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272
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007
Speed-Sensorless Estimation for Induction Motors
Using Extended Kalman Filters
Murat Barut, Student Member, IEEE, Seta Bogosyan, Member, IEEE, and Metin Gokasan, Member, IEEE
Abstract—In this paper, extended-Kalman-filter-based estimation algorithms that could be used in combination with the
speed-sensorless field-oriented control and direct-torque control of
induction motors (IMs) are developed and implemented experimentally. The algorithms are designed aiming minimum estimation error in both transient and steady state over a wide velocity
range, including very low and persistent zero-speed operation. A
major challenge at very low and zero speed is the lost coupling
effect from the rotor to the stator, which makes the information
on rotor variables unobservable on the stator side. As a solution to
this problem, in this paper, the load torque and the rotor angular
velocity are simultaneously estimated, with the velocity taken into
consideration via the equation of motion and not as a constant
parameter, which is commonly the case in most past studies. The
estimation of load torque, on the other hand, is performed as a
constant parameter to account for Coulomb and viscous friction
at steady state to improve the estimation performance at very
low and zero speed. The estimation algorithms developed based
on the rotor and stator fluxes are experimentally tested under
challenging variations and reversals of the velocity and load torque
(step-type and varying linearly with velocity) over a wide velocity
range and at zero speed. In all the scenarios, the current estimation
error has remained within a very narrow error band, also yielding
acceptable velocity estimation errors, which motivate the use of
the developed estimation method in sensorless control of IMs over
a wide velocity range and persistent zero-speed operation.
Index Terms—Extended Kalman filter (EKF), induction motor
(IM), low/zero-speed operation, sensorless control.
I. I NTRODUCTION
T
HERE has been extensive research in the sensorless fieldoriented control (FOC) and direct-torque control (DTC) of
induction motors (IMs) for the last two decades. Both control
methods require the accurate knowledge of the amplitude and
angular position of the rotor or stator flux with reference to
the stationary stator axis (in Cartesian coordinates). Additionally, information on the rotor angular velocity is required for
velocity control over a wide speed range and in the low and
zero-speed range for position-control applications. However,
although speed sensorless drives are now well-established in industry for medium and high-speed operation [1], their persistent
operation at very low and zero speed still constitutes a persisting
Manuscript received July 20, 2004; revised July 31, 2006. Abstract published
on the Internet September 15, 2006.
M. Barut and S. Bogosyan are with the Electrical and Computer Engineering Department, University of Alaska Fairbanks, Fairbanks, AK 99775 USA
(e-mail: [email protected]; [email protected]).
M. Gokasan is with the Electrical and Electronics Engineering Department,
Istanbul Technical University, Maslak, Istanbul, Turkey (e-mail: [email protected]
edu.tr).
Digital Object Identifier 10.1109/TIE.2006.885123
challenge [2]. The problems are due to parameter uncertainties,
signal acquisition errors, and noise in the very low speed range,
with an additional difficulty encountered at zero speed in steady
state, when the stator current ceases to convey information on
the rotor angular velocity [3], [4].
Model-based methods using IM state equations and signalinjection methods [5] using the anisotropic properties of the
machine have been competing for the improvement of the
zero/low-speed performance of sensorless IMs [2]. Speed sensorless control methods based on signal injection are capable
of long-term stability at zero stator frequency; however, they
are highly sophisticated and require customized designs for a
particular motor drive [3].
Recently, for the solution of the problem zero/very low
speed, model-based estimation methods have been proposed,
such as in [6]–[8], specifically addressing persistent operation
zero speed. Among those studies [6] uses a total-least-squarebased speed adaptive flux observer which enables zero-statorfrequency operation over an interval of 60 s, with mean and
maximum estimation error values of 1.34 and 38 r/min, respectively, at zero load. The study in [7] uses model-referenceadaptive-system-based linear neural networks, presenting
results with a maximum velocity estimation error of 95 r/min
and a persistent operation interval of 60 s at zero speed. The
study in [8] utilizes a continuous sliding-mode approach, for
which zero-stator-frequency results are obtained under load and
presented only for a very short interval of 4 s.
In addition to the aforementioned group of studies taking a
deterministic approach to the design of closed-loop observers,
there are also extended-Kalman-filter (EKF)-based applications
in the literature, taking a stochastic approach for the solution of
the problem. Model uncertainties and nonlinearities inherent to
IMs are well-suited for the stochastic nature of EKFs [9], [10].
With this method, it is possible to make the online estimation
of states while simultaneously performing identification of
parameters in a relatively short time interval [11]–[13], also
taking system/process errors and measurement noises directly
into account. The EKF is also known for its high convergence
rate, which improves transient performance significantly. Additionally, accurate estimation and convergence in steady state
requires high-frequency signals, which are also inherently met
by EKFs with the model and measurement noises included in
the model. These properties are the major advantages of the
EKF over other estimation methods and are the reasons why
the method finds wide application in sensorless estimation in
spite of its computational complexity, which also ceases to be a
problem with the developments in high-performance processor
technology.
0278-0046/$25.00 © 2007 IEEE
BARUT et al.: SPEED-SENSORLESS ESTIMATION FOR INDUCTION MOTORS USING EXTENDED KALMAN FILTERS
There have been a large number of EKF applications for the
sensorless control of IMs; studies using full-order [14], [15] and
reduced order [16], [17] estimators have been presented with
experimental results. The study in [18] compares the results of
EKF and Extended Luenberger Observer (ELO) for high-speed
operation using the IM model in the rotating axes, while the
study in [19] performs a comparison of EKF and Sliding Mode
Observer (SMO). A common feature in all these studies is the
estimation of velocity, which is taken into consideration as a
slow varying or constant parameter, except in [18]. Although
good results have been obtained in those studies in the relatively
low and high-speed operation region, the performance at zero
stator frequency or at very low speed is not satisfactory or not
addressed at all.
The major contribution of this paper is the design and experimental implementation of EKF-based estimation algorithms
developed for use with the speed sensorless DTC and direct
FOC of IMs over a wide speed range, including zero speed. For
this purpose, unlike previous EKF-based estimation studies,
by taking the angular velocity into consideration as a constant
parameter, ω is estimated as a state with the utilization of the
equation of motion. The inclusion of the mechanical equation
helps the estimation process by conveying the rotor–stator
relationship when the stator currents cease to carry information
on rotor variables at zero speed. Friction effects are also known
to deteriorate performance at low velocity and position-control
applications. To address this issue in this paper, the estimation
of tL is performed as a constant to account for friction effects,
particularly those of Coulomb and viscous friction at the steady
state. In the proposed EKF algorithms, the stator and rotor flux
amplitudes and positions are also estimated in addition to the
stator currents (referred to the stator stationary frame), which
are also measured as output. For improved estimation accuracy,
the EKF algorithms also take into consideration the control
input error arising due to the limited word length of the Analog
Digital Converter (ADC) [13]. This paper aims to address problems related to sensorless estimation in IMs over a wide speed
range, and closed-loop control of IMs is outside the scope of
this paper. The evaluation procedure of an estimator without the
use of a closed-loop control could, in a sense, be considered offline; to ensure a realistic evaluation of the online performance
of the EKF estimator in spite of the fact, pulsewidth-modulation
(PWM)-type input voltages have been applied to the IM via
the ac drive, and the actual ds1104-based motion-control unit
and motor are used to process the algorithm. The estimation
schemes are thus tested experimentally under instantaneous
load (linear with velocity and step-type) and velocity variations
to evaluate the performance over a wide speed range, as well
as during persistent operation at zero speed. Very low current
and velocity estimation errors have been obtained under the
developed scenarios, motivating the utilization of the developed
estimation approach in the sensorless control of IMs.
The paper is organized as follows: after the introduction in
Section I, the derivation of the extended models is discussed
in Section II for the estimation algorithms; Section III describes the development of the EKF algorithm for both models;
Section IV gives the hardware configuration, with Section V
presenting and discussing the experimental results for all three
273
scenarios. Finally, the conclusions and suggestions for future
improvements are given in Section VI.
II. E XTENDED M ATHEMATICAL M ODEL OF THE IM
As it is well known, IM is described by a fifth-order differential equation with two inputs and only three state variables
available for measurement [20]. For speed sensorless control,
the model consists of differential equations based on the stator
and/or rotor electrical circuits considering the measurement of
stator current and/or voltages. Being different from previous
EKF-based estimators, which estimate the rotor velocity using
the aforementioned equations, the extended IM model derived
in this paper also includes the equation of motion to be utilized
for the estimation of the rotor velocity. The EKF-based estimators designed for FOC and DTC are based on the extended IM
models in the following general form:
ẋe (t) = f e (xe (t), ue (t)) + wx1 (t)
= Ae (xe (t)) xe (t) + B e ue (t) + wx1 (t)
(1)
Z(t) = he (xe (t)) + wx2 (t) (measurement equation)
= H e xe (t) + wx2 (t).
(2)
Here, the extended state vector xe represents the estimated
states and load torque tL , which is included in the extended
state vector as a constant state with the assumption of a slow
variation with time. f e : nonlinear function of the states and
inputs. Ae : system matrix. ue : control input vector. B e : input
matrix. wx1 : process noise. he : function of the outputs. H e :
measurement matrix. wx2 : measurement noise. Based on the
general form in (1) and (2), the detailed matrix representation
of the two IM models can be given as below.
Model 1: Extended model of IM based on the stator flux is
shown by (3) and (4) at the bottom of the next page.
Model 2: Extended model of IM based on the rotor flux is
shown by (5) and (6) at the bottom of the next page.
The following are defined for (3)–(6). pp : number of pole
pairs. Lσ = σLs : stator transient inductance. σ: leakage or
coupling factor. Ls and Rs : stator inductance and resistance, respectively. Lr and Rr : rotor inductance and resistance referred
to the stator side, respectively. νsα and νsβ : stator stationary
axis components of stator voltages. isα and isβ : stator stationary axis components of stator currents. ψsα and ψsβ : stator
stationary axis components of stator flux. ψrα and ψrβ : rotor
stationary axis components of stator flux. JL : total inertia of
the IM and load. ωm : angular velocity.
III. D EVELOPMENT OF THE EKF A LGORITHM
An EKF algorithm is developed for the estimation of the
states in the extended IM model given in (3) and (4), or (5)
and (6), to be used in the sensorless control of the IM. The
KF method used for this purpose is a well-known recursive
algorithm that takes the stochastic state space model of the
system into account together with the measured outputs to
achieve the optimal estimation of states [19] in multi-input
multi-output systems. The system and measurement noises are
considered to be in the form of white noise. The optimality of
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007
the state estimation is achieved with the minimization of the
covariance of the estimation error. For nonlinear problems, the
KF is not strictly applicable since linearity plays an important
role in its derivation and performance as an optimal filter. The
EKF attempts to overcome this difficulty by using a linearized
approximation where the linearization is performed about the
current state estimate [21]. This process requires the discretization of (3) and (4), or (5) and (6), as below
xe (k + 1) = f e (xe (k), ue (k)) + wx1 (k)
Thus, the EKF algorithm can be given in the following recursive
relations:
N (k) = F e (k)P (k)F e (k)T + F u (k)Du F u (k)T + Q
(11a)
T
P (k + 1) = N (k) − N (k)H e
−1
× Dξ + H e N (k)H T
H e N (k)
(11b)
e
x̂e (k + 1) = fˆ (xe (k), ûe (k)) + P (k + 1)H T D−1
Z(k) = H e xe (k) + wx2 (k).
e
∂f e (xe (k), ue (k)) F u (k) =
∂ue (k)
(8)


i̇sα
 i̇sβ 


 ψ̇sα 


 ψ̇sβ  =


 ω̇m 
ṫL









−
Rs
Lσ
+
Rr Ls
Lr Lσ
−pp ωm
−Rs
0
p
− 23 JLp ψsβ
0
−
ẋe

(9)
−pp ωm
Rr Ls
+L
L
r σ
0
−Rs
3 pp
2 JL ψsα
0
Rs
Lσ
.
(10)
Rr
Lr Lσ
p ω
− pLσm
pp ωm
Lσ
0
0
0
0
0
0
0
0
Rr
Lr Lσ
0
0
0
0
0


  1
i
Lσ
 sα
 0
i



sβ
0 
 
ψ   1
0   sα  + 
ψ   0
0   sβ  
 0
 ωm
− J1L
tL
0
0
0
xe
Ae

0
Ae

isα
isβ 



1 0 0 0 0 0  ψsα 
isα
=

 + w12
0 1 0 0 0 0  ψsβ 
isβ


ωm
Z
He
tL
 R
2
Rr Lm
r Lm
− Lσs + R
0


L2
L2
r Lσ
r Lσ
i̇sα

2
R
L
R
L
s
m
r m
 i̇sβ  
− Lσ L pp ωm
0
− Lσ + L2 Lσ

 
r
r
ψ̇rα  
Rr
Rr


= 
L
0
−
m
Lr
Lr
ψ̇rβ  

 
Rr
0
pp ω m
 ω̇m  
Lr Lm
 − 3 pp Lm ψ
3 pp Lm
0
ṫL
2 JL Lr rβ
2 JL Lr ψrα
0
0
0
ẋe

isα
i 

 sβ 
1 0 0 0 0 0 ψrα 
isα
=

 + w22
0 1 0 0 0 0 ψrβ 
isβ


ωm
Z
He
tL
(11c)
Here, Q: covariance matrix of the system noise, namely model
error. Dξ : covariance matrix of the output noise, namely measurement noise. Du : covariance matrix of the control input
noise (νsα and νsβ ), namely, input noise. P and N : covariance matrix of state estimation error and extrapolation error,
respectively.
The algorithm involves two main stages: prediction and
filtering. In the prediction stage, the next predicted states fˆe (·)
and predicted state error covariance matrices P (·) and N (·)
are processed, while in the filtering stage, next estimated states
x̂e (k + 1) obtained as the sum of the next predicted states and
x̂e (k),ûe (k)
x̂e (k),ûe (k)
ξ
× (Z(k) − H e x̂e (k)) .
As mentioned before, EKF involves the linearized approximation of the nonlinear model [(7) and (8)] and uses the current
estimation of states x̂e (k) and inputs ûe (k) in linearization
by using
∂f e (xe (k), ue (k)) F e (k) =
∂x (k)
e
e
(7)
0



0 
 νsα +w11 (t)
1 
 νsβ
0  u
e
0
1
Lσ
(3)
Be
(4)
Lm
Lσ Lr pp ωm
0
Rr Lm
L2
r Lσ
0
−pp ωm
0
r
−R
Lr
0
0
0
0
0


  1
 isα
Lσ
0 
  isβ  
0


 
ψ



0
rα
0 
+
 ψrβ  
0

 
0 
 0
 ωm
− J1L  tL
0
0
x
0
e
0



0 
 νsα +w21 (t)
0 
 νsβ
0  u
e
0
1
Lσ
Be
(5)
(6)
BARUT et al.: SPEED-SENSORLESS ESTIMATION FOR INDUCTION MOTORS USING EXTENDED KALMAN FILTERS
275
TABLE I
RATED VALUES AND PARAMETERS OF THE IM USED IN THIS PAPER
Fig. 1.
Structure of the EKF algorithm.
Fig. 2.
Schematic representation of the experimental setup.
the correction term [second term in (11c)] are calculated. The
schematic representation of the algorithm is given in Fig. 1.
The algorithm utilizes the extended or augmented model in
(3) and (4), or (5) and (6), to generate all states required for
the sensorless control system, in addition to the load torque tL ,
using the measured phase currents and voltages.
IV. H ARDWARE C ONFIGURATION
The experimental test-bed for the EKF-based estimators is
given in Fig. 2. The IM in consideration is a three-phase fourpole 4-kW motor; the detailed specifications of which will be
given in the experimental results section. The EKF algorithm
and all analog signals are developed and processed on a Power
PC-based DS1104 Controller Board, offering a four-channel
16-bit (multiplexed) ADC and four 12-bit ADC units. The
controller board processes floating-point operations at a rate
of 250 MHz. A torque transducer rated at 50 N · m and an
encoder with 1024 counts/r are also used for the evaluation and
verification of the load torque and velocity estimates. The phase
voltages and currents are measured with high band voltage and
current sensors.
In the experiments, the IM is fed via an ac drive with a constant V/f PWM voltage instead of a sinusoidal input voltage to
achieve a more realistic performance test. Although the ac drive
is used in open loop, voltages with different frequency values
can be varied linearly with the acceleration and deceleration
times of the driver, which also allows velocity reversal. The load
is generated through a dc machine operating in generator mode
coupled to the IM. An array resistor connected to the armature
terminals of the dc machine is used to vary the load torque
applied to the IM, based on tL = kt2 ω/R, where kt is the torque
constant of dc machine, ω is the angular velocity, and R is the
total resistance (switched array + armature). The value of the
resistance is adjusted to 14.3 Ω to generate a load torque tL of
18 N · m at approximately 1400–1420 r/min, while for a tL of
10.4 N · m, the resistance is set to 29.4 Ω and to its maximum
value, respectively. Finally, the total inertia of the system does
not change in this application and is assumed to be constant.
It consists of the motor and generator inertia, which are both
determined accurately and reflected to the EKF algorithms, as
given in Tables I and II.
V. E XPERIMENTAL R ESULTS
The parameters for the IM and dc generator are listed in
Tables I and II. The values of system parameters and covariance matrix elements are very effective on the performance
of the EKF estimation. In this paper, to avoid computational
complexity, the covariance matrix of the system noise Q is
chosen in diagonal form, also satisfying the condition of positive definiteness. According to the KF theory, the Q, the Dξ
(measurement error covariance matrix), and the Du (input error
covariance matrix) have to be obtained by considering the
stochastic properties of the corresponding noises [22], [23].
However, since these are usually not known, in most cases,
the covariance matrix elements are used as weighting factor or
tuning parameters. In general, while the tuning of the initial
values of the P (estimation error covariance matrix) and the
Q is done by experimental trial-and-error to achieve a rapid
initial convergence and the desired transient and steady-state
behaviors of the estimated states and parameters, the Dξ and
Du are determined taking into account the measurement errors
of the current and voltage sensors and the quantization errors of
the ADCs, as given below.
For Model 1
Q = diag 1.4 × 10−12 A2 1.4 × 10−12 A2
× 1.3 × 10−12 (V · s)2 1.3 × 10−12 (V · s)2
× 9.6 × 10−14 (rad/s)2 1.7 × 10−12 (N · m)2
P = diag 10 A2 10 A2 10 (V · s)2 10 (V · s)2
× 10 (rad/s)2 10 (N · m)2 .
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007
TABLE II
RATED VALUES AND PARAMETERS OF THE DC MACHINE USED IN THIS PAPER
Fig. 3. Stator currents and voltages applied to the IM through the ac drive.
For Model 2
Q = diag 1.5 × 10−11 A2 1.5×10−11 A2 10−15 (V · s)2
×10−15 (V · s)2 10−15 (rad/s)2 10−15 (N · m)2
P = diag 1 A2 1 A2 1 (V · s)2 1 (V · s)2 1 (rad/s)2 1 (N · m)2 .
For both models
Dξ = diag 1.5 × 10−7 A2 1.5 × 10−7 A2
Du = diag 10−10 V2 10−10 V2 .
Fig. 3 demonstrates the transformed currents and voltages at
50 Hz and 380 V for a tL of approximately 20 N · m. The
performance of the IM is tested in open loop with PWM input
voltages/currents given in Fig. 3. The EKF algorithm takes
as the input of the transformed components of the current
and voltage. The following is a generalized description of this
transformation
xα = xa ;
1
xβ = √ (xb − xc )
3
torque values. The application considered in this paper does not
involve a change in the inertia; therefore, its rated value is used
in the models.
To evaluate the performance of the developed EKF schemes
for the stator and rotor oriented IM models—namely, Model 1
and Model 2, respectively—three scenarios are implemented
experimentally, with different variations given to the load
torque and velocity references. Besides the output current, the
velocity and induced torque are also measured in all three
cases to provide a basis of evaluation for the performance of
EKF schemes. The results are presented in Figs. 4–6. In these
figures, tind &t̂L , nm &n̂m , ψ̂sα , ψ̂sβ , ψ̂rα , and ψ̂rβ illustrate
the induced torque as obtained from the torque transducer and
estimated load torque, the actual and estimated velocity, and
the estimated α and β components of the stator and rotor
fluxes, respectively. e(·) error signals demonstrate the deviations
between the actual and the estimated components of the stator
current. The sampling rate used for the EKF estimation in the
experiments is Tsample = 100 µs. The estimation of states is
started with the assumption of no a priori information and with
initial values of zero.
(12)
where x: i and ν for current and voltage, respectively.
Due to the importance of system parameter values, prior to
the performance tests, the dc resistance is measured, and no
load and short circuit experiments are performed to calculate
the initial values of the parameters. These parameters are tuned
to obtain minimum error of the current, velocity, and output
torque between the actual system and its model. By applying
the same voltage inputs to the actual system, its model is
running simultaneously on the computer. The tuning process is
performed over a wide velocity range and for a variety of load
A. Scenario I—Step-Type Changes in tL (Fig. 4)
In this scenario, the EKF schemes for both models are tested
under step-type variations of the load torque, as can be seen in
Fig. 4. These step variations are created by switching the load
resistors ON and OFF. Inspecting the results for both models,
it can be noted that, in spite of the instantaneous switching
effects, isα and isβ peaks and variations remain within a very
low error band. The small value of this estimation error is an
important indicator for the good performance of the EKF in the
high-velocity range under load and no load. The estimated
BARUT et al.: SPEED-SENSORLESS ESTIMATION FOR INDUCTION MOTORS USING EXTENDED KALMAN FILTERS
Fig. 4.
277
Experimental results for step-type load torque variations at constant high velocity. (a) Model 1. (b) Model 2.
values of velocity and load torque also track their measured
values more closely throughout the operation range.
again, the current errors remain within the previously defined
error band, indicating the good performance of the algorithm
over a wide velocity range.
B. Scenario II—Velocity and Load Torque Reversal (Fig. 5)
In this scenario tested for both models, the velocity/load
torque (varying linearly with velocity) is reversed by changing
the input frequency from 50 to −50 Hz, while the motor
is running under a load torque of 19 N · m. The slope of
this variation is determined with the arbitrary choice of the
acceleration/deceleration rate given as an option on the ac drive.
By inspecting the results of this scenario, it can be noted that the
estimated load torque/velocity tracks the linear variation of the
measured torque/velocity through 1450 to −1450 r/min. Once
C. Scenario III—Zero and Low Velocities (Fig. 6)
In this scenario, while the motor is running at 10 r/min, at
t = 20 s, nm is stepped down to 0 r/min and is kept at zero for
64 s; at the end of this interval, nm is stepped up to 10 r/min for
Model 1. A similar scenario with the same duration of zerospeed operation is implemented for Model 2. The variations
are obtained by changing the speed reference on the ac drive.
As a result, the stator-based estimator yields a velocity error of
−4 r/min, while for the rotor-based estimator, this error remains
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007
Fig. 5. Experimental results for reversed load torque and velocity. (a) Model 1. (b) Model 2.
within −2 r/min. Also, a very low current error is obtained
in both models. Additionally, the flux amplitude and position
estimates for both the stator and rotor-based models at zero
speed appear to be stable and constant as expected, indicating
the good performance of the developed algorithm. The errors
obtained in the velocity and load torque estimates, on the
other hand, are mainly due to parameter uncertainties related
to Ls and Rs , stator inductance and resistance, respectively,
and Lr and Rr , rotor inductance and resistance, respectively,
as discussed in Section I. An indication of this fact is the
bigger velocity estimation error obtained with the EKF scheme
developed for the stator-oriented model, Model 1. The well-
known temperature-based variations of Rs at very low velocity
are more effective than Rr variations at low speed, thereby explaining the larger estimation errors in the flux with Model 1 at
low/zero speed, which in turn causes larger velocity estimation
errors. However, estimation errors in both cases remain within
an acceptable band, motivating the use of estimation scheme in
sensorless IM control.
VI. C ONCLUSION
In this paper, EKF-based sensorless estimation algorithms
are developed for the stator- and rotor-oriented models of IMs.
BARUT et al.: SPEED-SENSORLESS ESTIMATION FOR INDUCTION MOTORS USING EXTENDED KALMAN FILTERS
Fig. 6.
279
Experimental results for very low and zero velocity operation. (a) Model 1. (b) Model 2.
The load torque and velocity estimations are performed simultaneously, with the velocity taken into consideration using
the equation of motion and not as a constant parameter as in
most past studies. The stator (or the rotor) flux is estimated as
well, in addition to the stator currents, which are also measured
as output.
The estimation algorithms are tested experimentally under
challenging variations of load torque and velocity, also including persistent operation at zero speed. For all tested scenarios,
the current (estimation) errors have remained within a band for
both models, indicating the good performance of the proposed
method. Satisfactory velocity estimation errors ranging within
2–4 r/min have also been obtained for persistent operation of
zero speed. The advantage of the proposed estimation scheme
is that it does not require change of algorithms or adjustment of
gains/parameter signals for convergence at steady state. In that
sense, the developed EKF scheme offers a more generalized
and yet effective solution for the sensorless estimation of IMs
280
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007
over a wide speed range and at zero speed, motivating the use
of the estimation method with sensorless FOC and DTC of IMs.
The results can be further improved with the estimation of
temperature and frequency dependent uncertainties of stator
and rotor resistances and other system parameters based on the
application.
R EFERENCES
[1] M. Rashed and A. F. Stronach, “A stable back-EMF MRAS-based sensorless low-speed induction motor drive insensitive to stator resistance
variation,” Proc. Inst. Electr. Eng.—Electr. Power Appl., vol. 151, no. 6,
pp. 685–693, Nov. 2004.
[2] J. Holtz, “Sensorless control of induction machines—With or without
signal injection?” IEEE Trans. Ind. Electron., vol. 53, no. 1, pp. 7–30,
Feb. 2006.
[3] J. Holtz and J. Quan, “Drift- and parameter-compensated flux estimator
for persistent zero-stator-frequency operation of sensorless-controlled induction motors,” IEEE Trans. Ind. Appl., vol. 39, no. 4, pp. 1052–1060,
Jul./Aug. 2003.
[4] J. Holtz, “Sensorless control of induction motors—Performance and limitations,” in Proc. IEEE-ISIE Annu. Meeting, Puebla, Mexico, 2000, vol. 1,
pp. PL12–PL20.
[5] C. Caruana, G. M. Asher, and M. Sumner, “Performance of HF signal injection techniques for zero-low-frequency vector control of induction machines under sensorless conditions,” IEEE Trans. Ind. Electron., vol. 53,
no. 1, pp. 225–238, Feb. 2006.
[6] M. Cirrincione, M. Pucci, G. Cirrincione, and G.-A. Capolino, “An adaptive speed observer based on a new total least-squares neuron for induction
machine drives,” IEEE Trans. Ind. Appl., vol. 42, no. 1, pp. 89–104,
Jan./Feb. 2006.
[7] M. Cirrincione and M. Pucci, “An MRAS-based sensorless highperformance induction motor drive with a predictive adaptive model,”
IEEE Trans. Ind. Electron., vol. 52, no. 2, pp. 532–551, Apr. 2005.
[8] G. Edelbaher, K. Jezernik, and E. Urlep, “Low-speed sensorless control
of induction machine,” IEEE Trans. Ind. Electron., vol. 53, no. 1, pp. 120–
129, Feb. 2006.
[9] F. Cupertino, A. Lattanzi, L. Salvatore, and S. Stasi, “Induction motor
control in the low-speed range using EKF- and LKF-based algorithms,”
in Proc. IEEE-ISIE, Bled, Slovenia, 1999, vol. 3, pp. 1244–1249.
[10] S. Wade, M. W. Dunnigan, and B. W. Williams, “Comparison of stochastic
and deterministic parameter identification algorithms for indirect vector control,” in IEE Colloq.—Vector Control and Direct Torque Control
Induction Motors, London, U.K., 1995, vol. 2, pp. 1–5.
[11] L. Salvatore, S. Stasi, and L. Tarchioni, “A new EKF-based algorithm
for flux estimation in induction machines,” IEEE Trans. Ind. Electron.,
vol. 40, no. 5, pp. 496–504, Oct. 1993.
[12] O. S. Bogosyan, M. Gokasan, and C. Hajiyev, “An application of EKF for
the position control of a single link arm,” in Proc. IEEE IECON, Denver,
CO, 2001, vol. 1, pp. 564–569.
[13] M. Barut, O. S. Bogosyan, and M. Gokasan, “EKF based estimation for
direct vector control of induction motors,” in Proc. IEEE IECON, Seville,
Spain, 2002, vol. 2, pp. 1710–1715.
[14] K. Young-Real, S. Seung-Ki, and P. Min-Ho, “Speed sensorless vector
control of induction motor using extended Kalman filter,” IEEE Trans.
Ind. Appl., vol. 30, no. 5, pp. 1225–1233, Sep./Oct. 1994.
[15] 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
Trans. Ind. Electron., vol. 49, no. 1, pp. 124–133, Feb. 2002.
[16] C.-M. Lee and C.-L. Chen, “Observer-based speed estimation method
for sensorless vector control of induction motors,” Proc. Inst. Electr.
Eng.—Control Theory Appl., vol. 145, no. 3, pp. 359–363, May 1998.
[17] G. Garcia Soto, E. Mendes, and A. Razek, “Reduced-order observers
for rotor flux, rotor resistance and speed estimation for vector controlled
induction motor drives using the extended Kalman filter technique,” Proc.
Inst. Electr. Eng.—Electr. Power Appl., vol. 146, no. 3, pp. 282–288,
May 1999.
[18] T. Du and M. A. Brdys, “Shaft speed, load torque and rotor flux estimation
of induction motor drive using an extended Luenberger observer,” in Proc.
6th IEEE Int. Conf. Elect. Mach. and Drives, 1993, pp. 179–184.
[19] F. Chen and M. W. Dunnigan, “Comparative study of a sliding-mode
observer and Kalman filters for full state estimation in an induction
machine,” Proc. Inst. Electr. Eng.—Electr. Power Appl., vol. 149, no. 1,
pp. 53–64, Jan. 2002.
[20] R. Ortega, N. Barabanov, G. Escobar, and E. Valderrama, “Direct torque
control of induction motors: Stability analysis and performance improvement,” IEEE Trans. Autom. Control, vol. 46, no. 8, pp. 1209–1222,
Aug. 2001.
[21] G. C. Goodwin and K. S. Sin, Adaptive Filtering Prediction and Control.
Englewood Cliffs, NJ: Prentice-Hall, 1984.
[22] P. Vas, Sensorless Vector and Direct Torque Control. New York: Oxford
Univ. Press, 1998.
[23] Q. Ge and Z. Feng, “Speed estimated for vector control of induction motor using reduced-order extended Kalman filter,” in Proc. IEEE PIEMC,
Beijing, China, 2000, vol. 1, pp. 138–142.
Murat Barut (S’06) was born in Gaziantep, Turkey,
in 1973. He received the B.Sc. degree in electronics engineering from Erciyes University, Kayseri,
Turkey, in 1995, the M.Sc. degree in electrical
and electronics engineering from Nigde University,
Nigde, Turkey, in 1997, and the Ph.D. degree (with
Siemens Excellence Award) in computer and control engineering from Istanbul Technical University,
Istanbul, Turkey, in 2005.
Since August 2004, he has been conducting his
Ph.D. research studies at the Department of Electrical and Computer Engineering, University of Alaska Fairbanks, Fairbanks.
He is currently an Assistant Professor with the Department of Electrical
and Electronics Engineering, Nigde University. His current research interests
include power electronics, electrical drives, mechatronics, and motion control.
Prof. Barut is a Student Member of the IEEE Industrial Electronics Society.
Seta Bogosyan (M’95) received the B.Sc., M.Sc.,
and Ph.D. degrees in electrical and control engineering from Istanbul Technical University, Istanbul,
Turkey, in 1981, 1983, and 1991, respectively.
She conducted her Ph.D. studies at the Center for
Robotics, University of California, Santa Barbara,
where she was a Researcher and a Lecturer from
1987 to 1991. Within the last decade, she was an
Associate Professor at Istanbul Technical University.
She is currently a faculty member of the Department
of Electrical and Computer Engineering, University
of Alaska Fairbanks, Fairbanks. She is also the Principal Investigator of several
National Science Foundation and other federally funded projects. Her research
interests include motion control, sensorless control of induction motors, control
of hybrid electric vehicles, remote robotics, and applications of nonlinear
control/estimation techniques to electromechanical systems in general.
Prof. Bogosyan is an AdCom Member and the Vice President in Membership
Activities of the IEEE Industrial Electronics Society (IES). She is an Associate
Editor of the International Journal of Intelligent Automation and Soft Computing and the IEEE IES Magazine.
Metin Gokasan (S’82–M’88) received the B.Sc.,
M.Sc., and Ph.D. degrees from Istanbul Technical University, Istanbul, Turkey, in 1980, 1982,
and 1990, respectively, all in electrical and control
engineering.
He is currently an Associate Professor with the
Department of Electrical and Electronics Engineering, Istanbul Technical University. From 2004 to
2006, he conducted research at the University of
Alaska Fairbanks, Fairbanks, as a Visiting Scholar
and worked in several projects involving the control
of HEVs and sensorless control of induction motors. His research interests
include the control of electrical machinery, power electronics and electrical
drives, control of hybrid electric vehicles, and mechatronics systems.
Prof. Gokasan is a Member of the IEEE Industrial Electronics Society
(IES) and the Technical Committee on Education in Engineering and Industrial
Technologies within the IEEE IES.
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