International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 8-April 2015
Sensorless Direct Torque Control of Induction Motor Fed by Indirect
Space Vector Pulse width Modulated Matrix Converter
ATTILI V V KAMESWARA SURESH 1, Dr. K. VIJAYAKUMAR 2,
Department of Electrical Engineering, Faculty of Engineering and Technology, SRM University, Kattankulathur
603 203, TamilNadu, INDIA
Abstract— Matrix converter is a topology of direct conversion
from fixed input voltage and frequency to variable voltage and
frequency. This paper presents a sensorless direct torque and
flux controlled induction motor fed by indirect SVPWM matrix
converter. Control of stator flux and torque is achieved by using
PI controller. The closed loop speed control action is achieved by
PID controller which is later replaced by Fuzzy PID controller.
The output voltage is controlled with the help of indirect
SVPWM which are fed as firing pulses to switches. The DTC
scheme proposed uses a fuzzy PID controller as speed control
action that replaced PID controller which have an advantage of
giving better performance and control highly nonlinear systems
to overcome limitations of PID controller. The working principle
of svpwm mc and characteristics of Fuzzy PID are presented and
performance is tested at variable loading conditions.
the conventional PID and Fuzzy PID controller. The
simulation results show that this strategy Fuzzy PID controller
has fast dynamic response, good robustness and low
dependence on the model parameters when compared to
conventional PID controller.
Keywords— matrix converter, ISVPWM, DTC, Conventional
PID, fuzzy PID controller.
I. INTRODUCTION
The matrix converter that replaces the conventional
inverter fed to the induction motor due to the elimination of
bulky dc capacitor that reduces life of converter circuit, the
input and output currents are utmost sinusoidal, capability of
bi-directional power flow, and input power factor adjustability.
Furthermore, it also has the capability of high integration and
semiconductor structure is highly reliable. For extreme
temperatures and critical volume/weight applications the
matrix converter topology is recommended. However due to
difficult modulation techniques and switching compared to
conventional inverter it is limited for only few practical
applications.
When MC is exposed to harmonics and nonsinusoidal currents its performance deteriorates and Some
papers have been presented mitigation methods. Conventional
PID controller works well only when the mathematical model
of the system could be computed. However, it is difficult to
implement the conventional PID controller for complex as
well as variable and non-linear systems. So, Fuzzy PID
controller which does not require any precise mathematical
model and gives good response for complex applications that
can be applied easily. The Fuzzy PID controller based
controller is capable to embed the qualitative knowledge and
experience of an operator or field engineer about the process.
This paper is to present the complete modeling and simulation
analysis and performance comparison of MC by using both
ISSN: 2231-5381
Fig 1: Matrix converter basic circuit diagram.
II. SENSORLESS DTC OF INDUCTION MOTOR DRIVES FED BY
MATRIX CONVERTER.
The direct torque control of induction motor fed with
matrix converter is discussed in this paper. The voltage vector
selection is done with the help of voltage modulation
technique of ISVPWM and firing pulses are fed to matrix
converter switches.
A. Control Principles of Matrix Converter
The space-vector approach is based on the
instantaneous space vector representation of input and output
voltages and currents. Among the 27 possible switching
configurations available in three-phase to three phase matrix
converters. Among them only 21 are useful in the ISVM
approach. The first 18 switching configurations determine an
output voltage vector and an input current vector, having
directions fixed as shown in (Fig. 2). The vectors magnitude
depends upon the instantaneous values of the input voltages
and output line currents, respectively. The last three switching
configurations determine zero input current and output voltage
vectors. The SVM algorithm for MCs has the inherent
capability to achieve full control of both the output voltage
vector and the instantaneous input current displacement angle.
The two-stage SVM is a variation of the classic SVM
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International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 8-April 2015
technique which has some important features such as over
modulation. The output voltage vector and the input current
displacement angle are known as reference quantities at any
given sampling instant,. The input line-to-neutral voltage
vector is imposed by the source voltages and is recognized by
its measurements.
where mi is the modulation index
The duty cycles of VSR are
dαv = mv sin(π/3-θv)
(8)
dβv = mv sin(θ)
(9)
dov = 1-dαv-dβv
(10)
mv - VSI modulation index
Hence direct converter modulation can be derived
from the indirect transfer function. First modulation is carried
out as if the converter is an indirect. The switch control
signals for DMC are then derived based on the relation
between the VSR and VSI. The modulation index of the DMC
is given as
m = mi.mv
Fig 2 Available DMC vectors for ISVM (a) Voltage vector (b) Current vector
B. Torque and Flux Estimation mechanism
Then, the control of the input side can be achieved,
controlling the phase angle of the input current vector. Both
input current and output voltage vectors are synthesized by
considering the duty cycles. The duty cycles are calculated for
both the rectifier stage and inverter stage are multiplied to get
final output pulses to the 9 switches. The input voltage vectors
and current vectors are as follows.
= (2/3)
(1)
The measurement of quantities using sensors is
difficult, complex and unstable to output parametric
variations. So we will go for estimation of quantities. The
components of the current ( , ) and stator voltage ( , )
are obtained by transformation expressed in (11). The
stator flux components ( , ) are expressed in (12) and
(13). The stator flux linkage per phase and the
electromagnetic torque estimated are expressed in (17) and
(19) respectively. The electromagnetic torque and the
stator flux estimation depend on the stator voltage and the
stator current space vectors.
Similarly
= (2/3)
(11)
=
(2)
Vi =amplitude, wi=constant input angular velocity
Where x represents stator voltage and current
components.
For balanced three phase, load currents will be
= (2/3)
(12)
=
(13)
(3)
= (2/3)
=
(14)
(4)
= lagging phase angle of output current to the output
voltage.
o=
(15)
(16)
lagging phase angle of input current to the input voltage.
(17)
The duty cycles of VSR are
dαi = mi sin(π/3-θi)
(5)
dβi = mi sin(θ)
(6)
doi = 1-dαi-dβi
(7)
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(18)
(7)
(19)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 8-April 2015
(20)
proportional gain has 7 and the integral gain has 7 and the
derivative gain has 7. The 7 membership functions of the
inputs are as shown in Figure 5.
is the torque angle, torque can be directly
controlled using torque angle.
C. Direct torque control scheme with indirect space
vector modulation technique.
The DTC basic principle is to select the stator
voltage vectors directly from the errors of torque and flux
generated between estimated and reference values. Stator
fluxes are estimated using voltage model and current model
equations as shown in (12) and (13). Speed is calculated and
then compared with reference speed. The error is fed to speed
controller(PID or Fuzzy PID controller). The output of speed
controller is normalized as reference torque. The reference
torque is compared with estimated torque and error is
controlled with the help of torque controller (PI controller).
Similarly flux is also controlled. The output of torque
controller, and flux controller are compared with calculated
values as shown in figure 3 fed as input for ISVPWM which
leads to voltage vector selection. The output pulses generated
are fed as switching pulses to switches of matrix converter.
Fig 4:Structure of fuzzy PID controller.
Fig 5(a): Membership functions of input variables for error.
Fig 3: Basic block diagram of direct torque control.
D. Fuzzy PID Control of a Matrix Converter.
Fuzzy supervised scheme (Fuzzy PID) controller was
designed based on operational features and control
requirements of the matrix converter circuit. A Proportional
Integral and derivative (PID) controller is used along with
fuzzy supervisory control as shown in figure 4. Using the
error signal and its derivative, the fuzzy system adjusts
continuously the parameters of the PID controller to fit all
operating conditions. The Mamdani type fuzzy inference
system was suggested in the system which is used to develop
the controller.
The input signals of fuzzy controller are the error (e)
and its derivative of error, and the output signals are the
normalized value of the and the normalized value of the .
The input signals have 7 membership functions, while the
ISSN: 2231-5381
Fig 5(b): Membership functions of input variables for rate of change of
error.
The rules table for proportional, integral and derivative
constants are given in the following tables.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 8-April 2015
TABLE 2
Fuzzy rules for integral coefficient.
TABLE 1
Fuzzy rules for proportional coefficient.
e
NB
NM
NS
ZO
PS
PM
PB
NB
PB
PB
PM
PM
PS
ZO
ZO
NM
PB
PB
PM
PS
PS
ZO
NS
NS
PM
PM
PM
PS
ZO
NS
NS
ZO
PM
PM
PS
ZO
NS
NM
NM
PS
PS
PS
ZO
NS
NS
NM
NM
PM
PS
ZO
NS
NM
NM
NM
NB
PB
ZO
ZO
NM
NM
NM
NB
NB
TABLE 2
Fuzzy rules for integral coefficient.
E
NB
NM
NS
ZO
PS
PM
PB
NB
PS
NS
NB
NB
NB
NM
PS
NM
PS
NS
NB
NM
NM
NS
ZO
NS
ZO
NS
NM
NM
NS
NS
ZO
ZO
ZO
NS
NS
NS
NS
NS
ZO
PS
ZO
ZO
ZO
ZO
ZO
ZO
ZO
PM
PB
NS
PS
PS
PS
PS
PB
PB
PB
PM
PM
PM
PS
PS
PB
III. SIMULATION RESULTS
The PID and Fuzzy PID are applied to matrix
converter and simulations have been performed, using
matlab/Simulink. The system’s parameters are listed in below
table the simulation circuit is carried out without adding any
filter component. The parameters of Fuzzy PID controller is
tuned for fast and finest speed control purpose. Bidirectional
switches are considered ideal and ode23tb simulation solver
was used.
E
NB
NM
NS
ZO
PS
PM
PB
NB
PB
PB
PM
PM
PS
ZO
ZO
NM
PB
PB
PM
PS
PS
ZO
NS
NS
PM
PM
PM
PS
ZO
NS
NS
Stator resistance (
2.76(ohms)
ZO
PM
PM
PS
ZO
NS
NM
NM
Stator inductance(
11.8(m.H)
PS
PS
PS
ZO
NS
NS
NM
NM
Rotor resistance (
3.11(ohms)
PM
PS
ZO
NS
NM
NM
NM
NB
Rotor inductance (
11.8(m.H)
Mutual inductance (
118(mH)
PB
ZO
ZO
NM
NM
NM
NB
TABLE 3
Parameters of induction motor.
NB
The membership function used for error and rate of
change of error is of triangular type. The fuzzy rules are
implemented using if then rules and the rules are shown in the
following tables. The Fuzzy PID controller is used because it
is non linear and high sensitive towards disturbances and
parametric variations
Inertia(J)
0.3(Kg.
)
Frictional factor(F)
0.01(N.m.s)
Pole pairs (P)
2
A. For constant Load Torque
The simulation is carried out at a constant load torque of 4
N.m (Tl=4 N.m) and at a reference speed of 25 rad/sec. The
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outputs of the following current waveforms, speed and torque
waveforms are shown in the below figures.
Fig 6(a): Stator current wave forms for conventional PID
Fig 8(a): Motor torque wave forms for conventional PID
Fig 6(b): Stator current wave forms for Fuzzy PID controller.
Fig 8(b): Motor torque wave forms for Fuzzy PID controller.
The following wave forms are the presence of
harmonic distortion in the stator currents or load currents for
PID and Fuzzy PID controllers. In these waveforms the THD
produced by conventional PID controller 107.59% which is
higher than that of Fuzzy PID controller which is shown in
figure 9.
Fig 7(a): Speed wave forms for conventional PID
9(a): THD present in stator current for conventional PID
Fig 7(b): Speed wave forms for fuzzy PID controller.
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The simulation is carried out at a variable load torque
of 1N.m ( =1 N.m) up to the point of 60 msec and varied to 9
N.m ( =9 N.m) from 60 msec and at a reference speed of 25
rad/sec. The outputs of the following speed and torque
waveforms are shown in the below figures.
Fig 9(b): THD present in stator current for fuzzy PID controller.
Comparison of electromagnetic torque waveforms
for conventional PID and fuzzy PID are shown in the below
figure.
Fig 11(b): Motor speed and torque wave forms for fuzzy PID controller.
C.
For Variable Reference speeds
The simulation is carried out at a variable reference
speed of 10 rad/sec initially and 20 rad/sec from 60 msec and
varied to 25 rad/sec from 90 msec and at a constant load
torque of 4 N.m. The outputs of the following speed are
shown in the below figures.
Fig 10: Electromagnetic torque waveforms for conventional PID and
fuzzy PID controllers.
The comparison of torque of motor is carried out
where the variation of torque is observer to be comparatively
less for Fuzzy pid controller then that of conventional PID
controller (i.e ∇T=(T(max)-T(min)) is less for fuzzy PID
controller).
B. For Variable Load Torque
Fig 12: speed wave forms for conventional PID and fuzzy PID controllers.
Fig 11(a): Motor speed and torque wave forms for conventional PID
ISSN: 2231-5381
IV. CONCLUSION
In this paper, PID controller and Fuzzy PID
controller are used to control matrix converter. The direct
torque control of induction motor fed by matrix converter
replaces the use of conventional inverter. Fuzzy PID adjusts
continuously the controller’s parameters depending upon
the error. The performance of the Fuzzy PID is good when
compared to conventional PID controller. The transient
response provided by the FSC has been best compared to
conventional PID. The comparison waveforms for THD of
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International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 8-April 2015
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