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Rotor Time Constant Identification in Vector Controlled

Induction Motor Applied Flux Model Reference

Adaptive System

MRAS)

M. emli 0,

.

oussak

2),

M. ossa 1)

and

A.Chabri 1)

(1) Ecole Normale Suphieure de 1'Enseignement Technique (ENSET) de Tunis

5

AV.Taha Hussein, 1008 Tunis (BM) Montfleury

(2)Ecole Sup6rieure d'Ing6nieurs de Marseille

(ESIM)

IMT TechnopjledeChateauGombert 13451 Mafieille cedex 20 France

Absrracr Nowadays, Indirect Field-Oriented Control (IFOC)

technique brought

on

a renaissance in modem high-performance

control of PWM inverter fed induction motor drives. This method

requires the actual value of the rotor time constant which is used to

calculate the magnitude and the position of the rotor flux. This value

widely varies with rotor temperature and flux level of the machine. So,

The quality of the drive system decreases if nomeans for compensation

or

identification is applied. This paper describes a rotor time constant

identification method in order to update control gains of a vector

controlled induction motor. A flux Model Reference Adaptive System

(MRAS)

s used to estimate the inverse rotor

tim

constant by only

using measurements of the stator voltages and currents and rotor speed

of an induction motor. The estimate rotor time constant is used as

feedback in a vector speed control system for voltage-controlled pulse

width modulation (PWM) inverter fed induction motor. The proposed

method identify the inverse rotor time constant with a good accuracy at

any

load

and speed eferences. Simulation results point out the validity

of our proposed method.

INTRODUCIION

control method has been popularly used

for a long time. It will c%nue to be used in the future for low-

performance, low power, and cost-effective indusmal drives. In a

scalar control method, poles and zeros of machine transfer functions

vary at each operationg point because of the nonlinearity of the machine

model and the inherent coupling effect between the direct and

quadrature axes. For high performance application, field oriented

or

vector control techniques, developed in the early 1970's, are used to

eliminate the coupling problems between the d and q axes, then an ac

machine will behave like a separatly excited dc machine and therefore

fast transient response are obtained and the conventional stability limit

of the induction motor are eliminated.

Since the introduction of the microcomputer by Intel Corporation in

1971, the technology has gone through intense evolution in

the

control

of power electronics and drives. Microcomputers permit simplification

of control hardware (thus reducing size and cost), improve reliability,

and eliminate drift problems and made possible the

U=

of vector

control techniques (called Field-Oriented Control

FOC))

for nduction

motor in high-performance applications. This control methods has

found wide acceptance in applications such as paper mil ls , textile mills,

steel rolling mills, machine tools and robotics, where the system has to

be

robust or isensitive to parameter variations and load disturbance.

There are two varieties of vector control. The first variety proposed

by Blaschke is the Direct Field-Oriented Control (DFOC)or feedback

method. This method use direct measurement of the air-gap flux vector

by means of special sensors. In spite of it's accuracy and it's

insensitivity to variations in machine parameters, the application of this

technique remains limited

on

the sensor-flux equipped induction

machines and the harmful effect of harmonic noise in feedback signal

processing therefore the method is difficult to use

near

zero speed.

In

the second variety, developped by Hasse

and

called Indirect Field-

Oriented Control (IFOC) or feedforward method. The rotor flux is

estimated f m he stator current vector, voltage vector, rotor speed and

machine parameters. So, this method is more sensitive to variations in

machine parameters.

In

order to have decoupling between the rotor flux

and torque component of current, it is necessary to know:with good

accuracy the machine parameters especially the rotor

time

constant wich

widely varies with rotor temperature, skin effect and flux level of the

machine.

A simple open-loop volt

0-7803-1772-6/94/ 3.00@ 1994 EBE

Attemps are made to enhance the IFOC of PWM inverter fed

induction motor drives by parameter identification. Recently, much

attention has been given to the rotor time constant identification

problem and several publications have been presented in this field.

However, the rotor time constant identification problem remains a

challenge.

Chan C. et al. [SI proposed a rotor resistance identification basedon

the proper selection of coordinate axes, namely the a-axis of the

rotating

f rame

is set to be coicident with the stator current vector.

The method proposed by Matsuo et al. [9] where they injects a

prescribed negative sequence current perturbation signal and detects the

corresponding negative sequence voltage. This technique requires

additional hardware and can induce a strong second harmonic torque

pulsation due to the interaction of the positive and negative rotating

components of mmf

Tamai' et al. [1 11 proposed the application of the model reference

Adaptive System to the rotor resistance identification of induction

machine

equiped

with x m h oils wound closed to the stator winding.

A concept to measure the rotor time constant in real-time using a

Kalman filter was proposed by z i and Lip0 [12]. The method is

limited to situations where the load conditions are changing slowly and

also requires minimum of about 5% of rated

speed

and above.

Boussak et al. [2] have proposed another on-line rotor time constant

identification applying Recursive Least Squares (US) pproach with

variable forgetting factor based on measurment of the stator voltages

and currents and the rotor speed.Recently [3],[4], they have

propose

a method based on MRAS which is a promissing method to estimate

with good accuracy the rotor time constant. This contribution has

to

be

considered as a base of our works in order to improve the

accuracyof

the rotor tim constant identification in vector controlled induction

motor drive.

NmATIONS

:state space stator, rotor voltage vector,

:state space stator, rotor current vector,

:state space rotor flux vectot,

: tator,rotor electrical angular velocity,

: haft electricalspeed,

: haft dat iv eposition n synchronous reference

f rame

: iffmtial operatoror Laplace

operator,

:

omplex mot of unity,

:mechanicalrotor angular velocity,

:pole-pair number,

: q xis otor flux,

:d-q ax s stator current,

:

oad torque,

:

otal in-

: riction

coeff icient

797

Pmmneters:

: tator, rotor resistance,

4

4

T

: tator,

ID^

Self-inductance,

M :mutual nductance,

:

ota

time

constant,


2/4

P,

: eakage coefficient,

s

:

nverse rotor time constant,

:estimate inverse rotor time constant.

Rotor-flux observers

VECTOR

CONTROL

OF INDUCTION

MACHINE

The Indirect Field-Oriented Control (IFOC) system for Voltage-

regulated Pulse-Width Modulation (PWM) inverter-fed three phase

induction motor with squirrel-cage rotor or with a short-circuited

wound rotor was well developed in Jemli [6] and it's block basic

scheme is given in figure 1.

The dynamic behaviour of the induction motor is described in a d-q-o

reference frame rotating synchronously with the rotor flux. The rotor

flux is in line with the d-axis. The command references: stator currents

; and

I:

and the slip angular frequency u: re defined by:

a)

I 2

M (at steady state)

d r -

(3)

Figure 1: Block basic scheme of indirect-field

oriented control system.

If the value of /3 used in

(3)

deviates from the real value, the

decoupling control of the flux and the torque will be lost and the

indirect field oriented control will not be completed successefully.So,

it is necessary to proceed with an on-line rotor time constant

identification.

ROTOR

TIME

CONSTANT IDENTIFICATION

Modeling of induction motor

The dynamic model of a three-phase induction motor with a squirrel-

cage rotor or with a short-circuited wound rotor can be defined by

vector equations expressed in d-q reference frame, synchronously

rotating with electrical angular velocity m, by:

4) is the stator equation

5 ) is the rotor equation

r = L l r +MLr

Ls =

idr

iqs

From the equations 4) and 5). we can extract two expressions of

the complex rotor flux. The first derives from the stator equation and

the second from rotor equation.

-From stator equation:

( 9 )

; s the rotor flux-stator observation.

-From rotor equation:

9; M P, ,

s P,

( u - a,)-

9;s the rotor flux-rotor observation.

The P, parameter exists only in the complex rotor flux-rotor

observation. The rotor flux-stator observation can be obtained by a

single integration from equation

(9)

and it leads from rotor observation

as a first order differential equation solution.

Rotor time constant (MRAS) dentification

In this paper we propose the application of MRAS to identify the

rotor time constant of a vector controlled induction motor by using the

output error betwween the module of the rotor flux observations

(figure

2).

E

Adaptation

Mechanism

Digital Estimator System

L------------------------------------------------------------------~

Fgure

2:

Bloc scheme of (MRAS) for rotor time constant estimation

Two independant rotor-flux observers are built to estimate the rotor

flux vector, the fi st from stator equation

(9)

and the second from rotor

equation (10).The stator equation does not contain the P, parameter

and it's observer is considered as a reference model of the induction

machine. The rotor equation depends on the/?, parameter and it' s

,observer s considered as an adjustable model.

; The parameters /3 and P, are both time varying and each may be

seen as an input to the rotor equation

(10).

To investigate the dynamic

response of theMRAS rotor time constant identification, it is necessary

to linearize the stator and rotor equations for small deviation around a

working point.

So

the deviations of the error E are described by the

following linearized expression:

I

798


3/4

and the msfer t function relating A&to AP

is

expressed by:

-=E

s + P r o ) [ M ( C g o l b o C g ~ 0 1 q ~ o ) - l C g o 1 2 ]

Where, at steady state:

The closed loop diagram of the dynamic response of MRAS rotor

time constant identification can

be

built as follow:

Figure

3:

Closed -loop diagram of the dynamic response of

MRAS

IDENTIFIERSIMULATION

The msf er t function

H s)

admits two complex poles:

sl

=

P,o

duo mr0)

sz=

-P o -

wo

-ur0

15)

16)

Owing to the fact that

p,,

is always positive, The poles

s,

and

s,

are

with negative real parts .

So,

the

H s)

stability is confirmed. The

PI

regulator is justified by the fact that the estimator has to perform no

error at steady state and to converge in 'a reasonable bandwidth

compared to the dynamics speed response. Then the values of

K p l =

120and

K 300

are a good compromise.

I

The vector control is obtained by speed measurement and flux

estimation. The torque and flux current references are expressed in a

synchronously rotating d-q frame. The slip frequency reference

w:

s

obtained from torque reference current

1; ,

rotor flux and rotor time

constant estimation (figure

4).

The simulation is camed by starting the vector controlled drive to

reach

1000

rpm at no-load, applying the rated torque at

0.5s

and

reversing the speed reference at 0.75s with the same torque module

(figure

5).

The time response of the drive is 0.16s while, the estimator

converges in 0.15s. The load torque adds only a small transient

perturbation on the estimation. When the speed reverses at

0.75s

a

same

delay for convergence can be noted.

The speed overshoot observed in the f is t transient at time

t

=

0

is

explained by the fact that the flux is not yet initialised. The error

Rotor time

Constant Estimato

Figure4:Bloc scheme of indirect field oriented controlled induction

machine with rotor time constant MRAS estimation.

between the module

of

the stator and the rotor observations of the

rotor flux reaches a maximum at transient state then converges to a

practically nul value 0.008 wb ).The estimator is tested for low speed

200

rpm

(figure

6)

and high speed 300Orpm (figure

7).

Simulation

results show the good stability and accuracy of the estimator under any

load condition and any speed condition.

:

R . 2

5

Figure

5.

Inverse rotor time constant estimation.

a: speed control, real value (full line), reference value (dashed line)

b estimation, estimate (full line), real value (dashed line)

c:

e

etween stator and rotor-flux observations

d: error between real and estimate value of

p.

K ,

=

0.6

K ,

=

10 K,, =

120

Ki

300

799


4/4

W r C r d / s

\

Figure 6. Inverse rotor time constant estimation at low speed

control

a:

speed control, real value (full line), reference value (dashed line)

b: estimation, estimate (full line), real value (dashed line).

K = 0.6 K , = 10 K =

120

K

300

W r

r d / s

Figure 7. Inverse rotor time constant estimation at high

speed

control

a:

speed

control, real value (full line), reference value (dashed line)

b: estimation, estimate (full line), eal value (dashed line).

K

=

0.6

K

10

K,, =

120

K

300

The K K re the values of the PI speed regulator and the

K,,

, K

are the values of the PI regulator applied to the rotor constant estimator.

Appendix

The

machineperamacff am:

Ratedvoltagc: 38OV-w)Hz Rateedp~wer: 4kw

Ratedspeed: 148Orpm Numbexofpolepairs : 2

R ,: 1 . 2 0

R,: l a L :

0.1568H L,: 0.1554H

M:

0.15

H I,

bounded:

f

.8 A

I

bounded:

f

0

A

Total in en ia k 0.013

kg

m2 Friction coeficientf: 0.002 Nms/rad

CONCLUSION

Indirect field orienred control induction motor drive system are

presently concidered as viable altematives for replacing DC motor

drives. However, the variation of rotor time constant has amost

impanant effect

on

he performance of the drive. The major effect is to

destroy the decoupled condition of the rotor f lux and the torque.

Therefore, the on-line identification of the

rotor

time constant is

In this paper, the sensitivity to the rotor time constant variation is

analysed and a compensation method is proposed. The proposed

compensation method is

based

on lux model reference adaptive system

(MRAS). The identification method proposed in this paper is valid in

the

steady-state and m sients operation. The method produces desired

result under all operating conditions of the machine including the

operation under any speed range and any load condition. This

technique gives good stability and accuracy to estimate the rotor time

constant and to improve the induction motor drive systems.

In

practice situation, we use a PWM inverter as a voltage source, a

little identification error

is

caused by high harmonics , but this

is

reduced when the carrier frequency is increased.

to high-performance of the AC drive systems.

REFERENCES

[l] L, Ben Brahim and A. Kawamura,

A

Fully Digitized Field-

Oriented Controlled Induction Motor Drive Using Only

Current

sensors, in Proc. IEEE Trans.Industrial Electronics, vol.

E-39,

NO.3, June 1992.. pp. 241-249.

[2] M. Boussak and G.A. Capolino, Recursive Least squares Rotor

time constant Identification for vector controlled Induction

machine, i n

Journal of

the Electrical Machines and Power

System,

vo120,n02,1992, pp.137-147.

[3] M. Boussak,G.A. Capolino and M. Poloujadoff, Digital speed

Control and Parameter estimation in Vector Control Drive

Without

Speed

Sensor,

in

Proc. MCED'91, Marseille, 1991,

pp.Q 1-Q14.

[4]

M. Boussak G.A. Capolino and M. Poloujadoff. Parameter

Identification in Vector Controlled Induction Machine with Flux

Model Reference Adaptive System

(MRAS),

n P roc. ICEM'92,

Sept. 15-17 Manchester U.K., 1992, pp. 838-842.

[5] C.C. Chan and H. Wang, An Effective Method for Rotor

Resistance Identification for High-Performance Induction Motor

Vector Control, n Proc.

IEEE

Trans.Industrial Electronics,vol.

[6]

M.

Jemli, Contribution o Vector Control and to Rotor Time

Constant Jdentijkation

of

three Phase Induction Machines, (in

French), Memoire DEA ,2 4 Jully. 1993.

[7] M. Jemli , N. Hadjami, M. Boussak, M. Ksouri and A. Chaiiri,

Commande

Vectorielle en Vitesse

de

la Machine

b

Induction avec

estimation Adaptative (MRAS) de la Constante de Temps

Rotorique. in

Proc. JTEA'93,

NO.10, vol.

11,

Hammamet,

Tunisia, Feb. l y 3 , pp.397-406

[8] Y.D. Landau,

Adaptive Control: The Model Reference

Approach,

Marcel

Dekker Inc. 1979.

[9]

T.

Matsuo and T.A. Lipo, A Rotor Parameter Identification

Scheme for Vector-Conuolled Induction Motor Drives. in Proc.

E-37,

NO.6,

Dec 1990., pp. 477-482.

IEEE Trans. Indusny Applications,vol. IA-21, NO.4, MayIJune

1101 K.Ohnishi. Ueda Y nd K. Mivachi, Model reference Adautive

1985, pp. 624-632.

- -

System Against Rotor Resistaice Variation in Induction Motor

Drive, in Proc.

IEEE

Trans. Industrial Electronics, vol.

IE-

[ l11 S . Tamai and H. Sugimoto, Secondary Resistance Identification

of an Induction

Motor

Applied Model Reference Adaptive System

and its Characteristics, in Proc. IEEE Trans. Industry

Applications,

vol.

IA-23, NO.2. MarsWApril 1987,pp. 296-303.

[12] L.C. Zai

and

T.A. Lipo, An Extended

Kalman

Filter Approach

to Rotor Time Constant Measurment in PWM Induction Motor

Drives. Research Repon 87-14.1987, 7p.

33,N0.3, Aug.1986, pp. 217-223.

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