The performance of induction motor drives gets improved in the scalar control mode with various algorithms with speed /position feedback. In this paper load angle control of induction motor with speed observer is presented. This eliminates the physical presence of speed sensor. The basic control of rotor flux vector with stator current defines the dynamics of torque control. In this scheme, estimation of feedback variables is obtained by using algorithm with minimum number of machine parameters. The speed obtained is thus used in feedback loop to improve the machine performance. The proposed algorithm also has a capability to estimate the active and reactive power of the machine. This is further incorporated to improve the operating efficiency of the machine. The observer developed is tested for various dynamics condition to verify its operating performance in MATLAB/SIMULINK.

1. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
Speed Observer Based Load Angle Control of
Induction Motor Drive
Gaurav N. Goyal1 and Dr. Mohan V.Aware2
1
Shri Ramdeobaba Kamla Nehru Engineering College /Electrical Engg. Department, Nagpur, India
Email: gaurav.goyal13@gmail.com
2
Visvesvaraya National Institute of Technology/ Electrical Engg. Department, Nagpur, India
Email: mva_win@yahoo.com
Abstract— The performance of induction motor drives arrangement.Thus from the beginning of 1980’s there
gets improved in the scalar control mode with various were serious research works throughout the world to
algorithms with speed /position feedback. In this paper control induction machine without the need for speed
load angle control of induction motor with speed observer sensor [1]-[7]. It is possible to estimate the speed
is presented. This eliminates the physical presence of
speed sensor. The basic control of rotor flux vector with
signal from machine terminal voltage and currents
stator current defines the dynamics of torque control. In with the help of digital signal processor (DSP).
this scheme, estimation of feedback variables is obtained Different methods are used for flux and speed
by using algorithm with minimum number of machine estimation. The calculation method of state variable
parameters. The speed obtained is thus used in feedback may be classified as models and observers. Models in
loop to improve the machine performance. The proposed comparison with observers are less complicated in the
algorithm also has a capability to estimate the active and case of induction motor. The accuracy of these
reactive power of the machine. This is further variables depends on the motor operating point,
incorporated to improve the operating efficiency of the
exactness of the parameter used, and the sensitivity of
machine. The observer developed is tested for various
dynamics condition to verify its operating performance in the model to drift in these parameters. The voltage
MATLAB/SIMULINK. model is not precise at low frequencies; however it is
not sensitive to rotor resistance variations. On the
Index Terms— Speed sensorless induction motor, Load other hand, the current model is sensitive to rotor
angle control, speed observer, Energy efficiency resistance variations and is not accurate in calculating
the rotor speed, especially at high speed. However, it
I. NOMENCLATURE is more precise, compared to voltage model, and at
lower frequencies .the mixed model integrates the
us,is,Ψs, Ψr Stator voltage, current and flux, rotor
advantage of both models. Because of these
flux
inaccuracies in calculating the flux linkage, in many
Rs, Rr, Ls, Stator resistance, rotor resistance,
solutions an observer by introducing an additional
stator
feedback loop is used. The load angle is the angle
Lr, Lm inductance, rotor inductance,
between the flux ψr and the stator current I s. Since the
magnetizing inductance
flux is related to the applied voltage and is fixed, thus
ωr ,ωΨr ,ωI Rotor speed , rotor flux linkages speed, we cannot vary the magnitude of the vector ψr. But
stator current angular frequency the speed at which it is rotating is not constant.
x11,x12,x21,x22, variables of multiscalar motor model Similarly in case of current vector the magnitude can
Kω,Tω Rotor flux speed PI controller be controlled but not ωi. ωi depends on the applied
parameters frequency.
a3,a4,ωδ,σ Motorcoefficients
III. MATHEMATICAL MODEL OF
II. INTRODUCTION INDUCTION MOTOR
1
The speed sensor is an inconvenient device and Induction Motor Model
has many drawbacks. An incremental shaft mounted
speeder encoder is required for close loop speed or The fundamental equation, which is used to introduce
position control. A speed encoder is undesirable in a the relation ship for speed observer system, is the
drive because it adds cost and reliability problems, statorcircuit equation given by
beside the need for a shaft extension and mounting dψs
u s = Rs is + + jωψs
a (1)
dt
1Gaurav N Goyal is with Department of Electrical Engineering, The d-and q-voltage component presented in the d-
Shri Ramdeobaba Kamla Nehru College of Engineering, Nagpur as a
Asst.Professor (E-mail: gaurav.goyal13@gmail.com).
q reference frame with the rotor flux linkages oriented
M.V. Aware is with the Department of Electrical Engineering, in the d-axis are given by
Visvesvaraya National Institute of Technology, Nagpur,
Maharashtra, INDIA(E-mail: mva_win @ yahoo.com).
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2. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
ˆ dψsd
ˆ A. Mechanical Subsystem
usd = Rs isd + −ω ψsq
ˆψ ˆ (2)
dt r
dx12 1
dψsq
ˆ = − x12 + v1 (10)
ˆ
usq = Rs isq + +ω rψsd
ˆψ ˆ (3) dt Ti
dt dx11 Lm 1
= x12 − m0 (11)
X 11
com
-
X 12
com
Is
Is
pedictive
usα
com
INVERTER
dt JLr J
PWM
Load Angle Controller
ωi stater current
ωr controller us β
com U V W
ω2 +
ωr
ωi
isα
com isβ
com
isα isβ C. Electromagnetic Subsystem
iU
+ -
X 12 m
cal
P
cal
stater
current
measur
The basic simplified machine variables are
iV
represented as
atg atg of Q of
---
δ com MM powers
X 21
com
X 22
com X 22m variable
X 22m
X 21m X 12 m M dx 21 R RL
= −2 r x 21 + 2 r m x 22
X 21m simulation of
X 21 variable
isα
u sα
com
(12)
Rotor angular
speed
observer
isβ dt Lr Lr
ωr com
u sβ
dx22 1 RL 2
Figure 1. Proposed load angle control induction motor control = − x22 r m isx + v 2' (13)
dt Ti Lr
The estimated d-q components of stator flux where Ti is the time constant of the first-order delay
linkages are as follows element used for filtering stator current command, J is
dψsd
ˆ the inertia constant, and m0 the load torque.The new
ˆ
= u sd − Rs isd + ω ψ sq
ˆψ ˆ (4)
dt r state variables are not a function of the coordinate
system. Therefore, it is not necessary to transform
dψ sq
ˆ
ˆ
= u sd − Rs isq − ωψ ψ sd
ˆ ˆ (5) these variables from one coordinate to another one.
dt r
This is essential for the practical realization of control
Equation (2) and (3) present the voltage model of systems because it gives significant simplification of
induction motor in d-q reference frame. This flux the drive system. The fully decoupled subsystems
simulator operates in open loop without any feed back make it possible to use this method in the flux-
from the rotor flux error. The flux is identified weakening region and to obtain simple system
correctly when the motor parameters are exactly structures, which are not addressed in the case of
known .in a real system, motor parameter change with vector control methods. For control of the presented
operating point and temperature ,as a result, the system it is essential to know the actual value of the
estimator rotor flux and the actual flux are different, rotor flux vector. The use of the variables
and this different depends on the following: “instantaneous imaginary power” and
properties of the selected motor model; degree of “instantaneous real power” provides a simplification
accuracy of parameter identification; degree of of the control system [10]. They proposed these new
accuracy of current and voltage measurement and definitions of instantaneous powers in three-phase
motor operating point .the use of feedback minimizes circuits based on instantaneous voltage and current
the effect of the above factors on the identification of values
the rotor flux linkages.Four state variables have been p= usdisd + usqisq
proposed for describing the motor model [9]. These (14)
state variables may be interpreted as rotor angular q=usqisd -usdisq
speed, scalar and vector products of the stator current (15)
and rotor flux vectors, and the square of the rotor Taking into account the differential equations of
linkage flux, as follows: the stator current and rotor flux vectors in steady state
x11 = ωr and using the new state variables, the following is
(6)
obtained:
x12 = ψ rx isy − ψ ry isx = ψ r is sin(δ ) (7) Lm + 1
a 2 a
is + 4 P
a2 a2
x12 = (16)
x21 = ψ rx 2 + ψ ry 2 (8) ω r
i
L
Rr
x22 = ψ rx isx + ψ ry isy = ψ r is cos(δ ) (9) a Q − ωi I s
2
x 22 = 4 (17)
Where, δ is the angle between stator current and a 3ω i
rotor flux vectors. By using nonlinear feedback, it is Where
2 2
possible to obtain a new model for the induction R L + R r Lm
motor with two fully decoupled subsystems: a1 = − s r
mechanical and electromagnetic. This property is not
Lr ω i
a function of the motor source [10]. L R L L
a3 = m
a = r m a = r
ω , 2 Lr ωδ , 4 ω
δ δ
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3. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
Lm
2
The advantage of the above solution is that it is not
ωδ = δ Lr Ls & δ = 1 − sensitive to any precise measurement or identification
Lr Lr
of rotor speed.
The use of the above relationships avoids exact β
is
measurements of the flux, resistance, and angular ω ψr
i
ωr
speed of the rotor. Increasing the accuracy of δ
ψ
calculation of the new variables is possible using an ωa = 0 α
observer of the following form: Figure 2. Stator current and rotor flux vector
ˆ
dx12 1
= − x12 + v1 + k01 ( x12 − x12 m )
ˆ (18) B. Speed Observer System
dt Ti
The rotor flux observer is based on the
dx22 1
= − x22 + is 2 + v2 + k20 ( x22 − x22 m )
ˆ (19) voltage model given by [9].
dt Ti dψ sd
ˆ
dt
ˆ (
= u sd − Rs isd + ω rψ sq + k1 ψ rd
ˆψ ˆ com
−ψrd
ˆ ) (25)
The index denotes the calculated values using
dψ sq
ˆ
power measurement. After assuming that motor = usq − Rs isq − ωψ rψ sd + k1 (ψ rq com −ψ rq )
ˆ ˆ ˆ ˆ
parameters are known and constant, it is possible to dt
identify the variable (26)
Lr L L ˆ
ψrd =
ˆ ψsd −δ s r isd
ˆ (27)
x21 using the following model: Lm Lm
ˆ
dx21 R RL Lr Ls Lr ˆ
= −2 r x21 + 2 r m x22
ˆ ˆ (20) ψrq
ˆ = ψsq −δ
ˆ isq (28)
dt Lr Lr Lm Lm
At steady state the left side of the above equation is In (4) and (5), a command flux quantity in feedback
zero, therefore, it is possible to show that the variable path is used instead of the actual quantity. Correction
x21 is part in (29) and (30) appears with K1 gain, which
needs to be tuned in the simulation. The commanded
x21 = Lm x22 m (21) components of rotor flux linkages are as follows:
ψ rq com = 0 & ψ rd com = Lmiˆsd (29)
IV. LOAD ANGLE AND SPEED OBSERVER
Based on the estimated quantities of flux components,
A. Load Angle Calculation it is possible to identify the angular speed of rotor
During the control of an induction motor, the flux linkage vector using PI controller with zero
position of each vector relative to the stationary command signal
coordinate system is not important. The vectors,
which have position relative to each other, have (30)
significant meaning. This relationship can be
observed in the electromagnetic torque description
me = k . Im(ψ r i s ) = kψ r i s sin δ (22)
The vectors of stator current and rotor flux are Rr i sq
presented in Fig. 2. If it is assumed that the magnitude ω =ω −
ˆr ˆψ (31)
of stator current and rotor flux vectors are kept at the
r
Lr i sd
same level by control system, then it is possible to Where ωψ r
ˆ is the estimated angular speed of the
control the motor torque by changing load angle δ .
By using the definition of new state variables it is rotor flux linkage vector. And isq & isd are the
possible to calculate the load angle (the angle estimated currents using the measured currents and
between rotor flux linkage and stator current vectors) defined in the stationary reference frame and using
as follows: the transformation from αβ system to dq reference
x12 frame using the estimated angle
δ = arctg (23)
x 22
After substituting (16) and (17) in (23) the load 1
Θ= ω r
ˆψ (32)
angle is obtained as s
(24) Rotor speed estimation is good only at steady state,
but during the transients there is an error, which
increases with a decreasing speed response [8], [9].
This is relative to the delays provided by integrating
the q -axis component of the rotor flux vector. A
decrease in this error may be achieved by providing a
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4. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
proper initial value for the integrator. In this case, a usα
com
proper initial value might be the angular speed of isd
isq ωψr
αβ usd ωψr
dq Flux ψ rq Rotor
rotor flux vector at steady state. From the steady state
--
PI
com
u sq ψ rq = 0 Simulator
com controlle r speed
u sβ
relationships, it is possible to calculate the rotor speed isα equation ψ rd
+
ω ψ rm calcul ωr
isd
com
ψ rd +
as follows [9], [10]. αβ Lm ω rm + ω isd isq
dq 2m
X12m
−a3 x12 −ωi i 2 s + a4 q isβ isq • Rr Lm
ωrm
•
= (33)
X 21m Lr
a3 x22
Where ω i and is are the angular frequency and Θ 1
S
stator current vector, respectively.
Figure 3. Rotor angular speed observer system
Using the steady state relationships of induction
motor, it is possible to modify the described estimator B. Proposed Speed Sensorless Control
(31) in the following form:
The block B in fig.4 represents the estimator which
is replaced by the estimator represented by block A.
 1   1  Lm x12 m  (34)
ωψ r = − K 1 +
ˆ  T s ψ rq + 1 + T s  ω rm + Rr L x 
ˆ    This modified speed sensor has many advantages
 w   w  r 21m  over open loop estimator which can be better
understand by performance result. The control
Where Tw is the time constant of the first order strategy of modified speed sensor is as explained
delay filter. The first part of (34) is the equation of PI below.
controller (30) and the second part is the filtered
value of the rotor flux vector. The block diagram of a
modified speed observer is presented in Fig. 3. As
will be shown in the simulation results for the speed
observer system from Fig. 1, the error at steady state
is about 2%. This error is less than the case of using
an observer without taking into account angular speed
of flux linkages calculated from the steady state
condition.
V. PROPOSED CONTROL SCHEME
A. Control scheme with speed feedback Figure 4. Actual and Proposed Scheme
In fig 4, block A represents the estimator which is
described and presented in fig 5.This is an open loop In the presented system, the vectors are stator
estimator which estimates the slip frequency ωsl as a current and rotor flux linkage. The load angle may be
result of which we can get rotor speed ωr in the kept constant by changing the position of stator
stationery reference frame. The simulation parameters current vector as a result of tuning its pulsation. The
are given in Table1. current frequency ω i may be changed directly using
TABLE 1
load angle controller or indirectly by changing the
Parameters of Induction Motor for Simulation
slip frequency ω 2 .
Rotor Squrrel Frequency 50Hz
Type Cage ωi = ω2 + ωr (35)
Voltage 440V Nominal 2238W The calculated stator current frequency is provided to the
PWM block. The command values of load angle δ
(Vrms) Power com
Stator Rs=1.05Ω Rotor Rr=0.98Ω
resistance and stator current amplitude Is, are adjusted by the
resistance
Stator Rotor
Proportional–integral (PI) controllers. Rotor angular
inductance Lls=0.004 inductance Llr=0.004 speed may be measured
Mutual
H
0.13H Friction
4H
0.005752 (I com 2
) =
(x 12 ) + (x
com 2
22
com 2
) (36)
inductance Factor(f) N.ms
s
(x ) 21
com
(Lm) And the load angle is
Inertia(J) 0.2 kg.m^2 Pair of
Poles(P) 2  x com 
δ com = arctg  12 com 
x 
(37)
 22 
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5. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
Usd + control simplifies the structure of the control system
Σ Lr/Lm 1/p by eliminating the stator voltage filtering block.
-
Isd VI. SIMULATION AND PERFORMANCE EVALUATION
Rs+Ls’p
+
Lm/Tr
ωr The Proposed scheme with its controller action is
Σ /
simulated in MATLAB/SIMULINK. The induction
- +
Σ motor with load is presented in details with voltage
+ source inverter in SVPWM mode in SIMULINK. The
Isq Rs+Ls’p performance results are presented in the following
sections:
-
Usq + A. Open Loop Control Scheme
Σ Lr/Lm 1/p
The proposed control scheme is simulated in
MATLAB/SIMULINK and performance is observed
ω sl under different dynamic conditions.
Ψ rd - ωr 1.Step change in load
p
+Σ
R P
Ψ rq
The shaft load is changed after the free running
of the motor. The performance is shown in fig. 8 to 9.
Figure 5. Estimator represented by Block A The dynamic performance of motor as well as
estimator under load TL=70 N-m applied at time
Controller for state variable X12 and X21are used in t=2000 ms, with with the terminal voltage V=440V.
this research. The controller command signals of the The estimated torque and speed are shown the fig.
com com
variables X 12 and X 22 on the basis of these 8 and 9 respectively.Because of the stator voltage
quantities the square of the current amplitude is characteristics it is essential to filter the voltage to get
calculated as the fundamental harmonic. Filtering the voltage signal
com com complicates the control system and provides undesired
X 11 X 12 delay in the measurement channel.
Is
- com
X 11 Is
com
X 21
atg
δ com
com
--
X 22
X 21m
Fig 6
As a result, the control system performs using
actual values of stator currents and delayed values of
stator
voltage, which leads to non precise variable
identification.
B. Simulation of the Proposed Speed Sensorless control
In the proposed control system, two different current
Induction Motor
controllers, hysteresis [7] and predictive [8], [9] are
used. In the control system it is possible to use 1. Step change in Load
command stator current and predicted voltage, which The performance results are shown for step change
appears at the output of the predictive controller with load torque from 0 to 70 N-m at time t=0.2 sec
because there is an access to first harmonics of the with voltage V=440V in Fig. 12 to Fig.18. The
currents and voltages. The use of predictive current estimated and actual speed of the motor are shown the
controller in the control system with load angle fig.12. The stator current is observed and is shown in
the fig.13. There is slight increment in the stator
current because of increase in load torque at 0.2 sec.
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6. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010
CONCLUSION
A speed observer system for sensorless control of
induction is developed. The rotor peed as been
calculated using steady state relationship applied to
the observer system. It has high accuracy and behaves
satisfactory under all the speed range. An observer
system has been adopted for the nonlinear control of
The state variables of the estimator are shown in fig induction motor. The simulation results illustrated
14 to fig 16. The estimated active power and reactive that the system operates correctly for the different
power is shown in fig.18. This shows that there is motor running conditions. The proposed scheme is
increment in the active power at t=0.2sec and also the working in closed loop control of the induction motor
slight increment in reactive power. control. The speed sensorless induction motor with
torque angle control has better dynamic performance.
The power estimate algorithm is also tested with the
given induction motor model.
References
[1] Guoliang Zhang and Philip T. Krein “Torque-Angle
Oriented Control of Induction Machines”
[2] A. B. Plunkett, J. D. D'Atre, and T. A. Lipo,
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1979.
[3] N. R. N. Idris, A. H. M. Yatim, "An improved stator
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