A Performance Study of PI controller and Fuzzy logic controller in
V/f Control of Three Phase Induction Motor
Using Space Vector Modulation
Safdar Fasal T K & Unnikrishnan L
Department of Electrical and Electronics Engineering,
Rajagiri School of Engineering And Technology, Cochin, India
E-mail : safdarfasal@gmail.com & unnikrishnanl@rajagiritech.ac.in
Abstract – This paper presents a comparative study of the
proportional integral controller and the fuzzy logic
controller in V/f control of three phase squirrel cage
induction motor drive using space vector modulation
technique. Here the speed control is possible by varying
supply frequency using a voltage source inverter while
keeping voltage to frequency ratio as a constant.
Proportional integral controller input is speed error while
in fuzzy logic controller inputs are speed error and speed
error variation. The controller output used to control the
reference of space vector modulation. Hence, the
fundamental frequency and fundamental voltage of voltage
source inverter output can be varied to control the rotor
speed. The performance of proportional integral controller
and fuzzy logic controller under load torque variation is
evaluated using simulation results in MATLAB/Simulink.
Proportional integral (PI) controllers are normally
used in V/f control of induction motors. In this case a
mathematical model of the real plant is required for the
controller design with conventional methods.
Identifying the accurate parameters for a complex
nonlinear and time-varying nature of real plant is
difficult. Also fine tuning of parameters is time
consuming. PI controllers are sensitive to parameter
variations inherent in real plant operations.
Conversely, the V/f control using fuzzy logic
controller(FLC)
overcomes
disadvantages
of
Conventional PI controllers [4]-[6]. FLCs have the
ability to adapt with nonlinearity. Also the control
performance is not much affected by plant parameter
variations. FLCs are based on certain well defined
linguistic rules; hence necessity of precise mathematical
model of a real plant can be avoided.
Keywords – Three phase Induction motor, Proportional
integral controller, Fuzzy logic controller, Space vector
modulation, Voltage source inverter.
I.
This paper is organized as follows. In section II,
modeling of three phase IM in stationary reference
frame in per-unit system is explained. Section III
describes the basics of Space vector pulse width
modulation (SVPWM)[3] technique. In section IV
Induction motor with PI controller is presented. In
section V, Fuzzy logic controller design is described. In
section VI, Induction motor with fuzzy logic controller
is presented. In section VII, comparative analysis of PI
controller and FL controller under various conditions is
discussed based on simulation results using
MATLAB/Simulink [7]. Finally, section VIII gives
conclusion of this work
INTRODUCTION
Now-a-days Three Phase Induction Motors are
widely used in industries because of its rugged
construction, easy speed control, low cost of repairs and
adaptation to speed and load torque deviations. Usually
Induction motor (IM) drives are used in fan, pump and
conveyor applications for energy saving by speed
control.
Scalar control and Vector control are the two
important methods of speed control of three phase
induction motor [1].
V/f control is a scalar control which has wide
application. Several studies are going on in the field of
vector control due to better dynamic response. However,
Scalar control has wide applications in industries
because of its simple structure characterized by low
steady-state error. Therefore, constant voltage-frequency
ratio (V/f) scalar control is considered in this paper for
comparison [2].
II. INDUCTION MOTOR PER-UNIT MODEL
In this section per-unit modeling of three phase
squirrel cage induction motor in stator reference frame
is discussed. The modeling equations for per unit
currents are as follows:
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ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)
(1)
(2)
(3)
(4)
Where,
and
are per unit stator currents in q-axis
and d-axis respectively.
and
are per unit stator
voltages in q-axis and d-axis respectively.
and
are per unit rotor current in q-axis and d-axis
respectively.
is base frequency.
and
unit
stator
and
rotor
respectively.
and
III. SPACE VECTOR MODULATION
are per
resistance
Space vector modulation is a one of the advanced
pulse width modulation (PWM) technique used for
inverter switching. Usually there are eight possible
switching states in an inverter. In these six are active
vectors viz. V1,V2, V3, V4, V5, V6 and two are null
vectors viz. V0, V7 as shown in Fig. 2. We utilize only
six active vectors in sinusoidal pulse width modulation
but SVPWM uses six active vectors and null vectors to
generate the required space voltage vector.
are per unit stator and rotor
reactance respectively.
is per unit mutual reactance.
The modeling equations for per unit flux linkages are as
follows
(5)
(6)
(7)
(8)
Where, Ten is per-unit electromagnetic torque produced
by IM. Tln is load torque in per unit. wrn is rotor speed in
per-unit and Jn is Inertia constant in per-unit.
Figure. 1 shows Simulink model of three phase IM
using (1) to (10). Here Vasn, Vbsn and Vcsn are the input
voltages to the IM. Using this model, simulations are
done in section VII to analyze the performance of PI
controller and FLC.
Figure 2. Basic active vectors and null vectors
The required space vector Vref can be generated
using two neighboring active vectors V1 and V2 for a
time period of t1 and t2 respectively along with null
vectors for a time period of (T s-(t1+t2)), where Ts is the
switching period.
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ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)
IV. INDUCTION MOTOR WITH PI CONTROLLER
Figure. 3 shows basic block diagram of three phase
IM with PI controller. IM motor is supplied from a
variable voltage variable frequency (VVVF) Voltage
source inverter (VSI). The switching signal for VSI is
obtained by Space vector pulse width modulation
(SVPWM). Speed is measured using speed sensor and is
compared with reference speed. Speed error is input to
the PI controller which gives the frequency variation to
achieve the reference speed as output. This frequency
variation is added to the actual frequency obtained from
the actual speed to get the reference frequency.
Figure 5. Output variable of fuzzy system (Δe)
TABLE I.
Figure 3. Basic block diagram of IM drive with PI
controller
Reference frequency is multiplied with constant voltage
to frequency ratio (V/f) to obtain the amplitude of
reference signal for SVPWM.
FUZZY RULES
NL
NM
NS
ZZ
PS
PM
PL
NL
NL
NL
NL
NM
NS
NVS
ZZ
NM
NL
NL
NM
NS
NVS
ZZ
PVS
NS
NL
NM
NS
NVS
ZZ
PVS
PS
ZZ
NM
NS
NVS
ZZ
PVS
PS
PM
PS
NS
NVS
ZZ
PVS
PS
PM
PL
PM
NVS
ZZ
PVS
PS
PM
PL
PL
PL
ZZ
PVS
PS
PM
PL
PL
PL
V. FUZZY LOGIC CONTROLLER DESIGN
In the case of three phase IM drive, speed error (e)
and speed error variation (Δe) are input variables to the
FLC. Frequency variation (Δf) is the output obtained
from the FLC based on certain linguistic rules defined in
FLC to achieve the reference speed.
Frequency variation has nine membership functions
vary between the interval [-1,1] . The membership
functions are described as follows: ―NL‖ is ―Negative
and large‖; ―NM‖ is ―Negative and Medium‖; ―NS‖ is
―Negative and Small‖; ―NVS‖ is ―Negative and Very
small‖; ―ZZ‖ is ―Zero‖; ―PVS‖ is ―Positive and Very
small‖; ―PS‖ is ―Positive and small‖; ―PM‖ is ―Positive
and Medium‖; ―PL‖ is ―Positive and Large.‖ The
linguistic rules used in FL controller are shown by
TABLE I.
The linguistic rules of fuzzy system can be explained
using examples:

If (speed error is NL) and (change in speed error is
NL) , Then (frequency variation is NL)

If (speed error is ZZ) and (change in speed error is
NS) , Then (frequency variation is NVS)

If (speed error is PM) and (change in speed error is
PL), Then (frequency variation is PL) and so on.
Figure 4. Input variables of fuzzy system (e)and (Δe)
Input variables, speed error (e) and speed error
variation (Δe), have same membership functions which
vary between the interval [-1, 1].
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ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)
VI. INDUCTION MOTOR WITH FLC
Fig. 6 shows the basic block diagram of an IM drive
with FLC.
Figure 6. Basic block diagram of IM drive with FL
controller
(b)
As explained in section IV, inputs to the FLC are speed
error and speed error variation. By giving these inputs to
the fuzzy logic controller, the output can be obtained as
frequency variation according to the linguistic rules of
the FLC. The working of SVPWM generator, VSI and
IM are similar to that of a drive which uses PI controller
as explained in section IV.
Figure 6. Performance of PI controller (a)Rotor speed
(pu) (b) Torque (pu)
In fig. 7, Rotor speed is increased gradually and
settled to reference value at 5sec. Due to application of
load torque of 0.5 pu at 5sec, speed is suddenly reduced
to a lower value compared to reference speed. Also,
torque is increased gradually and settled to 0.5 pu at
8sec with irregularity.
VII. SIMULATION RESULTS
Performance study of PI controller and FLC are
carried
out
using
simulation
result
in
MATLAB/Simulink. Per- unit IM model in section II is
used for simulation of a 1hp, 380V, 50Hz, 6 pole three
phase squirrel cage induction motor. All simulation
values are in per unit.
B. Performance of FLC under load torque variations
Fig. 8 shows the performance of FLC under load
torque variation. Here, reference speed is 1pu. Step load
of 0.5pu is given at 5sec.
A. Performance of PI controller under load torque
variations
Fig.7 shows performance of PI controller under
load torque variations. Here, reference speed is 1pu.
Step load of 0.5pu is given to IM at 5sec.
(a)
(a)
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VIII. CONCLUSION
In this paper FLC for V/f control of induction motor
is designed. The designing has been done with the help
of MATLAB/Simulink. This controller takes inputs, viz.
speed error (e) and speed error variation (Δe) and gives
an output as frequency variation. The output changes
according to the rules of fuzzy system.
From simulation results it is proved that performance
of FLC is much better compared to the PI controller.
Under load torque variations, FLC response is rapid and
rotor speed is able to follow the reference speed. In
addition, desired load torque can also be achieved.
The performance of controller can be further
increased by using a combination of PI controller and
FLC. This ensures precise control of speed under load
torque and speed variations.
IX. REFERENCES
Figure 7. Performance of FL controller (a) Rotor speed
(pu) (b) Torque ( pu)
[1]
Bimal K. Bose, ―Modern Power Electronics and
Ac Drives,‖ Prentice Hall, 2001.
.In fig. 8, Rotor speed is increased gradually and
settled to reference value at 5sec. Application of load
torque of 0.5 pu at 5sec cause a very small dip in rotor
speed but within seconds rotor speed follow reference
speed. Also, torque is increased suddenly and settled to
0.5 pu within mille-seconds.
[2]
R. Krishnan, Electric Motor Drives—Modeling,
Analysis, and Control.Upper Saddle River, NJ:
Prentice-Hall, 2001.
[3]
Barry W Williams,―Principles and Elementsof
Power Electronics,‖University ofStrathclyde
Glasgow,2006.
[4]
Marcelo Suetake, Ivan N. da Silva, Member,
IEEE, and Alessandro Goedtel ―Embedded DSPBased Compact Fuzzy System and Its
Application for Induction-Motor Vf Speed
Control‖- IEEE trans on industrial electronics,
vol. 58, no. 3, March 2011.
[5]
D. Neema R. N. Patel, A. S. Thoke,―Speed
Control of Induction Motor using Fuzzy Rule
Base,‖International
Journal
of
Computer
Applications (0975 – 8887),Volume 33– No.5,
November 2011.
C. Comparison between PI controller and FLC
performance
The comparison between PI controller and FLC can
be explained using simulation results shown in figure. 7
and figure. 8, important observations are:

Initial torque variations in IM drive using PI
controller is much higher compared to the IM drive
using FLC.

Torque ripple is high in the case of PI controller but
torque ripple is very small in the case of FLC.

In the case of PI controller, under load torque
variations, there have some irregularity in torque
produced which is absent in FLC
[6]

Under load torque variations, speed is settled to a
lower value of reference speed in the case of PI
controller. But the rotor speed follows reference
speed in the case of a FLC.
N B Muthuselven, Subharansu Sekhar Dash, P
Somasundaram ―A High Performance IM Drive
System Using Fuzzy Logic Controller‖- IEEE
2006.
[7]
MATLAB/SIMULINK® version 2009a, The
MathWorks Inc., USA.


Under load torque variations, the desired torque can
be obtained gradually in the case of PI controller.
While using FLC desired torque can be obtained in
a fraction of a second.

So, overall performance of FLC is much better than
PI controller.
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