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International Journal of Advanced Engineering and Nano Technology (IJAENT)
ISSN: 2347-6389, Volume-2 Issue-4, March 2015
5
Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication Pvt. Ltd.
Abstract— Voltage source inverter is widely used in many
industrial applications such as robot, electric vehicle and machine
tool. The performance of the drive system depends upon the
method of control for converter and motor control method. From
the most performance method is a space vector pulse width
modulation technique. Here the field oriented control of
permanent magnet synchronous motor with using space vector
modulation is used to controlling the inverter and improving the
performance characteristics of the motor such as speed, currents
and the electric torque by reducing their ripples. This occurs
through adding PI controller for flux and simple model to track
the torque and speed when varying load is applied. In the PI
controller, the d-axis flux is compared to rotor permanent magnet
flux to solve the problem arises from non-sinusoidal of the
magnetic flux. The output of the PI controller is added to the
reference d-axis current. The new d-axis current will reach the
best value of THD. The simple model is used to generate new q
axis torque current controller comes from lookup table and
adding to reference q axis current controller to control the motor
speed. The effect of improvement can be seen through the torque
ripples, THD and motor speed. This work is simulated by matlab
simulink.
Index Terms—Matlab simulink, PI, PMSM and SVM.
I. INTRODUCTION
In the past DC motors are used to get accurate speed, fast
dynamic response and high performance characteristics
nearer zero speed but these motors have drawn back such as
need regular maintenances due to presence of brushes and
commutators. With development of power electronics and
microcontroller, the DC motors are replaced with AC motors.
Here the PMSM is used this is because this motor has
many advantages such as high torque to inertia ratio, high
torque to current ratio, high power factor, rotor lossless and
high efficiency. The performance of these motors (PMSMS)
in drive systems depend upon the motor control and method
of current control in power converter. From the most
important methods to control the power converter are current
and voltage controls. The current control is preferable. This is
because it is simple. The quality control of this method
depends upon the quality of the waveform is generated by
current controlled of converter. To get good power waveform
this depends upon switching frequency of the PWM,
modulation method and current waveform. The method of
motor control is very important in the drive system. This is
because the operation of the PMSM under effect of scalar
Manuscript Received on March 2015.
Eng. Hamdy Mohamed Soliman, Cairo Metro Greater, Egypt.
Prof. Dr. S. M. EL-Hakim, Department of Electrical Power Engineering
and Machines, Cairo University/ Faculty of Engineering/ Giza, Egypt.
control is suffered from complicated coupling nonlinear
dynamic performance. This problem can be solved by field
oriented control (FOC). PMSM with FOC emulates the
separately excited DC motor. In this method of control, the
stator current can be decupled into flux and torque current
components. They can be controlled separately. In four
quadrant with keeping magnetic circuit linear and applying
the principles operation of the FOC, the linear relation can be
described the motor torque. The performance of the motor
suffers from uncertainties, parameters variation, harmonics in
both motor and inverter. These problems affect motor
performance. To solve this problem, the machine design and
control technique are used. The first method is complicated
and high cost so the other method is preferable[1-3]. Many
control techniques are used to solve this such as:
Space Vector Pulse Width Modulation (SVPWM) which has
some features such as, [4,5]
1. Its can able to adjust with the varying fundamental
frequency to switching frequency ratio.
2. Its hardware implementation is very simple
3. It has lower base band harmonics than regular
PWM
4. Fifteen percent more output voltage than
conventional modulation.
5. More efficient use of dc supply and avoids
unnecessary switching.
Also some programs are used to cancelation the harmonics
but these methods require full knowledge about the machine
parameters. These methods become undesirable if the
operating point changes [6-7]. The current control scheme
with an adaptive internal model is proposed in many
researches as [8]. Passive filter is used to reducing the ripples
in [9] but higher circulating current arises between filter and
inverter. Active filter is used to reducing the ripples but this
method is higher cost [10].
Proportional integrator controller (PI), it is the most
common controllers used in a wide range in the industrial
applications. The popularity of PI control can be attributed to
its simplicity. The integral controller has drawback such as
saturation. This phenomenon can be avoided by introducing a
limiter to the integral part of the controller before adding its
output to the output of the proportional controller. The output
of the PI is used as the input of controlled voltage source
inverter which is fed to the motor for controlling its speed
[11-13]. Many researches used PI controller to improve the
position and speed controllers this is because it affects the
performance of the drive system especially torque and speed
oscillations. The PI controller is sensitive to uncertainties
Simple Model and PI Controller to Improve the
Performance Characteristics of PMSM under
Field Oriented Control with Using SVPWM
Hamdy Mohamed Soliman, S. M. EL-Hakim
Simple Model and PI Controller to Improve the Performance Characteristics of PMSM under Field Oriented Control
with Using SVPWM
6
Published By:
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variation such as motor parameters, disturbance and
temperature variations. So In this study new proportional
integrator corrector controller are used to optimize
conventional PI controllers with using space vector pulse
width modulation to control the inverter and simple model is
used to tracking the motor speed and motor torque. The PI
controller is used to reduce the noise, distortion and ripple in
the stator currents and torque this can be done by reducing the
distortion in the stator flux. The estimated torque is used to
track the motor torque and speed. This system is simulated
through matlab simulink. The simulated model with proposed
new PI controllers is compared with conventional SVPWM to
investigate the advantages of the new proposed modle. This
paper is organized as follows. Section I introduction. Section
II mathematical model of PMSM. Section III SVM. In section
IIIV proposed field oriented control with SVM is introduced.
Section V for PI controller. Section VI is for simulation.
Section VII is for conclusion.
II. M
ATHEMATICAL MODEL OF
PMSM
The mathematical model of a PMSM is similar to that of
wound rotor synchronous motor. The rotor winding of
synchronous motor is replaced with high resistivity permanent
magnet material, hence, induced current in the rotor are
negligible. The permanent magnets on the rotor are shaped in
such a way as to produce sinusoidal back EMF in stator
windings.
The following equations represent the model of PMSM
.
s d
d d d e q
d
dt
v i i
r L
ω λ
= + −
(1)
.
s q
q q q e d
d
dt
v i i
r L
ω λ
= + −
(2)
.
d
d d m
i
L
λ λ
= +
(3)
.
q
q q
i
L
λ
=
(4)
.
e L
m m
d
Jdt
T T
β
ω ω
= − −
(5)
3
[ ( ) ] .
4
e d q
m d q
P
i i
T L L
λ
= + −
(6)
.
2
e m
P
dt
θ ω
=
∫
(7)
Where
d
v
-
q
v
dq axis stator voltages,
d
i
-
q
i
dq axis stator
current,
d
λ
-
q
λ
dq axis stator flux,
m
λ
rotor permanent
magnet flux,
d
L
-
q
L
dq stator axis inductance,
s
r
stator
resistance,
d
dt
is derivative,
e
T
electrical torque
L
T
load
torque,
J
moment of inertia,
β
frictional viscous,
m
ω
mechanical speed,
P
number of poles and
e
θ
electrical position.
With applying the field oriented control,
*
d
i
becomes zero so
the electrical torque becomes
3
.
4
e
m q
P
i
T
λ
=
(8)
III. S
PACE
V
ECTOR
M
ODULATION
Space vector modulation technique is used to switching the
three phase inverter in drive system. This can be seen in Fig.1.
It is consists of six switches that shape the output voltages.
When any upper switch is on, the lower switch in the same
arm is off so by known the upper switched case the output
voltage can be determined. The relation between the line to
line voltages and switching state can be calculated from the
following relation
1 1 0
0 1 1
1 0 1
ab
bc dc
ca
a
b
c
v
v v
v
−
= −
−
(9)
The relation between the phase voltages and switching state
can be calculated from the following relation
2 1 1
1 2 1
31 1 2
an
dc
bn
cn
a
b
c
vv
v
v
− −
= − −
− −
(10)
From Fig.1 it is found that, eight possible connections state
(on off patterns) these pattern states
(
0
V
,
1
V
,
2
V
,
3
V
,
4
V
,
5
V
,
6
V
,
7
V
) are given in table1.
From this table, the eight switching vector can be
represented as Fig.2. Each of these space vectors in Fig.2
resulted from two adjacent vectors and any zero vectors
(
0
V
,
7
V
).
Space vector pulse width modulation (SVPWM) can be
implemented in the following steps:
1. Calculate
v
α
,
v
β
,
ref
v
and angle
α
2. Calculate the time duration
1
T
,
2
T
and
s
T
3. Calculate the switching time of each switches
(
T1
to
T6
)
A. Calculating
v
α
,
v
β
,
ref
v
and angle
α
Depending upon Fig.3 the
v
α
,
v
β
,
ref
v
and angle
α
can
be calculated as
2 2
ref
v v v
α β
= +
(11)
arctan
v
v
β
α
α
=
(12)
B. Calculating time duration
1
T
,
2
T
and
s
T
Depending upon Fig.3 to calculate the time duration in
sector1 on the real and imaginary axes it is found that;
1 1
1 2
cos60 cos
V V
ref
s s
m
T T v
T T
α
+ = (13)
22
sin60 sin
V
ref
s
m
Tv
T
α
= (14)
International Journal of Advanced Engineering and Nano Technology (IJAENT)
ISSN: 2347-6389, Volume-2 Issue-4, March 2015
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Published By:
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Fig.1. Power circuit inverter and PMSM
Voltage
vector
Switching
on
Line to neutral
voltages
Line to line
voltages
an
v
bn
v
cn
v
ab
v
bc
v
ca
v
0
V
T1,T3,T5
0 0 0 0 0 0
1
V
T2,T3,T5
2/3 -1/3 -1/3 1 0 -1
2
V
T2,T4,T5
1/3 1/3 -2/3 0 1 -1
3
V
T1,T4,T5
-1/3 2/3 -1/3 -1 1 0
4
v
T1,T4,T6
-2/3 1/3 1/3 -1 0 1
5
V
T1,T3,T6
-1/3 -1/3 2/3 0 -1 1
6
V
T2,T3,T6
1/3 -2/3 1/3 1 -1 0
7
V
T2,T4,T6
0 0 0 0 0 0
Table 1. modes of operations of three phase voltage
source inverter (the voltage in term of
dc
v
)
Fig.2. Switching space vector and sector
Fig.3. voltage vector
ref
v
From eq13 and eq14 it is found that;
1
3
sin(60 )
2
s
m
T T
α
= −
(15)
2
3
sin
2
s
m
T T
α
=
(16)
0 1 2
( )
s
T T T T
= − +
(17)
Where
1
s
s
T
f
=
,
s
f
is switching frequency and
m
is
modulation index
From that the switching time duration at any sector can be
calculated as:
1
3
sin( )
2 3
s
m n
T T
π
α
= −
(18)
2
3
sin(( 1) )
2 3
s
m n
T T
π
α
= − −
(19)
Where
n
is number of sector
C. Calculating the switching time of each switches
Table2 shows the switching time in inverter
IV. P
ROPOSED
FIELD
O
RIENTED
C
ONTROL
SVM
The conventional structure of the field oriented control is
shown in Fig.4. The error in q axis current is introduced to PI
current controller to produce q axis voltage reference also the
error in d axis current is delivered to PI current controller to
produce d axis voltage reference. These voltages are
transformed with help of electrical rotor position into two
dimensional voltages varying in time which used to generate
gating signals to drive the inverter through SVM. In this
traditional control (FOC), the drive is influenced by
uncertainties, electromagnetic interface, non-sinusoidal of
stator current and permanent magnet rotor flux or all of them.
They reflect on the torque and current causing unwanted
problems such as ripple and noise. PI speed controller which
is used to generate the q-axis current isn't sufficient to
overcome the noise and ripples in torque and current. So this
paper introduced modified structure controller to improve
these problems.
The modified structure of the field oriented control is
shown in Fig5. In this structure, the modified block can be
seen in details in Fig6 and simple model is shown in Fig7.To
minimize the ripple and noise in the torque and controlling the
speed so simple estimated model is used; this model estimated
the load torque and deduced from that new q axis current
controller through lookup table which is added to reference q
axis current controller this new q axis current is comparing to
measure q axis current and the error is used to generating q
axis voltage through PI controller.
With this enhanced in the q-axis current component, the
distortion of the current doesn’t reach the best value. To reach
the best value another PI controller is used. The input of this
PI controller arises from comparing the estimated d-axis flux
with permanent magnet flux. The output of this PI controller
is added to the reference d-axis current which is forced to zero
at constant flux region. This new d axes current is compared
to actual d axis current and introduced to PI controller to
regulate d axis voltage .
The d axis voltage and q axis voltage are transformed with
help of electrical rotor position into two dimensional voltages
varying in time which used to generate gating signals to drive
the inverter through SVM.
Simple Model and PI Controller to Improve the Performance Characteristics of PMSM under Field Oriented Control
with Using SVPWM
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sector Upper switches
(
T1,T3,T5
) Lower switches
(
T2,T4,T6
)
1
0
1 2
T1
2
T
T T
= + +
0
2
T3
2
T
T
= +
0
T5
2
T
=
0
T2
2
T
=
0
1
T4
2
T
T
= +
0
1 2
T6
2
T
T T
= + +
2
0
1
T1
2
T
T
= +
0
1 2
T3
2
T
T T
= + +
0
T5
2
T
=
0
2
T2
2
T
T
= +
0
T4
2
T
=
0
1 2
T6
2
T
T T
= + +
3
0
1 2
T1
2
T
T T
= + +
0
2
T3
2
T
T
= +
0
T1
2
T
=
0
1 2
T2
2
T
T T
= + +
0
T4
2
T
=
0
1
T6
2
T
T
= +
4
0
T1
2
T
=
0
1
T3
2
T
T
= +
0
1 2
T5
2
T
T T
= + +
0
1 2
T2
2
T
T T
= + +
0
2
T4
2
T
T
= +
0
T6
2
T
=
5
0
2
T1
2
T
T
= +
0
T3
2
T
=
0
1 2
T5
2
T
T T
= + +
0
1
T2
2
T
T
= +
0
1 2
T4
2
T
T T
= + +
0
T6
2
T
=
6
0
1 2
T1
2
T
T T
= + +
0
T3
2
T
=
0
1
T5
2
T
T
= +
0
T2
2
T
=
0
1 2
T4
2
T
T T
= + +
0
2
T6
2
T
T
= +
Table 2. Switching time duration
V. P
I
C
ONTROLLER
PI controller is a type of feedback controller which has output
depending upon the error. This error is used to adjust the input
of the other process. Two parameters are used to design this
controller. These parameters are proportional gain (
p
K
) and
integral gain (
i
K
). This controller can represent as
( )
i
p
G s
s
k
k
= +
Proportional gain is used to improving the rise time and
integral gain which is used to eliminate the steady state error.
These parameters can be deduced by many methods such as:
trial and error, Ziegler-Nichols method and internal model of
control.
Fig.4. Conventional structure field oriented control
Fig.5. Modified field oriented control
Fig.6. Modified block
Fig.7. Simple model
The parameters of the PI controller are determined
depending upon [15-16].
International Journal of Advanced Engineering and Nano Technology (IJAENT)
ISSN: 2347-6389, Volume-2 Issue-4, March 2015
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VI. S
IMULATION
S
TUDY
Here conventional and modified models are compared. These
comparisons are used to showing the effectiveness of
modified model on the motor speed responses, torque
responses and THD in current. Table3 shows the
improvement in the torque ripples and THD due to use the
simple model and PI controller. Table4 shows the motor
parameters. During the simulations, the torque set value is at
rated. In all Figs the time axis is in seconds and the following
cases are simulated
1. Motor starting with loading.
2. Sudden applied load.
3. Dynamic load
Where it is found that,
A. The first Case (starting with load)
In Figs (8-9), dq axes currents are simulated with
conventional and modified model respectively. In
conventional model (Fig8), the dq axes currents have some
distorted. In modified model (Fig9), both q-axis current
component and d-axis current component are enhanced.
Fig.8. Idq-axis current with conventional method
Fig.9. Idq-axis current with modified method
The torque responses in Fig.11 showed that, the torque ripple
is improved with modified model if it is compared to the
conventional model (Fig.10).
Figs.(12-13) show that the speed with conventional model and
the modified model approximately the same.
In Fig.15, the stator currents become smoother with
modified model due to improvement in the dq-axes current
components. In conventional model (Fig.14), the stator
current has some distortion due to noise and electromagnetic
interference.
Fig.10. Torque with conventional method
Fig.11. Torque with modified method
Fig.12. Speed with conventional method
Simple Model and PI Controller to Improve the Performance Characteristics of PMSM under Field Oriented Control
with Using SVPWM
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Fig.13. Speed with conventional method
Fig.14. Stator current with conventional method
Fig.15. Stator current with modified method
B. The Second Case (sudden applied load)
Here the motor start without load, at 0.1 sec. sudden load is
applied, at 0.25 the load is suddenly removed where it is
found that,
Fig. 16 shows the oscillation and distortion in the dq-axes
currents with conventional method where found that higher
oscillations and distortions in both dq axes current while in
modulation method the distortion and oscillations are
improved as shown in Fig.17.
Fig.16. Idq-axis current with conventional method
Fig.17. Idq-axis current with modified method
The effect of applied and load removal can bee seen in Figs
(18-19). In conventional method (Fig.18), the motor torque is
very increasing when suddenly load is applied and decreased
when load is removed but in modified model when the load is
suddenly applied or removal the effect of this can be
neglected i.e. with modified model the motor torque
responses is improved (Fig.19).
Fig.18. Torque with conventional method
International Journal of Advanced Engineering and Nano Technology (IJAENT)
ISSN: 2347-6389, Volume-2 Issue-4, March 2015
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Fig.19. Torque with modified method
The effect of simple model can be seen in Fig.21 with
sudden applied or removal the load. The same effect can be
studied with conventional method (Fig. 20) where it is found
that,
Little change in the motor speed can be seen when suddenly
load is applied or removal when compared to conventional
model which has higher effect on the motor speed for the
same case.
Fig.20. Speed with conventional method
Fig.21. Speed with conventional method
In Fig.23, the stator currents become smoother with
modified method due to reduction of the noise in the stator
flux and suppresses in electromagnetic interference. With
adding PI current controller, the stator currents become less in
the total harmonics distortion if it is compared to the
conventional model (Fig.22).
Fig.22. Stator current with conventional method
Fig.23. Stator current with modified method
C. The Third Case (dynamic load)
Here the motor start with increasing load gradually, at 0.1 sec.
the load reached full load, at 0.25 the load is gradually
decreased at 0.35 sec. the load reached zero and continuous
without load at 0.4 sec.
Oscillations in dq-axes currents with conventional method
can be seen in Fig.24. In modulated method the oscillations
are improved (Fig.25).
Fig.24. Idq-axis current with conventional method
Simple Model and PI Controller to Improve the Performance Characteristics of PMSM under Field Oriented Control
with Using SVPWM
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Fig.25. Idq-axis current with modified method
In Fig.26, the ripple torque is reduced with modified methods
if it is compared to conventional method (Fig. 27) this occurs
due to less in the electromagnet interface and improvement in
q-axis current component with modified model.
Fig.28 shows the motor speed with conventional method
and Fig.29 shows the motor speed with modified methods.
From these Figs. It found that;
The variation of the speed due to varying load can be
neglected due to use the simple model where the variation of
the motor speed with conventional method can not be
neglected.
Fig.26. Torque with conventional method
Fig.27. Torque with modified method
Fig.28. Speed with conventional method
Fig.29. Speed with conventional method
In Fig.31, the stator currents become smoother with modified
method due to reduction of the noise in the stator flux and
suppresses in electromagnetic interference. With adding PI
current controller, the stator currents become less in the total
harmonics distortion if it is compared to the conventional
model (Fig.30).
Fig.30. Stator current with conventional method
International Journal of Advanced Engineering and Nano Technology (IJAENT)
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Fig.31. Stator current with modified method
VII. C
ONCLUSION
This paper is addressed the dynamic performance of
permanent magnet synchronous motor under effect of field
oriented control with simple model and PI controller with
using space vector pulse width modulation. SVPWM is made.
Simple model to control the motor torque and motor speed is
proposed. PI current controller is used to affect the inverter
switching frequency to reduce the ripples in the torque and
current. The stator current waveforms become smoother. The
results show that, the q-axis current becomes smoother which
reflects on the motor torque to keep quit operation. The d-axis
current reduced to zero which reflects on total harmonic
distortion in current. Simple model reduced from effect of
sudden applied load, removal load and dynamic load on
motor speed and motor torque.
Motor control Torque
ripples THD in current
Conventional field
oriented control 0.62 0.83
Modified field
oriented control 0.5 0.71
Table 3. Effect of modified method on torque ripples and
THD in current.
Output power in Watts 900
Motor speed in R.P.M. 1000
Line to line voltages in volts 110
Rated torque N.M 8.59
Number of poles 10
Stator resistance in ohm 0.43
d axis stator inductance in Henry 0.00697
q axis stator inductance in Henry 0.00697
Permanent magnet flux in voltage.S/Rad 0.11
Moment of inertia N.m. S
2
0.001118
Table 4. Motor parameters
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