model.

dq

abc

dq

*r

r s *sl

*sd i

*sqi

*

eT

r

sd isqi

*

squ

*

sd u

*

su

*

su

sd u squ

sqcu

sdcu

r r

sqm

T

i L

r pm

r

n LT L 3

2

rd

Fig.1 Diagram of the proposed scheme

In the stationary reference coordinate, if ( , , , , , )s s r r L x i i = the extended model of IM is

given as follows

21 1 3 2 4 5

21 2 2 3 5 4

1 3 4 5

2 3 5 4

3 1 4 3 2 3 6

( ) [ ( ), ( ), ]

1

1

1

1

0

s

s

m

r r

m

r r

x t f x t u t t Q

aa x x a x x u

L

aa x a x x x u L

L x x x x

Q

L x x x x

pa x x a x x x

J

= +

+ + +

+ +

= +

+

+

&

, (17)

where2

332

m

r

L pa

J L= ,

21 2 5 2 4

21 2 5 2 3

5 4

5 3

3 4 3 3 3 2 3 1

0 0

0 0

10 0

10 0

0

0 0 0 0 0 0

r

r

m

k sr r

m

r r

aa a x a x

aa a x a x

L x x

I T

L x x

pa x a x a x a x

J

= +

.

Similarly, in the synchronous reference coordinate,( , , , , )sd sd rd r L x i i = the model of IM can be given

by

2 21 1 4 2 3

3

24 1 1 2 2 3 4

3

1 3

3 2 3 5

( ) [ ( ), ( ), ]

1( )

1( )

1

0

msd

r r

msq

r

m

r r

x t f x t u t t Q

L x aa x x x x u

x L

L x x x a x a x x u

x LQ L

x x

pa x x x

J

= +

+ + + +

+ +

= +

&

, (18)

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22 22

1 4 223 3

2 1 2 14 1 2 4 1 2 32

3 3 3

3 3 3 2

20

( ) 0

10 0 0

0 0

0 0 0 0 0

k

m m

r r r

m m m

r r r

sm

r r

I

L x L x aa x x

x x

L x L x L x x x a a x x a x

x x x T L

pa x a x

J

= +

+

+ +

The speed and load torque can be observed simultaneously

according to the extended model above. The observed loadtorque can also be compensated to the system as afeedforward to calculate the command of the q axes current.And the dynamic performances can be improved thanks tothe observation load torque. Fig. 2 shows the compensationof the load torque.

*r

r

*

eT

LT

Fig.2 Feedforward of the load torque.

V. SIMULATION RESULTS

To test the performances of the proposed schemes,simulations are carried out on an IM with the followingparameters:

Pn = 2200W UL=380V In=5.9A f n =50Hz p=3 Ls=L r=0.1801 H, L m =0.1893 H, R s = 2.75 , R r = 2.27

J=0.21kg.m 2

Fig. 3 and 4 shows the estimation of flux and speed whenthe method I and method II is employed respectively. Themotor is magnetized from 0 to 1.5 second, and accelerates to600rpm from 1.5 second. A rated load torque is imposed onthe motor at 3 second. The simulation results show that theobserved speed and flux can trace the real one quicklyenough.

The simulation results of EKF with load torque observerrespectively in stationary and synchronous referencecoordinate show in Fig. 5 and 6. The motor operates at 600rpm, and a rated load torque is imposed at 2.5 second. It canbe seen that if the observed load torque is compensated to thesystem, the ripple of speed caused by a sudden change of load torque can be reduced obviously. Comparatively, thespeed ripple using the proposed scheme in the synchronousreference coordinate is much smaller than that in stationaryone.

VI. EXPERIMENTAL RESULTS

A platform with a TMS320F2812 DSP is used to confirm

the validity of the proposed schemes. The control period is125us. For the restriction of the computational accuracy, theperformances obtained from the experiments may be not thebest. But the following experimental results are the best wecan achieve using this hardware and the conclusions arederived from the experimental results we got. The real speedis measured by the encoder of 1000 p/r. The parameters of motor using in experiments are same with that usinginsimulations. A DC motor with a resistance is used as theload of the induction motor.

Fig. 7 and 8 shows the performances of the proposedmethod I and II. The condition of acceleration and suddenchange of load torque is considered. From the figures, the

0 1 2 3 4 50.0

0.3

0.6

0.9

1.2

R o t o r

f l u x

( W b )

Time(s)

Real fluxEstimated flux

0 1 2 3 4 5-200

0

200

400

600

800

R o t r o s p e e

d ( r p m

)

Time(s)

Real speedEstimated speed

0 1 2 3 4 50.0

0.3

0.6

0.9

1.2

R o t o r

f l u x (

W b )

Time(s)

Real fluxEstimated flux

0 1 2 3 4 5-200

0

200

400

600

800

R o t r o s p e e

d ( r p m

)

Time(s)


(a)Real and estimated flux (b) Real speed and estimated speed (a) Real and estimated flux (b) Real speed and estimated speed

Fig.3 Simulation result of the method I Fig.4 Simulation result of the method II

0 1 2 3 4 50

200

400

600

800

R o t o r s p e e

d ( r p m

)

Time(s) 0 1 2 3 4 50

200

400

600

800

R o t o r s p e e

d ( r p m

)

Time(s)0 1 2 3 4 5

-0.3

0.0

0.3

0.6

0.9

1.2

1.5

L o a d

t o r q u e

( p . u

)

Time(s)

Observed load torqueReal load torque

(a) Rotor speed without feedforward of load torque (b) Rotor speed with feedforward of load torque (c) Real and estimated load torqueFig.5 Simulation result using EKF based on stationary reference coordinate. (The rated load torque is imposed on the motor at 2.5 second)

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two methods based on the synchronous reference coordinateboth show the acceptable steady and dynamic performances.The ripple of speed and torque current when using method Iare smaller than that using method II.

Fig. 9 and 10 shows the experiment results when the EKFbased on the model respectively in stationary andsynchronous reference coordinate with load torque observerare employed. The speed estimation, torque current andobserved load torque is shown. The condition when theobserved load torque is compensated and not compensated iscompared. Firstly, it can be seen visibly that the speed andtorque ripple in steady state is much smaller than that whenthe load torque is not included as a state variable. Secondly,the speed ripple caused by the sudden change of load torque

can be reduced obviously if the observed load torque iscompensated to the system as a feedforward.

VII. CONCLUSION

A novel speed sensorless field-oriented control scheme of IM using EKF based on the synchronous reference coordinateis presented in this paper. Two methods are derived andcarried out which use the rotor speed or synchronous speed asstate variable respectively. The load torque is also included asa state variable and compensated to the system as afeedforward. In this case, the speed and torque ripple can beobviously reduced either in steady or dynamic states.

0 1 2 3 4 50

200

400

600

800

R o t o r s p e e

d ( r p m

)

Time(s)0 1 2 3 4 5

0

200

400

600

800

R o t o r s p e e

d ( r p m

)

Time(s)0 1 2 3 4 5

-0.3

0.0

0.3

0.6

0.9

1.2

1.5

L o a d

t o r q u e

( p . u

)

Time(s)

Estimated load torqueReal load torque

(a) Rotor speed without feedforward of load torque (b) Rotor speed with feedforward of load torque (c) Real and estimated load torque

Fig.6 Simulation result using EKF based on synchronous reference coordinate. (The rated load torque is imposed on the motor at 2.5 second)

0 2 4 6 8 100

200

400

600

800

R o t o r s p e e

d ( r p m

)

Time(s)


0 2 4 6 8 10

0

200

400

600

800

R o t o r s p e e

d ( r p m

)

Time(s)


0 2 4 6 8 100

1

2

3

4

5

T o r q u e c u r r e n

t ( A )

Time(s) (a) method I (a) Real speed and estimated speed. (b) Torque current

0 2 4 6 8 100

200

400

600

800

R o t o r s p e e

d ( r p m

)

Time(s)


0 2 4 6 8 100

200

400

600

800

R

o t o r s p e e

d ( r p m

)

Time(s)


0 2 4 6 8 100

1

2

3

4

5


t ( A )

Time(s) (b) method II (c) Real speed and estimated speed. (d) Torque currentFig.7 Speed estimation when the motor Fig.8 Speed estimation and torque current when the motor operates at 600rpm

accelerates from 20rpm to 600rpm using method I and II. with a sudden load torque imposed using method I (a and b) and II (c and d).

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REFERENCES

[1] L. Salvatore, S. Stasi, and L. Tarchioni, "A new EKF-based algorithmfor flux estimation in induction machines," IEEE Transactions onIndustrial Electronics, vol. 40, pp. 496-504, 1993.

[2] T. Iwasaki and T. Kataoka, "Application of an extended Kalman filterto parameter identification of an induction motor," in IAS, 1989, pp.248-253 vol.1.

[3] M. Barut, O. S. Bogosyan, and M. Gokasan, "EKF based estimation fordirect vector control of induction motors," in IECON 02, 2002, pp.1710-1715 vol.2.

[4] M. Barut, M. Gokasan, and O. S. Bogosyan, "An extended Kalmanfilter based sensorless direct vector control of induction motors," inIECON 2003, pp. 318-322 vol.1.

[5] A. Dell'Aquila, F. Cupertino, L. Salvatore, and S. Stasi, "Kalman filterestimators applied to robust control of induction motor drives," inIECON 1998, pp. 2257-2262 vol.4.

[6] J. W. Finch, D. J. Atkinson, and P. P. Acarnley, "Full-order estimatorfor induction motor states and parameters," in IEE Proceedings- ElectricPower Applications, 1998, pp. 169-179.

[7] B. Murat, B. Seta, and G. Metin, "Speed-Sensorless Estimation forInduction Motors Using Extended Kalman Filters," IEEE Transactionson Industrial Electronics, vol. 54, pp. 272-280, 2007.

[8] F. Schutte, S. Beineke, A. Rolfsmeier, and H. Grotstollen, "Onlineidentification of mechanical parameters using extended Kalman filters,"in Industry Applications Conference, 1997, pp. 501-508 vol.1.

[9] K. Young-Real, S. Seung-Ki, and P. Min-Ho, "Speed sensorless vectorcontrol of induction motor using extended Kalman filter," IEEETransactions on Industry Applications, vol. 30, pp. 1225-1233, 1994.

[10] C. Manes, F. Parasiliti, and M. Tursini, "A comparative study of rotorflux estimation in induction motors with a nonlinear observer and theextended Kalman filter," in IECON 1994, pp. 2149-2154 vol.3.

[11] K. L. Shi, T. F. Chan, Y. K. Wong, and S. L. Ho, "Speed estimation of

an induction motor drive using extended Kalman filter," in PowerEngineering Society Winter Meeting, 2000, pp. 243-248 vol.1.[12] K. L. Shi, T. F. Chan, Y. K. Wong, and S. L. Ho, "Speed estimation of

an induction motor drive using an optimized extended Kalman filter,"IEEE Transactions on Industrial Electronics, vol. 49, pp. 124-133, 2002.

[13] T. Du and M. A. Brdys, "Shaft speed, load torque and rotor fluxestimation of induction motor drive using an extended Luenbergerobserver," in International Conference on Electrical Machines andDrives, 1993, pp. 179-184.

0 2 4 6 8 100

200

400

600

800

R o t o r s p e e

d ( r p m

)

Time(s)


0 2 4 6 8 10

0

2

4

6


t ( A )

Time(s) 0 2 4 6 8 10

0

5

10

15

20

O b s e r v e

d l o a d

t o r q u e

( N . m

) )

Time(s) (a) Real speed and estimated speed. (b) Torque current. (c) Observed load torque.

0 2 4 6 8 100

200

400

600

800

Time(s)

R o t o r s p e e

d ( r p m

)


0 2 4 6 8 10

0

2

4

6


t ( A )

Time(s) 0 2 4 6 8 10

0

5

10

15

20

O b s e r v e

d l o a d

t o r q u e

( N . m

)

Time(s) (d) Real speed and estimated speed (e) Torque current (f) Observed load torque

Fig.9 The motor operates at 600 rpm when a sudden load torque is imposed without (a,b,c) and with (d,e,f) the feedforward of the load torque.(EKF with load torque observation in the stationary reference coordinate)

0 2 4 6 8 100

200

400

600

800

R o t o r s p e e

d ( r p m )

Time(s)


0 2 4 6 8 10

0

2

4

6


t ( A )

Time(s) 0 2 4 6 8 10

0

5

10

15

20

O b s e r v e

d l o a d

t o r q u e

( N . m

)

Time(s) (a) Real speed and estimated speed. (b) Torque current (c) Observed load torque

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0 2 4 6 8 100

200

400

600

800

R o t o r s p e e

d ( r p m

)

Time(s)


0 2 4 6 8 100

2

4

6


t ( A )

Time(s) 0 2 4 6 8 10

0

5

10

15

20

O

b s e r v e

d l o a d

t o r q u e

( N . m

)

Time(s) (d) Real speed and estimated speed. (e) Torque current (f) Observed load torque

Fig.10 The motor operates at 600 rpm when a sudden load torque is imposed on without (a,b,c) and with (d,e,f) the feedforward of the loadtorque. (EKF with load torque observation in the synchronous reference coordinate)

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A Novel Speed Sensor Less Field-Oriented Control Scheme of IM Using Extended Kalman Filter With Load...

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