ISSN 2319-8885
Vol.02,Issue.12,
September-2013,
Pages:1281-1289
www.semargroups.org,
www.ijsetr.com
Simulation of Field Oriented Control of Sensor less Induction Motor
Drives using MRAS-Based Speed Estimator
A. NARENDER CHARY1
T. RAVICHANDRA 2
Asst. Prof, Dept of EEE, AVN Institute of Technology,
Hyderabad, AP-India, E-mail:naresh34@gmail.com.
Asst. Prof, Dept of EEE, AVN Institute of Technology,
Hyderabad, AP-India, E-mail: ravichandra34@gmail.com.
Abstract: MRAS based techniques have been proven to
be one of the best methods to estimate the rotor speed due
to its good high performance ability and straight-forward
stability approach .The proposed techniques use two
different models (the reference model and the adjustable
model) which have made the speed estimation a reliable
scheme especially when the motor parameters are poorly
known or having large variations. The proposed scheme
uses the error vector from the comparison of both models
as the feedback for speed estimation. In this scheme, the
performance of the rotor flux based MRAS (RF-MRAS)
and back EMF based MRAS (BEMF-MRAS) for
estimating the rotor speed is studied. Both schemes use the
stator equation and rotor equation as the reference model
and the adjustable model respectively. The output error
from both models is tuned using a PI controller yielding
the estimated rotor speed. The dynamic response of the
RF-MRAS and BEMF-MRAS sensor less speed
estimation is examined in order to evaluate the
performance of each scheme. The results obtained justify
the dynamic performance of the RF-MRAS and BEMFMRAS estimators.
Keywords: EMF, MRAS, RF-MRAS, BEMF-NRAS.
I. INTRODUCTION
In order to implement the vector control technique, the
motor speed information is required. Tacho generators,
resolvers or incremental encoders are used to detect the
rotor speed.However; these sensors impair the ruggedness,
reliability and simplicity of the IM. Moreover, they
require careful mounting and alignment and special
attention is required with electrical noises. Speed sensor
needs additional space for mounting and maintenance and
hence increases the cost and the size of the drive system.
However, in one aspect, the speed sensor elimination
reduces the total cost of the drive system. On the other
hand the sensor less drive system is more versatile due to
the absence of the numerous problems associated with the
speed sensor as discussed previously. Therefore it is
encouraged to use the sensor less system where the speed
is estimated by means of a control algorithm instead of
measuring. However eliminating the speed sensor without
degrading the performance is still a challenge.
In this dissertation, the speed sensor less estimation
concept via implementation of Model Reference Adaptive
System (MRAS) schemes was studied. It is well known
fact that the performance of MRAS based speed estimators
is beyond par from other speed estimators with regards to
its stability approach and design complexity. Although this
thesis is all about MRAS based speed estimators, but it is
also the aim of this project to investigate several speed
sensor less estimation strategies for IMs. Explanations on
the type of control strategies also were briefly discussed.
As far as simulation works concerned, the MRAS based
speed sensor less estimation schemes in this thesis has
been implemented in the field oriented structure (FOC) to
evaluate the estimator’ performance.
Significance of study: With the maturing technology of
the vector-controlled drives, the need for speed
information is crucial for control purposes and
traditionally, this information can be extracted using
mechanical sensor mounted on the motor shaft. However,
the presence of such sensor has reduced the system
reliability and increases the drives system’s size and the
overall cost. These problems have attracted the interest of
many researchers to develop techniques that can eliminate
the use of shaft sensor. This effort has led to growth of
various speeds sensor less estimation schemes based on
the simplified motor models. Therefore, the intention of
this work is to share the motivation of the previous
researchers to study the speed sensor less estimation
strategies. The reason behind adopting the MRAS based
speed sensor less estimation strategies in this research is
so obvious because it has been proclaimed as one of the
best methods available, especially when the motor
parameters are poorly known or have large variations.
Though the performance of MRAS based estimators is
Copyright @ 2013 SEMAR GROUPS TECHNICAL SOCIETY. All rights reserved.
A. NARENDER CHARY, T. RAVICHANDRA
considerably good at high speed but operation at low and
zero speed is still a problem to overcome.
II.SPEED SENSORLESS ESTIMATION TECHNIQES
The speed estimation schemes based on the direct
synthesize of the IM equations can be broadly group into
two groups. The first one is the open loop observer which
does not have the feedback correction and the other one is
the closed loop observer which make use of the feedback
correction to improve the estimation accuracy. The open
loop calculation method is simple to implement but prone
to error because of high dependency on the machine
parameters. The closed loop group observers for speed
estimation are much more versatile in terms of
performance such as the Luenberger observers, Kalman
Filter observers, MRAS estimators and rotor slot
harmonics estimator. Each of these speed estimation
schemes differs from each other in terms of equations and
structure used but they share the same objective to provide
the speed information and to improve the performance of
the IM drive system.
Model reference adaptive system estimators: The MRAS
approach uses two models. The model that does not
involve the quantity to be estimated (the rotor speed,  r ) is
considered as the reference model. The model that has the
quantity to be estimated involved is considered as the
adaptive model (or adjustable model). The output of the
adaptive model is compared with that of the reference
model, and the difference is used to drive a suitable
adaptive mechanism whose output is the quantity to be
estimated (the rotor speed). The adaptive mechanism
should be designed to assure the stability of the control
system. A successful MRAS design can yield the desired
values with less computational error (especially the rotor
flux based MRAS) that an open loop calculation and often
simpler to implement. Figure below illustrates the basic
structure of MRAS. Different approaches have been
developed using MRAS, such as rotor flux based MRAS
(RF-MRAS), back e.m.f based MRAS (BEMF-MRAS),
and reactive power based MRAS (RP-MRAS) and
artificial intelligence based MRAS (ANN-MRAS). In the
following a basic description of these schemes will be
discussed.
(b)
Fig1. General Structure of MRAS based estimator
scheme. (a) Basic scheme using space vector notation.
(b) Basic scheme using space vector components
III. RF-MRAS VS BEMF-MRAS SPEED
ESTIMATORS
This research decided to use the RF-MRAS and BEMFMRAS based estimators to perform the simulation and
evaluation on the performance of the estimators as
mentioned earlier in the objectives of the study. These two
estimators have been chosen intentionally since they
uniquely differ in terms of the quantity used in the
reference model and the adjustable model but they share
almost the same realization in terms of structure. Both
structures also have been widely referred in the literature.
Hence, a fair comparison of the estimators can be
performed and the results from this study will enrich the
materials available for references in future. Therefore, this
chapter will discussed in detail the realization of the two
estimators from the IM dynamic equations up to the
construction of the estimators in the MATLAB/
SIMULINK.
A. RF-MRAS
The RF-MRAS estimator was initially proposed by
Schauder as an improvement to the drawbacks incurred in
the open loop estimator. It is possible to estimate the rotor
speed by using two models (the reference model and
adjustable model) which independently estimate the rotor
flux linkage components in the stationary reference frame
and by using the difference between these flux linkages
estimates to drive the speed of the adjustable to that of the
actual speed. The expressions for the rotor flux linkages in
the stationary reference frame can be obtained from the
stator voltage and rotor voltage equations of the IM as
described in chapter 2. Stator voltage and flux equations of
(2.11)-(2.12) and (2.5)-(2.6) have been manipulated and
simplified to obtain the rotor flux linkages as given by the
following equations:
(a)
International Journal of Scientific Engineering and Technology Research
Volume.02, IssueNo.12, September-2013, Pages:1281-1289
Simulation of Field Oriented Control of Sensor less Induction Motor Drives using MRAS-Based Speed Estimator
s
 qr

Lr
Lm
 drs 
 (v
Lr
Lm
qs
 (v

(1)

(2)
s
s
 Rs iqs
)dt  Ls iqs
ds
s
s
 Rs ids
)dt  Ls ids
2
Where   1  Lm
Ls Lr
Whereas, the rotor voltage and flux equations have
been rearranged and simplified to give the derivatives of
rotor flux linkages in the stationary reference frame as
given by the following equations:
d qrs
dt

L
1 s
 qr   r drs  m iqss
Tr
Tr
(3)
d drs
L
1
(4)
   drs   r qrs  m idss
dt
Tr
Tr
Equations (1) and (2) were implemented as the
reference model since it is independent of rotor speed and
the equations (3) and (4) were implemented as the
adjustable model as it is speed dependent. The tuning
signal driving the adaption mechanism of this structure is
the error output due to comparison of both models. It
varies the rotor speed in order to force to zero the error
vector. The block diagram of the RF-MRAS structure is
shown in figure2. The adaption mechanism used in the
speed estimator structure is either P-I controller or fuzzy
based controller or artificial neural network based
algorithms. Here the P-I controller is used as the adaption
mechanism. In the next section the stability of RF-MRAS
will be discussed.
the actual value can be assured with suitable dynamic
characteristics. When designed according to these rules,
the stator error equations of the MRAS are guaranteed to
be globally asymptotically stable. The adaption
mechanism can be derived from the following state error
equations which is obtained by subtracting equations (3)
and (4) from the corresponding reference model equations
(1) and (2).
d d
1
(5)
   d   r  q ˆ q ( r  ˆ r )
dt
Tr
d q
1
(6)
   q   r  d   d ( r  ˆ r )
dt
Tr
or in matrix form, d    A   W  Since ̂ r is a
dt
.
function of the state error, these equations describing a
nonlinear feedback system as illustrated in Figure 3.
Fig3. MRAS equivalent nonlinear feedback system
To ensure the hyper stability of the system can be
achieved, two criterions must be established. Firstly, the
linear time-invariant forward path transfer matrix
(sI  A) 1 must be strictly positive real and secondly, the
nonlinear feedback (which includes the adaption
mechanism) must satisfy Popov’s criterion for stability.
Popov’s criterion for stability requires a finite negative
limit on the input or output inner product of the nonlinear
feedback system. A candidate adaption mechanism which
satisfies the criterion can be obtained as given in the
following explanation. Let
t
ˆ r   2     1  d
(7)
0
Popov’s criterion requires that:
t1
   W dt
T
Fig2. Speed estimation using RF-MRAS.
B. RF-MRAS stability
It is important to design the adaption mechanism of the
MRAS based estimators according to the hyper stability
concept. This will results in a stable and quick response
system where the convergence of the estimated value to
  02
For all t1  0
(8)
0
Here,  02 is a positive and constant. Substituting for   ,
W  and ̂ r in this inequality, Popov’s criterion for the
present system becomes;

  ˆ
t
0

d
q
t

 
  qˆ d  r  2 ( )   1 ( )d  dt   02
0

 

International Journal of Scientific Engineering and Technology Research
Volume.02, IssueNo.12, September-2013, Pages:1281-1289
(9)
A. NARENDER CHARY, T. RAVICHANDRA
The following relation can be used to solve this inequality:
t1
1
 k ( p. f (t )) f (t )dt   2 k. f (0)
2
,k  0
(10)
0
Using this expression, it can be shown that Popov’s
inequality is satisfied by the following functions:
1  K1 ( qˆ d   dˆ q )  K1 ( qˆ d  dˆ q )
(11)
2  K P ( qˆ d   dˆ q )  K P ( qˆ d  dˆ q )
(12)
Substituting equations (11) and (12) into equations (7)
yields the estimated rotor speed as follows:
K
(13)
ˆ r  ( K P  I )( qˆ d   dˆ q )
p
The MRAS speed identification based on this adaption
mechanism is illustrated in figure 4 as being implemented
in the MATLAB/SIMULINK. This simulink blocks will be
used in the simulation to examine the performance of the
estimator. The factors Lr in (3.1)-(3.2) and Lm in (3)Lm
Tr
(4) have conveniently been incorporated into the
adaptation mechanism gains constants KP and KI. Although
the structure is quite simple in construction, the
performance of this system is poor at close to zero speed,
due to the presence of pure integration and the stator
resistance effect. In order to solve the problems with initial
conditions and drift, modification of the pure integration in
the voltage model by a low pass filter is used. Another way
is by inserting a linear transfer function in form of high
pass filter in both the reference and the adjustable model.
Tajima and Hori improved Schauder’s work by proposing
a robust flux observer of which poles are designed in
function of rotor speed and rotor time constant. As a result,
the system is completely robust to the rotor resistance
variation.
C. BEMF-MRAS
The problem at low speed region can be somehow
resolved by replacing the pure integration of the stator
voltage with a filter. However, the natural delay related to
a filter is still present. To avoid completely the integration,
the back e.m.f quantity is used instead of the rotor flux
linkage. This MRAS technique was originally proposed by
Peng and Fukao to provide an improvement to the RFMRAS technique. The BEMF-MRAS based technique as
depicted in figure 5 does not require any pure integration in
its reference model. The estimator uses the induced back
e.m.f in its reference and adjustable models instead of rotor
flux linkages as applied in the RF-MRAS. The equations
for the direct and quadrature-axis back e.m.f in the
reference and adjustable models follow from equations (1)(4), as given by these equations:
(1) Reference model
emd  vds  ( Rs ids  Ls
dids
)
dt
(14)
emq  vqs  ( Rs iqs  Ls
diqs
(15)
dt
)
(2) Adjustable model
eˆmd 
L2m
1
1
(ˆ r imq  imd  idss )
Lr
Tr
Tr
eˆmq 
L2m
1
1
(ˆ r imd  imq  iqss )
Lr
Tr
Tr
dim
1
1
  r  im  im  i s
dt
Tr
Tr
(16)
(17)
(18)
D. BEMF-MRAS stability
As far as the design of the adaptation mechanism is
concerned, hyper stability approach is important to ensure
the stability of the system and the estimated quantity will
converge to the actual value. Referring to figure 3, instead
of using the rotor flux, the design considers the back e.m.f
as it input. The design of BEMF-MRAS adaptation
mechanism is almost the same as carried out for RFMRAS.
Differentiating both sides of equations (16) and (17),
the following equations can be obtained.
dem
L2 dis
1
(19)
  r  em  em  m
dt
Tr
Lr Tr dt
Letting   em  eˆm and subtracting (19) for the adjustable
model and from (19) for the reference model giving the
appropriate state error equation:
d
1
  r      (ˆ r   r )  eˆm
dt
Tr
(20)
Or in matrix form, d    A   W  . Since ̂ r
is
dt
Fig4. Block diagram of RF-MRAS estimator.
produced by the adaptation mechanism, these equations
International Journal of Scientific Engineering and Technology Research
Volume.02, IssueNo.12, September-2013, Pages:1281-1289
Simulation of Field Oriented Control of Sensor less Induction Motor Drives using MRAS-Based Speed Estimator
describe a nonlinear feedback system as shown in figure 3.
To ensure stability of system, Popov’s criterion for hyper
stability as given in equation (21) must be satisfies.
t1  0
t1
 Wdt   
2
0
(21)
0
comparative assessment of the estimator’ performance can
be evaluated and conclusion made applied to both
estimators.
IV.SIMULATION RESULTS
A. BEMF-MRAS SPEED ESTIMATION
Letting
ˆ r  ( K P 
KI
)(eˆm   )
p
(22)
Speed Response Dynamics:
And substituting for W in equality (3.21) gives the
following simplified equation.
t1
 (  eˆ
0
m
)( r  ( K P 
KI
)(eˆm   ))dt   02
p
(23)
Using the same quantity equation as in (10), inequality
in (23) has been satisfied. Rewriting equation (22) yields
the estimated rotor speed of the estimator.
K
(24)
ˆ r  ( K P  I )(eˆm  em )
p
The MRAS speed estimation system based on this
adaptation mechanism can be obtained as depicted in
figure5. The factor Lr
has been conveniently
L2m
Fig6. RF-MRAS speed estimator
incorporated into the adaptation mechanism gain constants
K P and K I . The structure is constructed in the MATAB/
SIMULINK for simulation and evaluation purposes.
Fig7. BEMF-MRAS speed estimator
Tracking capability:
Fig5. Block diagram of BEMF-MRAS estimator.
As being mentioned earlier, these two estimators were
chosen as candidates for comparison because of its
similarity (almost similar) in terms of structure realization
(refer Figure 4 and 6). Whereas the parts that differentiate
them are only quantities used in the models, and the
presence of pure integrator in the RF-MRAS. Those
criteria should give the clear stand on the reason for
choosing these two estimators. Therefore a fair
Fig8. Reference speed of 100 rad/sec.
International Journal of Scientific Engineering and Technology Research
Volume.02, IssueNo.12, September-2013, Pages:1281-1289
A. NARENDER CHARY, T. RAVICHANDRA
BEMF-MRAS:
Fig9. RF-MRAS speed estimation
Fig12. P=0.009 and I=0.1
B. TUNING THE ADAPTIVE GAIN CONSTANTS RFMRAS
Fig13. P=0.009 and I=1.7
Fig10. P=1 and I=1
C. SENSITIVITY TO PARAMETER VARIATION
(a) Stator resistance (Rs) variation:
RF-MRAS incorrect Rs setting
Fig11. P=1 and I=100
(a) 1.0 Rs
International Journal of Scientific Engineering and Technology Research
Volume.02, IssueNo.12, September-2013, Pages:1281-1289
Simulation of Field Oriented Control of Sensor less Induction Motor Drives using MRAS-Based Speed Estimator
(b) Rotor resistance (Rr) variation
RF-MRAS incorrect Rr setting
(b)
1.2 Rs
Fig14.
(a) 1.0 Rr
BEMF-MRAS incorrect Rs setting:
(b)1.2 Rr
(a)1.0 Rs
BEMF-MRAS incorrect Rr setting:
1.2 Rs
Fig15.
(a)1.0 Rr
International Journal of Scientific Engineering and Technology Research
Volume.02, IssueNo.12, September-2013, Pages:1281-1289
A. NARENDER CHARY, T. RAVICHANDRA
BEMF-MRAS, estimation of rotor speed is not
feasible for both estimators.

RF-MRAS estimator has significant effect from
the parameters variation (especially stator resistance)
but the BEMF-MRAS is robust to parameter
variation.
Therefore, as a whole, considering all the key criteria
for comparison, it can be concluded that the BEMFMRAS embrace the requirement as a versatile estimators.
It is good in tracking capability and superb in insensitivity
to parameter variation.
VI. REFERENCES
(b) 1.2 Rr
V.CONCLUSIONS
This thesis has been devoted to provide a complete
comparison of the MRAS based speed estimators of the
induction machine and that objectives have been achieved.
RF-MRAS and BEMF-MRAS are two estimators which
are uniquely differ in terms of quantity used but almost
similar in the structure realization. The estimator’s
performance has been investigated using three key criteria
of comparison; tuning the adaptation gain constants, the
speed tracking capability and sensitivity to parameters
uncertainty. From the simulation and literature study, the
works in this project has arrived at the following
conclusion:

RF-MRAS based speed estimator is simple and
straightforward in implementation but BEMF-MRAS
based speed estimator is quite complex.

In case of RF-MRAS based speed estimator, low
values of adaptation gains do not yield in convergence
of the speeds, increasing the gains yield in better
convergence of the estimations. So the adaptation
gains must be taken as large as possible and limited
only by noise consideration. In case of BEMF-MRAS
based speed estimator, the relationship between the
adaptive gain constants and the tracking performance
is not as simple as in the case of RF-MRAS based
speed estimator. The non-linearity in tuning the
adaptation gain constants has made the process of
tuning the BEMF-MRAS speed estimators a difficult
one.

RF-MRAS
estimator
has
good
tracking
performances at high speed and even at low speed
operation but the BEMF-MRAS estimator show better
and superior performance overall. At low speed close
to zero operation, due to effect of stator value in RFMRAS and instability of back e.m.f quantity in
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Mr A.Narender chary,
Assistant Professor in Department of
EEE AVNIET –Hyderabad. Obtained
his B.Tech., from JNTU Hyderabad,
and M.Tech., from JNTU, Anantapur,
having
the
overall
teaching
experience of 5 Years and Industrial
experience in vishakapatnam steel
plant and guided good number of B.
Tech., and M. Tech., Projects.
Mr T.Ravichandra,
Assistant Professor in Department
of EEE, AVNIET–Hyderabad.
Obtained. B.Tech, from JNTU
Hyderabad, and M.Tech, from
JNTU, Anantapur, having the
overall teaching experience of 5
Years and guided good number of
B. Tech., and M. Tech., Projects.
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International Journal of Scientific Engineering and Technology Research
Volume.02, IssueNo.12, September-2013, Pages:1281-1289