onlinear Compensation Empyoing Matrix Converter with DTC Controller

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 7, No. 1, February 2017, pp. 107~124
ISSN: 2088-8708, DOI: 10.11591/ijece.v7i1.pp107-124  107
Journal homepage: http://iaesjournal.com/online/index.php/IJECE
Nonlinear Compensation Empyoing Matrix Converter with
DTC Controller
Khalaf S. Gaied1
, Ziad H. Salih2
, Ahmed R. Ajel3
, Mehdi J. Marie4
1
College of Engineering, Tikrit University, Iraq
2
College of Petroleom and Mineral Engineering, Tikrit University, Iraq
3
Institute of Technology, Baghdad, Iraq
4
Al-Zawraa state company, Ministry of Industry, Iraq
Article Info ABSTRACT
Article history:
Received Sep 10, 2016
Revised Jan 7, 2016
Accepted Jan 21, 2017
This paper describes a nonlinear harmful speed and torque controller for
fourth order induction motor model. The investigation of optimality and cost
function for that base on estimation of Hammerstein-Wiener model with the
compensated mathematical model. The matrix converter with direct torque
control combination is efficient way to get better performance specifications
in the industry.The MC and the DTC advantages are combined together.The
reduction of complexity and cost of DC link in the DTC since it has no
capacitors in the circuit. However, the controlling torque is a big problem it
in DTC because of high ripple torque production which results in vibrations
response in the operation of the IM as it has no PID to control the torque
directly. The combination of MC with DTC is applied to reduce the
fluctuation in the output torque and minimize the steady state error. This
paper presents the simulation analysis of induction machine drives using
Maltlab/Simulink toolbox R2012a. Design of constant switching frequency
MCDTC drive,stability investigation and fault protection as well as
controllability and observability with minimum steady state error has been
carried out which proved the effectiveness of the proposed technique.
Keyword:
Direct torque control
Fault diagnosis
Matrix converter
Nonlinear compensation
Space vector modulation
Copyright © 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Khalaf S. Gaied,
Electrical Engineering Department,
Tirit University,
Tikrit state, +9647703057076, Iraq.
Email: gaeidkhalaf@gmail.com, salim_hazim2000@siswa.um.edu.my
NOMENCLATURES
ADRC Auto Disturbance Rejection Controller Ls Stator Inductance
ASD Adjustable Speed Drive Lr Rotor Inductance
DTC Direct Torque Control Lm Mutual Inductance
DTCIM Direct Torque Control Induction Motor is Stator Current
DSC Direct Self Control ir Rotor Current
FPE Final Predicted Error vs Stator Voltage
MC Matrix Converter es Electromotive Force Vector
MCDTC Matrix Converter with Direct Torque Control tsp Sampling Period
IM Induction Motor Vop Output Voltage Vector
PI Proportional Integral Vip Input Voltage Vector.
Rr Rotor Resistance

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IJECE Vol. 7, No. 1, February 2017 : 107 – 124
108
1. INTRODUCTION
In industry life all systems are nonlinear, to make the investigation(analysis and design), most of
these systems considered as linear. DTC and control of non-linear levels in the systems are considered the
most important techniques for achieving high performance in AC machines [1]. The induction motors (IM)
plays an important role. in the industry due to their low cost and operational reliability [2]. Adjustable speed
drives (ASDs) are frequently used in many applications, such as air conditioning, elevators, electrical
vehicles, ventilation, pumps, fans, heating, robotics [3]. In 1984, I. Takahashi developed a new technique for
the torque control of IM which is one kind of variable speed drives named as Direct Torque Control
(DTC) [4]. The principle is emulate both flux and torque as in the DC machines by the orientation control of
the magnetic field. The DTC configuration for direct MC has been presented in [5]. In a DTCIM drive, a
decoupled control of torque and flux can be achieved by two independent control loops [6].
This configuration play vital role in the industry due many reasons like ability to adjust input power
factor, no need to DC link capacitor, ensure sinusoidal waveforms for the input and output and power flow
control in the forward and backward directions. Comprehensive researches studies on direct MC with
DTC [7]. The available literature on DTC drives too are mainly confined to performance enhancement in
terms of torque ripples. Since the steady state as well as dynamic performance of a DTC drive is greatly
affected by the flux control loop which in turn depends upon flux estimation algorithm [8]. Nonlinear robust
controller for MC fed IMD in which a nonlinear robust ADRC is applied to the MC fed IM drive system,
taking the place of PI controller [9]. Fuzzy logic controller of multilevel inverter, the SVM presented in [10].
In [11] the inverter voltage vector selected from the switching table is applied for the time interval needed by
the torque to reach the upper limit or lower limit of the band, where the time interval is calculated from a
suitable modelling of the torque dynamics. AC-DC-AC sparse direct power converter introduced in [12].
Control of a two stage direct power converter with a single voltage sensor mounted in the intermediary
circuit presented in [13]. The DTC can be divided into two types, either DSC or SVM. DTCSVM for IM
driven by MC using a parameter estimation strategy done by [14]. The switching table has many drawbacks
such as variable switching frequency due to hysteresis bands of both torque and flux as well as the change of
speed motor. According to this variation in switching frequency, uncontrolled small region will be generated
especially in the beginning of operation of induction motor. The main drawbacks of the DTC system are the
variable inverter switching frequency and high torque output ripple due to usage of hysteresis based
comparators to control the output torque [15]. To obtain good solution for that, SVM with DTC and MC has
been used. The stability is one of the most important demands in the control system after being subjected to a
disturbance [16]. The MC can be used in the compressors, fans (blowers), mixers, general pumps or heat
pumps and escalator drive system [17]. In this paper, a combination of fixed switching frequency DTC with
MC scheme is presented, which developed to minimize the steady state error of input torque due highly
torque noise in the DTC scheme that should be suppressed.
2. DTC BACKGROUND
DTC can achieve field orientation without feedback, using motor theory to calculate the motor
torque. It is said to use the fastest digital signal processing hard-ware available and a more advanced
mathematical understanding of how motors work [18].
Look up table
Torque
hysteresis
Controller
Flux
hysteresis
Controller
Flux and torque
estimation
Phase currents
Phase voltages
Reference flux
Reference torque
Transistor
control
signal
flux
torque
Flux selector
Figure 1. Principle of the DTC
The DTC technique principle is shown in the Figure 1 can be illustrated as follow: At the first step,
the phase currents and voltages of the system are measured. The outcome of forwarding such values to the

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109
flux and torque estimator will be the actual flux and torque of the system. The estimated torque is com-pared
with their reference values in three levels torque hysteresis controller. At same time, the flux is compared
with the reference flux values in two levels flux hysteresis controller. In order to construct the transistor
control signal, the outputs of the stator flux and torque controllers further to the flux selector are used as
inputs of the DTC switching look up table.
The transistors control signals which are divided into nine different sections are used for controlling
the three levels MC, as can be shown in the Figure 2.
Figure 2. Simulink Implementation of the Three Levels MC [19]
The internal connection of each level shown above will as in Figure 3.
Figure 3. Simulink Implementation of the First Level
The details information of each block shown in Figure 3 will be as in Figure 4.
Figure 4. Details Connection of each Block shown in Figure 3
The general selection table for the DTC, being (k) which is the sector number can be shown in
Table 1.
Table 1. General Selection Table
Ψs sector K Torque
Flux
Increase Decrease
Increase Vk+1 V000
Decrease Vk+2 V111

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DTC zero sequence (V000 or V111) vectors are used to maintain the torque constant and not including
during the switching period.The switching table in DTC allows selecting the vector position to apply to the
MC according to the DC of the stator flux and the electromagnetic torque as can be shown in Table 2. From
Table 1, one can notice that the switching frequency of the IGBTs used in this scheme is not constant. If we
control the tolerance bands, the average switching frequency can be kept at its reference value, hence the
ripple current and torque will be minimized [20].
Table 2. DTC switching Table
Sector
1 2 3 4 5 6
dφ= +1
dT= +1 V2 V3 V4 V5 V6 V1
dT= 0 V0 V7 V0 V7 V0 V7
dT= -1 V6 V1 V2 V3 V4 V5
dφ= -1
dT= +1 V3 V4 V5 V6 V1 V2
dT= 0 V7 V0 V7 V0 V7 V0
dT= -1 V5 V6 V1 V2 V3 V4
The MCDTC proposed algorithm can be shown in Figure 5.
Figure 5. The Proposed Fixed Frequency DTC Scheme using MC
3. MATRIX CONVERTER
A device which converts AC input supply to the required variable AC supply as output without any
intermediate conversion process whereas in case of Inverter which converts AC - DC - AC which takes more
extra components as diode rectifiers, filters, charge-up circuit but not needed those in case of MC [21] device
which converts AC input supply to the required variable AC supply as output without any intermediate
conversion process whereas in case of Inverter which converts AC - DC - AC which takes more extra
components as diode rectifiers, filters, charge-up circuit but not needed those in case of MC. The Eupec
Economac matrix module with nine back-to-back IGBT switches can be seen in Figure 6.

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Figure 6. The Eupec Economac Matrix Module
The advantages of the MC compared to conventional inverter types are as follows:
a. Waveforms of both Input and output are very clear [22-23]
b. Minimal higher order harmonics are obtained
c. Capability of sub harmonics omitting
d. Capability of bi-directional energy flow
e. It has no DC link capacitors
f. Control of input power factor can be performed easily
The disadvantages of the MC are as follows:
a. Maximum efficiency cannot be obtained in all cases
b. The conventional AC-AC has fewer components compared to the MC
c. Each bi-directional switch should have its arrangement
d. Sensitive to input voltage system
e. No monolithic bi-directional switches exist
The system consists of a 3-phase MC constructed from 9 back-to-back IGBT switches. The MC is
supplied with three phase source and drives a static resistive load. The switching algorithm is based on SVM
described earlier which considers the MC as a rectifier and inverter connected via a DC link with no energy
storage. Indirect SVM allows direct control of input current and output voltage and hence allows the power
factor of the source to be controlled. The switching algorithm utilizes a symmetric switching sequence
mentioned before. First of all the Simulink implementation of the MC is carried out. MC consists of nine bi-
directional sectors with reverse blocking capability, arranged as three sets of three so that any of the three
input phases can be connected to any of the three output lines. A bi-directional 18 diodes is used for blocking
the voltage in MC [24]. The inversion matrix sequence of the SVM when the voltage mod input to generate
(v1-v2-v7- v8) with the switching pattern is constructed as in the Figure 7.
Figure 7. MCSVM Symmetric Switching in the Voltage Mod Input
In the first position (0-60) degree, the torque will be decreased while the flux will be increased. In
the positions (60-120) or (-120- (-60)) there is a flux ambiguity, in the position (-180- (-120)) the torque and

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the flux will be decreased and last position (180-120) the torque will be increase while the flux will be
increased. There are two position between(30-(-30)) are not used because the torque will increased or
decreased in the same sector depending on the position if it's in the position of 30 or( -30).
The symmetric sequence unit used the current mod as the input to generate (v1-v2-v0) also used.
SVM symmetric sequence unit for generation of v1_v2_v7_v8 sequence can be implemented using
Matlab/Simulink as in Figure 8.
Figure 8. SVM Symmetric Sequence Unit of the above Figure
An IM can be described in the stationary frame by the following flux and voltage equations.
rmsss iLiL  (1)
rmsmr iLiL 
(2)
dt
d
iRv s
sss

 (3)
rr
r
rr j
dt
d
iR 

0 (4)
The stator flux variation can be expressed as:
spsspsspssss tvtetiRv  )(
(5)
Figure 9. Switching Signal Construction

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To generate the control signal, the MC gates can be constructed from two lookup tables. First one
when the magnitude of the flux equal one and the other one when the flux is equal to minus one.
The combinations from 1 to 9 which are the sectors (v0-v1-v2-v3-v4-v5-v6 -v7-v8) are used as a
gate signal of the IGBT transistor as can be shown in the Figure 9.
The first 6 states can be constructed from the current mode (qR) and the other 6 state as constructed
from the voltage mode circuit (ql). The combinations of these 12 signals are used to construct the SVM used
to control the MC. Where in g is the output angle in the SVM rectification system to generate left (gl) and
right (gR) axis of the sector when the voltage and current mode acts as the inputs to the circuits.
4. MC SWITHING SEQUENCE
The MC can be used as one of the following.
1. MC applicable as a cyclo-converter.
2. MC applicable as a cyclo inverter.
3. MC applicable as a Dual Converter, rectifier and inverter [25]
The control requirement of the switches of MC through the duty cycle depends on the average
output voltages to construct the required sinusoidal frequency and magnitude of the three phase voltage [26].
The MC switching generation signal combination with the SVM rectification sequence can be shown in
Figure 10.
Figure 10. MC switching Generation Signal
The reduction of harmonics in the input power supply can be obtained by MC compared with
conventional inverter as well as there is cost reduction [27].
The SVM modulation of the proposed algorithm, required to measure any line voltages. Then, Vi/p
and φ i/p are calculated as:
)(
9
4 22
/
2
bcabbcabpi VVVVV  (6)
)
3/13/2(3
(tan 1
/
bcab
bc
pi
VV
V


 

(7)
The ratio between input and the output voltages is calculated as
pi
po
v
V
V
R
/
2
/
2
 (8)
The switching function of any IGBT switch can be expressed as in [28]. Where K= {A, B, C} is
labelled input phase and j= {a, b, c} is labelled the output phase. The condition of the switching function can
be expressed by the following relationship:
1 CJBJAJ SSS (9)
1
g
gR
gI
gmatrix converter switching
mod gSVM Rectif sym seq
mod gSVM Rectif sym seq
2
volt mod
1
curr mod

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Under these constrains, a 3×3 MC has been implemented with 27possible switching states. Let
dKj (t) be the duty cycle of switch SKj, defined as:
10&/)(  KJsamplingKJKJ dtttd (10)
The low frequency of MC can be obtained by:











)()()(
)()()(
)()()(
)(
tdtdtd
tdtdtd
tdtdtd
tD
CcBcAc
CbBbAb
CaBaAa
(11)
The Simulink implementation of duty cycle unit can be shown in Figure 11.
Figure 11. Simulink Implementation of Duty Cycle Calculation
||))*866.0/5.0sin()3/()(cos(_ 21 vdd   (12)
 210 _1 ddd (13)
The low-frequency component of the output phase voltage as in (14)
)().()( / tVtDtV piop  (14)
The low frequency component of the input current as in (15)
)().()( tItDtI op
T
ip  (15)
The torque can be affected directly by the stator current as well as number of poles, mutual
inductance and rotor inductance as in (16)
))(( dsqrqsdr
r
m
e ii
L
L
pT   (16)
The SVM technique is one of the most important modulations used for the DMC due to the
advantages of this technique like the reduction of total harmonic distortion and the controlling the duty cycle
100%. The SVM rectifier system switching sequence can be implemented using two states current and
voltage stages to yield the MC switching and hence the gates signals of the IGBTs of the MC as can be seen
in the Figure 10.
The input current modulator and the voltage modulator are used for controlling of gates signals in
efficient way. The DTC with MC proposed technique depends completely on the best choice of the switching
mechanism to get better steady state error of both torque and flux compared to their references. The matric
configuration switching technique used in this method can be illustrated in Table 2.
Simulink implementation of hysteresis controllers of the torque and flux can be shown in Figure 12.
1
d1_d2_d0
0.5/0.866
pi/180
deg2rad
sin
cos
1
pi/3
Trigger
1
deg_mag
d0
d1 d2
theta
mag

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Figure 12. Simulink Implementation of the Torque and Flux Hysteresis Controllers
The Simulink implementation of voltage in alpha and beta coordinate can be shown in Figure 13.
Figure 13. Simulink Implementation of Alpha & Beta Voltage Components
5. SIMULATION RESULTS
To investigate the proposed algorithm, the Simulink program has been used first to model the IM,
MC, DTC and speed controller. A nonlinearity compensation strategy has been developed to make better the
speed control performance in all operation regions. The simulation has been carried out assuming that the
sampling period is 20e-6 sec and ideal switching devices, 0.8 Wb flux reference. The results of the DTC
control simulation are shown in the following figures. The MCDTC technique is simulated with Simulink to
investigate the performance of the proposed control scheme.
Figure 14 shows the speed command and the speed tracking which is completely coincided when
the speed command is changed from (0-650) RPM then increased and setteled with 1500 RPM.
Figure 14. Speed Reference and Actual Speed Response
3
Flux_est
2
H_Te
1
H_phi
dTe/2
dPhi
NOR 2Convert
-dTe/2
4
Flux
3
Torque
2
Flux*
1
Torque*
2
Vbeta
1
Valpha
sqrt(2/3)
sqrt(3)/2
sqrt(3)/2
sqrt(2/3)
1/2
1/2Demux1
Vabc
0 0.5 1 1.5 2 2.5 3
0
200
400
600
800
1000
1200
1400
1600
Time(sec)
Speed(RPM)
actual speed
reference speed

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The triangular reference torque compared to the actual torque to investigate the error that will be
high frequency triangular waveform. Figure 15 shows the actual torque without constant switching
frequency. The variable switching frequency in the basic DTC is due to the variation of the time taken for the
torque error to achieve the upper and lower hysteresis bands. The dynamic performances of the proposed
MCDTC control method are tested for a variable torque command. The waveform and the steady state error
slopes are highly dependent on operating conditions. Consequently, the torque ripple will remain high, even
with small hysteresis band.
The fluctuation in the DC voltage during the operation period can be shown in Figure 16. The torque
ripples which are generated due to the operation of hysteresis controller are reduced by using the proposed
control method as can be shown in Figure 17.
Figure 15. Actual (blue) and Reference Torque Dynamic without Constant Frequency DTC
Figure 16. DC Voltage without Constant Frequency DTC
Figure 17. Actual and Reference Torques with Proposed DTC
0 0.5 1 1.5 2 2.5 3
0
25
50
75
100
125
Time(sec)
Torque(N.m)
0 0.5 1 1.5 2 2.5 3
0
100
200
300
400
500
600
700
800
900
Time(sec)
DCvoltage(Volt)
0 0.5 1 1.5 2 2.5 3
0
25
50
75
100
125
Time(sec)
torque(N.m)

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Stator current with proposed method can be shown in Figure 18.
Figure 18. Stator Current with the Proposed DTC Scheme
The stator current in the Figure 18 shows acceptable results of the proposed strategy. The switching
frequency of the IGBTs is 6 kHz and can be realized up to 20 kHz.
To ensure better design of the proposed algorithm, 20 samples residues autocorrelation and cross
correlation for both input and input combinations proves good results as can be shown in Figure 19.
Figure 19. Autocorrelation and Cross Correlation Residuals
The transfer function of system from torque to the speed as in (17):
1134.274.253.10055.0
12901.5949.56744.200024.0
234
23


 

essess
eseses
G (17)
The speed controller PI controller transfer function with zero delay time designed as in (18)
677.87,0
,233.0),exp(*
1




pd
pd
p
p
PID
TT
KsT
sT
K
G
(18)
0 0.5 1 1.5 2 2.5 3
-400
-300
-200
-100
0
100
200
300
400
Time(sec)
StatorCurrent(Amp)
10
20
30
40
50
60
Stator current
-20 -15 -10 -5 0 5 10 15 20
0
0.5
1
Autocorrelation of residuals for output (speed)
-20 -15 -10 -5 0 5 10 15 20
0
0.5
1
Samples
Cross corr for input (torque) and output (speed) resids

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The minimum difference between the input and the output has been tested through many fitting
methods to ensure better performance in the IM as can be shown in Figure 20.
Figure 20. Nonlineary (blue) Test of the Output Regions
The values of of Figure 20 fitting method can be listed in the Table 3 using identification
Matlab/Simulink toolboxes [29].
Table 3. Fitting Method to get the best Output Model
Nonlinear torque and speed harmful residual cross correlation can be shown in Figure 21.
Figure 21. Nonlinear Torque and Speed Harmful Residual Cross Correlation
0.5 1 1.5 2 2.5 3 3.5
-1500
-1000
-500
0
500
1000
Time(sec)
Differencebetween(Measured&Simulated)
Measured minus simulated model output
10
20
30
40
50
60
First Fitting Method
Second Fitting Method
Third Fitting Method
Fourth Fitting Method
Fifth Fitting Method
Sixth Fitting Method
-100 -80 -60 -40 -20 0 20 40 60 80 100
-1
-0.5
0
0.5
1
Autocorrelation of residuals for speedh
arm
-100 -80 -60 -40 -20 0 20 40 60 80 100
-0.1
0
0.1
0.2
Samples
Cross corr for nonlinear torque and speed
h
arm resids
10
20
30
40
50
60
The Fitting Method The value Name
First Fitting method -623.1 Nlarx1
SecondFitting method 21.92 N4s4
Third Fitting method 323.2 N4s1
Fourth Fitting method -148.9 arxqs
Fifth Fitting method -148.8 Arx441
Sixth Fitting method 0.194 Nlarx2

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Estimation of the nonlinearity of the output before and after applying the proposed algorithm will be
listed in the Table 4.
Table 4. Nonlinearity Information with and without Proposed Algorithm
The state space model of the system will be 4th order, Matlab instruction is used to find whether the
system is controllable, observable or not as in (19) & (20).
),( BAcntrbCo  (19)












0.8818-0.63500.0344-0.8181-
3.89171.58925.4898-0.2165
1.7762-7.4653-5.33070.2133-
0.0507-0.11750.0676-0.0028
=Co
),( CAobsvObsv  (20)
















0.8859-0.17660.0520-0.0000-
0.4595-0.0226-0.11900.0004-
0.97200.1128-0.0450-0.0000
0.4993-0.08750.0439-1.6710
*03+1.0e
=Obsv
With rank of 4, the system is completely controllable and observable. The stability test determines if
all roots of the input polynomial lie inside the unit circle. Implemented using the Schur-Cohn algorithm can
be shown in Figure 22. The output is containing the value 1 or 0. The value 1 indicates that the system is
stable while the value 0 indicates that the system is unstable.
Figure 22. Stability Test according to Schur-Cohn Algorithm
6. MODEL IMOROVMENT
To insure best controller design, Estimation of Hammerstein-Wiener model before and after
controller design can be used as can be shown in Table 5 and Table 6. The block diagram represents the
structure of a Hammerstein-Wiener model can be shown in Figure 23.
Because acts on the output port of the linear block, this function is called the output nonlinearity. If
system contains several inputs and outputs, you must define the functions f and h for each input and output
signal.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time (sec)
output
stability
without constant switching Frequency With constant switching frequency
Fit (%) FPE Loss Function Fit (%) FPE Loss Function
90.21 1.303 1.086 99.9 1.918E-4 1.872E-4

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Input
nonlinearity
f
Linear
block
B/f
output
nonlinearity
h
U(t) W(t) X(t) Y(t)
Figure 23. Block diagram of Hammerstein-Wiener
where: w(t) = f(u(t)) is a nonlinear function transforming input data u(t). w(t) has the same
dimension as u(t). x(t) = (B/F)w(t) is a linear transfer function. x(t) has the same dimension as y(t).
where B and F are similar to polynomials in the linear Output-Error model. For ny outputs and nu
inputs, the linear block is a transfer function matrix containing entries:
)(/)( ,, qFqBBlocklinear ijij (21)
where j = 1,2,...,ny and i = 1,2,...,nu.
y(t) = h(x(t)) is a nonlinear function that maps the output of the linear block to the system output.
w(t) and x(t) are internal variables that define the input and output of the linear block, respectively. Because f
acts on the input port of the linear block.
Table 5. Estimation of Hammerstein-Wiener model
at the beginning
itr Cost Step size Optimality bisection
0 1.056e+04 3359
1 1e+04 16.15 5.627e+04 0
2 1e+04 2.201 5.595e+04 9
3 9983 7.226e-05 3.276e+04 6
4 9982 1.763 3.329e+04 8
5 9982 1.102 3.492e+04 9
6 9979 43.82 3.328e+04 5
7 9978 4.269 1.704e+04 6
8 9977 1.174 1.986e+04 8
9 9976 1.137 2.031e+04 8
10 9975 0.795 2.031e+04 8
11 9973 1.51 2.041e+04 7
12 9972 0.7719 4.065e+04 8
13 9967 1.56 5.533e+04 6
14 9965 2.422 6.329e+04 6
15 9965 1.319 1.076e+05 5
16 9906 4.393 1.716e+04 3
17 9901 4.524 1.047e+05 4
18 9900 0.2971 1.046e+05 8
19 9757 0.3872 1.191e+04 1
20 9735 0.3884 8956 1
Table 6. Estimation of Hammerstein-Wiener model
after design the compensation
Itr cost Step
size
Optimality Bisection
0 2307 2.037e+04
1 1118 4.992 3.044e+05 3
2 785.6 25.44 1.315e+05 2
3 570.2 97.79 7.755e+04 2
4 306.1 64.22 1.695e+04 2
5 275.5 16.95 3.714e+04 4
6 264.4 2.193 6.382e+04 5
7 260.9 5.671 9.427e+04 5
8 257 1.376 1.01e+05 6
9 254.8 0.916 1.094e+05 6
10 254.1 1.219 1.206e+05 6
11 252.4 1.053 1.246e+05 7
12 251 0.5565 1.286e+05 7
13 249.8 0.5298 1.331e+05 7
14 248.8 3.35 1.379e+05 7
15 248 0.9778 1.42e+05 7
16 247.1 11.4 1.453e+05 7
17 246.5 4.16 1.493e+05 7
18 246 4.628 1.54e+05 7
19 245.6 1.2 1.58e+05 7
20 245.1 1.754 1.602e+05 7
The nonlinearity level in the circuit of IM can be shown as in Figure 24.
Figure 24. Nonlinearly Level after Design the Compensator
uNL Linear Block yNL
0 50 100 150 200 250 300 350 400 450 500
10
15
20
25
30
Input to nonlinearity at input 'u1'
NonlinearityValue
nlhw1:pwlinear

IJECE ISSN: 2088-8708 
121
The continuous canonical state space model of the given system will be as in the following form:
eDuCxy
KeBuAxX

.
(22)
With the following values:














166.005.1028.057.2
1000
0100
0010
e
A ,














0001.0
0008.0
58.4
01.0
e
B ,  0001C
 0D ,













09.0
12.0
21.0
55.0
K
Another evidence to show the model improvement is the power distribution along with the operation
of the system as shown in Figure 25.
Figure 25. Power spectrum distribution
There are no sensitive parameters during the IM running with higher speeds, but at low speeds the
stator flux estimation becomes so important and critical due to error in stator resistance property [30], [31].
7. FAULT DIAGNOSIS
The control of electrical machines, vehicle, space exploration faulty is very important in all
industrial applications. The fault tolerant control princible are needed with these applications according to
safety of operation of system operation. There are difference in operation and control between faulty and
healthy machines. The danger of significant oscillations in faulted machine such as speed and torque
oscillation is the main cause for damage of the machines [32]. The IM model is constructed with the
following assumptions [33].
1. The air gap is of constant
2. No eccentricity effect,
3. The system works under balanced load ,
4. Pure simusoidal input source.
10
-1
10
0
10
1
10
0
10
1
10
2
10
3
Frequency (rad/s)
Powerspectrum
Power Spectrum
power spectrum
10
20
30
40
50
60

 ISSN: 2088-8708
122
Shutting down the IM operation is another improvement especially when the motor performance is
deteriorated. In Figure 26, both motor and the controller works presicely untle 0.6 sec after that we simulate a
fault between (0.6-1) sec to investigated the protection circuit which is reacts in a very good manner and
stoped the operation to avoid the motor damage.
Figure 26. protection circuit activation
8. CONCLUSIONS
Hammerstein-Wiener is proposed as identified optimization model. DTC and MC modelling and
simulation have been carried out. The proposed algorithm tested to ensure better performance specifications.
DTCMC converter is used for supplying the IM. Minimizations of the steady state error of the torque with
lowest final predicted error are obtained. Stability has been tested according to Schur-Cohn algorithm. The
proposed algorithm with the constant switching frequency helped to design controllable, observable states of
the given system. Protection circuit isn extra improvement for the proposed scheme which is not mentioned
in detail in this paper. State space transfer function and design of the PI controller investigated with
identification facilities of the Matlab/Simulink as well as the torque, the speed and current waveforms proves
the effectiveness of the control scheme.
REFERENCES
[1] B. Sebti, et al., “Reduction of Torque Ripple in DTC for Induction Motor using in-put-output feedback
linearizatio,” Turk J Elec Eng & Comp Sci, vol/issue: 20(3), pp. 273-285, 2012.
[2] K. Gaeid, et al., “Sliding Mode Control of Induction Motor with Vector Control in Field Weakening,” Modern
Applied Science, vol/issue: 9(2), pp. 276-288, 2015.
[3] A. Aziz, et al., “A Simulation on Simulink AC4 model (200hp) DTC induction motor drive using Fuzzy Logic
controller,” Computer Applications and Industrial Electronics Conference, pp. 553–557, 2010.
[4] T. Noguchi and I. Takahashi, “Quick torque response control of an induction motor based on a new concept,” IEEJ
Tech. Meeting Rotating Mach, pp. 61–70, 1984.
[5] C. Reza, et al., “A review of reliable and energy efficient direct torque controlled induction motor drives,”
Renewable and Sustainable Energy Reviews, vol. 37, pp. 919–932, 2014.
[6] D. Casadei, et al., “The Use of Direct power converters in Direct Torque Control of Induction Machines,” IEEE
Trans. Industrial Electronics, vol/issue: 8(6), pp. 1057-1064, 2001.
[7] G. Buja and M. Kazmierkowski, “Direct torque control of PWM inverter-fed AC motors a survey,” IEEE
Transactions on Industrial Electronics, vol/issue: 51(4), pp. 744–757, 2004.
[8] T. Nabil, et al., “An Improved Fixed Switching Frequency Direct Torque Control of Induction Motor Drives Fed
by Direct Matrix Converter,” International Journal of Computer Science and Information Security, vol/issue: 7(3),
pp. 198-206, 2010.
[9] S. Bhoopendra, et al., “Direct Torque Control Induction Motor Drive with Improved Flux Response,” Advances in
Power Electronics conference, pp. 1-11, 2012.
[10] R. Gupta, et al., “Direct Torque Control of Matrix Converter Fed Induction Motor Drive: A Review,” Proc. of the
Intl. Conf. on Advances in Computer, Electronics and Electrical Engineering, pp. 387-393, 2012.
[11] M. Kazmierkowski and G. S. Buja, “Direct Torque Control of PWM Inverter-Fed AC Motors A Survey,” IEEE
Trans.on Industrial Electronics, vol/issue: 51(4), pp. 744-758, 2004.
[12] A. Vanja, et al., “Band constrained technique for direct torque control of induction motor,” IEEE Transactions on
industrial Electronics, vol/issue: 51(4), pp. 776-784, 2004.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0
100
200
300
400
500
600
Time(sec)
Speed(RPM)
10
20
30
40
50
60
protection period when the motor in bad performaance

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[13] I. Kolar I., et al., “Novel three-phase ACDC- AC sparse direct power converter,” Proceeding APEC, pp. 777-791,
2002.
[14] C. Klumpner, et al., “Control of a Two Stage Direct Power Converter with a Single Voltage Sensor Mounted in the
Intermediary Circuit,” 35th Annual IEEE PESC, pp. 2385-2392, 2004.
[15] K. Lee and F. Blaabjerg, “DTC-SVM for Induction Motor Driven by Matrix Converter Using a Parameter
Estimation Strategy,” IEEE Trans. on Industrial Electronics, vol/issue: 55(2), pp. 512-521, 2008.
[16] K. Behera and S. Behera, “A Novel Control Strategy of Indirect Matrix Converter Using Space Vector
Modulation,” International Journal of Power Electronics and Drive Systems (IJPEDS), vol/issue: 7(3), 2016.
[17] N. Tha, et al., “Estimating Stability of MTDC Systems with Different Control,” J Electrical Engineering
Technology, vol/issue: 10(2), pp. 443-451, 2015.
[18] T. Friedli, et al., “Comparative Evaluation of Three-Phase AC–AC Matrix Converter and Voltage DC-Link Back-
to-Back Converter Systems,” IEEE Transactions on Industrial Electronics, vol/issue: 59(12), pp. 4487-4510, 2012.
[19] Fourth gen DTC promises better speed and torque control at: http://www.drivesncontrols.com/news/fullstory, 2014.
[20] K. Vijayakumar, et al., “Application of Sinusoidal Pulse Width Modulation Based Matrix Converter as
Revolutionized Power Electronic Converter,” Power Electronics and Renewable Energy Systems, Springer India,
2015.
[21] K. Gaeid, “DTC Controller Design for IM with Wavelet Noise Reduction,” European Journal of Scientific
Research, vol/issue: 101(4), pp. 546–556, 2013.
[22] J. Kolar, et al., “Novel Three-Phase AC-AC Sparse Matrix Converters,” Transactions of Power Electronics,
vol/issue: 22(5), pp. 1649–1661, 2007.
[23] V. Patra, et al., “Integration of Matrix Converter with DTC of Induction Motor Drive Applications,” International
Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, vol/issue: 2(10), pp.
5220-5231, 2013.
[24] D. Sharon, et al., “Three Phase to Three Phase Direct Matrix Converter using SPWM Technique,” International
Journal of Soft Computing and Engineering, vol/issue: 3(2), pp. 297-300, 2013.
[25] M. Abhijit and N. Manoj, “Performance Comparison of Matrix Converter fed Induction Motor Drive using PI and
PID Control,” Journal of Electrical and Electronics Engineering, vol/issue: 4(2), pp. 12-19, 2013.
[26] A. Alesina and M. Venturini, “Solid-state power con-version: a Fourier analysis approach to generalized
transformer synthesis,” Proc IEEE Trans Circuit System, vol. 28, pp. 319–330, 1981.
[27] L. Kyo and B. Frede, “Improved Direct Torque Control for Sensorless Matrix Converter Drives with Constant
Switching Frequency and Torque Ripple Reduction,” International Journal of Control, Automation, and Systems,
vol/issue: 4(1), pp. 113-123, 2006.
[28] D. Abdelkader and M. Benyounes, “High Performance Motor Drive Using Matrix Converter,” Acta Electrotechnica
et Informatica, vol/issue: 2(7), pp. 1-8, 2007.
[29] www.mathwork.com/Matlab toolboxes.
[30] M. Kazmierkowski, et al., “High Performance Motor Drives,” IEEE Industrial Electronics Magazine, vol/issue:
5(3), pp. 6–26, 2011.
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[32] M. Jannati, et al., “A Novel Method for Vector Control of Faulty Three-Phase IM Drives Based on FOC Method,”
International Journal of Electrical and Computer Engineering (IJECE), vol/issue: 5(6), pp. 1284~1291, 2015.
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BIOGRAPHIES OF AUTHORS
Khalaf S.Gaeid received the B.Sc. degree in electrical engineering/Control from MEC,
Baghdad, Iraq in 1993 and the M.Sc. degree in Control Engineering from University of
Technology, Baghdad, Iraq in 2004. He graduated from University of Malaya, Malaysia in 2012
with the PhD degree in control system and machine drives. His doctoral research was in the
development new fault tolerant controller based wavelet for induction machines. He is currently
assistant professor in control systems at the Department of Electrical Engineering, College of
Engineering, Tikrit University, Tikrit, Iraq. His research interests include fault tolerant control,
wavelet, fault diagnosis, machine drives and their applications in electrical engineering. He is
IEEE member with a lot of publications in high rank journals and confrences.

 ISSN: 2088-8708
124
Ziad H. Salih was born in Kirkuk, Iraq in 1966. He received his Bachelor's (1989), Master's
(1996) Degrees from University of Technology (Iraq) and Ph. D. from the University of
Technology (2008). He has been a lecturer of Control Theory I, II, Electronics and Electrical
Networks at the Tikrit University, College of Engineering. He is the dean of the petroleum and
mineral engineering college since 2014. Assistant prof. Dr. Ziad had achieved a lot of Journal
articles and conference papers in the field of control and systems engineering. His current
research and development interests are mainly in the following areas: PLC control, computer
interfacing, self-tuning control and system identification, intelligent control, controller design for
linear and non-linear systems, control design, industrial applications particularly in the oil
industry.
Mehdi J. Marie was born in Baghdad, Iraq in 1970. He received his Bachelor's (1993), Master's
(2004) Degrees from University of Technology (Iraq) and Ph. D. from the University of Basrah
(2014). He has been a lecturer of Control Theory I, II, Electronics and Electrical Networks at the
Al-Nahrain University, College of Engineering. He is currently a senior engineer at Al-Zawaraa
State Company, Ministry of Industry and Minerals (Iraq). Dr. Mehdi had achieved over seven
Journal articles and two conference papers in the field of control and systems engineering. His
current research and development interests are mainly in the following areas: self-tuning control
and system identification, controller design for linear and non-linear systems, industrial
applications particularly in the processing industry (for example refining, cement, plastic and
food industry).
Ahmed R. Ajel, has been a full-time lecturer in the Institute of Technology Baghdad/Iraq,
Ministry of higher education and scientific research/Iraq. Received his BSc. (1992), MSc. In
control engineering, (1996) and PhD Degree in Electrical and Electronics engineering from the
University of Technology (2006), Baghdad/Iraq, Head of Information and Communication
Technology in Institute of Technology Baghdad/Iraq from 2012-2015, and head of the
Consulting & the Scientific Bureau in Institute of Technology Baghdad/Iraq from 2016 to yet.

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