Proceedings of the 14th International Middle East Power Systems Conference (MEPCON’10), Cairo University, Egypt, December 19-21, 2010, Paper ID 268.
FUZZY-BASED SPEED CONTROL OF FIVE-PHASE
INDUCTION MOTOR
I. Bedir1, Abd El-wahab Hassan1 , M. A. El khazendar1, and S. A. Mahmoud2
1
2
Faculty of Engineering - Tanta university
Faculty of Engineering, Shebin El-Kom - Minoufiya university
sources. The AC terminal voltages of each bridge are
connected in series. Unlike the diode clamp or flyingcapacitors inverter, the cascaded inverter does not require
any voltage clamping diodes or voltage balancing
capacitors. This configuration is useful for constant
frequency applications such as active front-end rectifiers,
active power filters, and reactive power compensation [5].
The interest in multi-phase motor drives has increased in
recent years due to several advantages when compared to
three-phase drives [6, 7]. Some of these advantages are
known from the early days of the multiphase drives [8],
although they have recently considered with high-level
analysis [9]. These advantages are inherent to the own
structure of the machine, and include less torque ripple,
less acoustic noise and losses, reduced current per phase
or increased reliability due to the additional number of
phases [6-9]. These advantages make multi-phase drives
suitable for high power/current applications such as
electrical vehicles, traction or electric ship propulsion.
Abstract-This paper presents the simulation of fivephase nine levels inverter fed five-phase induction motor. The
poor quality of voltage and current of a conventional inverter fed
induction machines is due to the presence of harmonics which
increases their losses. For five phases induction motor fed from
multi-level inverters, the current stress of the semiconductor
devices decreases, torque ripple is reduced and the rotor
harmonic currents are smaller. The dynamic behavior of the
induction motor has been examined for constant v/f operation
and the simulation results have been given. This paper presents a
rule-based fuzzy logic controller applied to a scalar closed loop
V/f induction motor (IM) control with slip regulation. The
simulation results are obtained and compared with that of
conventional PI controller method.
I. INTRODUCTION:
Power Electronics is playing an important role in the
torque and speed control of motor drive. Variable speed AC
induction motor drives are replacing the conventional DC
Drives in industrial drive environment [1]. DC motors have
excellent speed and torque response, they have inherent
disadvantage of commutator and mechanical brushes, which
undergo wear and tear with time [1]. AC induction machines
are single excited, mechanically rugged and robust, but speed
and torque control of these machines are more complex and
involved, compared to DC machines [1]. The advent of
controlled switches the speed and torque control of induction
machines have become relatively easier. A voltage source
inverter can run the induction machines by applying three
phase square wave voltages to its stator windings [2]. A
variable frequency square wave voltage can be applied to the
motor by controlling the switching frequency of the power
semiconductor switches. The square wave voltage will induce
low frequency harmonic torque pulsation in the machine. Also
variable voltage control with variable frequencies of operation
is not possible with square wave inverters [3]. The recent
advancement in power electronics has initiated to improve the
inverter levels instead of increasing the size of filters [Ref].
The total harmonic distortion of the classical inverters is very
high which can be improved by multilevel inverters. The total
harmonic distortion is analyzed between multilevel inverters
and other classical inverters [4]. A nine levels inverter consists
of a series of an H-bridge inverter units connected to five
phase induction motor. The general function of this multilevel
inverter is to synthesize a desired voltage from several DC
II. CASCADED H-BRIDGE MULTILEVEL
INVERTER:
A cascade multilevel inverter consists of a series
of H–bridge (single-phase full-bridge) inverter units. The
general function of this multilevel inverter is to synthesize
a desired voltage from several separate DC sources
(SDCSs), which may be obtained from solar cells, fuel
cells, batteries, ultra-capacitors, and any DC sources. Fig.
(1) shows a single-phase structure of a cascade H- bridge
inverter with SDCSs. Each SDCS is connected to a singlephase full-bridge inverter. Each inverter level can generate
-Vdc by
three different voltage outputs, +Vdc, 0 and
connecting the DC source to the AC output side using
different combinations of the four switches, S1, S2, S3 and
S4. The AC output of each level’s full-bridge inverter is
connected in series such that the synthesized voltage
waveform is the sum of all of the individual inverter
outputs. The number of output phase voltage levels in a
cascade multilevel inverter is then 2S +1, where S is the
number of DC sources. The output phase voltage is given
by Van = Va1 + Va2 + …….. + Vas . Each H-bridge unit
generates a quasi-square waveform by phase-shifting its
positive and negative phase legs switching timings. In this
paper, all DC voltages are assumed to be equal. Fig. (2)
702
shows the power circuit for five-phase nine levels inverter fed
five-phase induction motor.
The modulation methods used in multilevel inverters
can be classified according to switching frequency, low
switching frequency and high switching frequency, [11, 12].
The popular methods in industrial applications for high
switching frequency are the classic carrier-based sinusoidal
pulse width modulation (SPWM), selective harmonic
elimination (SHEPWM) and space vector PWM (SVPWM)
[13-15]. The popular methods in industrial applications for
low switching frequency are the multilevel selective harmonic
elimination, and Space vector control [16-17]. In this paper
we use the classic carrier-based sinusoidal pulse width
modulation (SPWM) with triangular carriers. Some methods
use carrier disposition and others use phase shifting of
multiple carrier signals. In this paper we used phase shifting
of multiple carrier signals. A number of S–cascaded cells in
one phase with their carriers shifted by an angle of 180o/S and
using the same control voltage produce a load voltage with the
smallest distortion. For multi-phase inverter the reference
signals are shafted by 360/ (phases number).
Fig. 2 Five-phase nine level inverter fed five-phase induction motor
III. FIVE-PHASE INDUCTION MOTOR MODEL
The winding axes of five stator winding are
displaced by 72 degrees. By increasing the number of
phases, it is also possible to increase the torque per
ampere for the same volume machine. In this analysis the
iron saturation is neglected. The line-to-neutral voltages
can be transformed to the d-q planes using the following
transformation matrix K [18]:
⎡
⎢cosθ
⎢
⎢ sinθ
⎢
2⎢
K = cosθ
5⎢
⎢
⎢ sinθ
⎢
⎢ 1
⎣⎢ 2
2
cos(θ − π )
5
2
sin(θ − π )
5
4
cos(θ + π )
5
4
sin(θ + π )
5
1
2
4
cos(θ − π )
5
4
sin(θ − π )
5
2
cos(θ − π )
5
2
sin(θ − π )
5
1
2
4
cos(θ + π )
5
4
sin(θ + π )
5
2
cos(θ + π )
5
2
sin(θ + π )
5
1
2
2 ⎤
cos(θ + π )⎥
5
2 ⎥
sin(θ + π )⎥
5 ⎥
4
cos(θ − π )⎥⎥
5
4 ⎥
sin(θ − π )⎥
5 ⎥
1
⎥
2
⎦⎥
The general equations of five-phase induction motor
model can be introduced as follows.
The stator Quadrature axes voltage is given by:
v qs = rs iqs +
dλ qs
dt
+ ωλ ds
(1)
The stator direct axes voltage is given by:
v ds = rs ids +
Fig. (1) Single-phase Cascaded H-bridge m-level inverter.
dλ ds
− ωλ qs
dt
(2)
For the stationary reference frame ω = 0, substitute into
Equations (1) and (2) yields:
v qs = rs iqs +
703
dλ qs
dt
(3)
v ds = rs ids +
dλ ds
dt
-Change-of-error (Δe), that is the derivative of speed
error, and
-Output, defined as the change-of-control (Δωsl), that
added to the motor speed (ωm) is the input (ω*e) to the
converter. These error inputs are processed by linguistic
variables, which require to be defined by membership
unctions [20]. Fig.5 shows a scalar IM control structure
with fuzzy knowledge based controller (FKBC). The FLC
includes four major blocks: one that computes the error
into two input variables, a fuzzification block, an
inference mechanism, and the last step is defuzzification.
The speed reference control is ω*m.
(4)
The stator Quadrature axes flux linkage is given by:
λqs = Lsiqs + Lmiqr = ( Lls + Lm )iqs + Lmiqr
λqs = Llsiqs + Lm ( iqs + iqr )
(5)
The stator direct axes flux linkage is given by:
λds = Lsids + Lmidr = ( Lls + Lm )ids + Lmidr
λds = Llsids + Lm ( ids + idr )
(6)
The electromagnetic torque is given by:
[
5 p
λds iqs − λqs ids
22
dω
Te − Tl = J
+ Bω
dt
Te =
Where:
rs:
iqs:
ids:
iqr:
idr:
Ls:
Lls:
Lm:
Tl:
J:
B:
]
Fig 3 shows the triangle-shaped membership functions of
error (e) and change-of-error (Δe). The fuzzy sets are
designated by the labels: NB (negative large), NM
(negative medium), NS (negative small), Z (zero), PS
(positive small), PM (positive medium), and PB (positive
large).
(7)
(8)
is the stator phase resistance (ohm)
is the stator Quadrature axes current (A)
is the stator direct axes current (A)
is the rotor Quadrature axes current (A)
is the rotor direct axes current (A)
is the stator equivalent inductance (H)
is the stator leakage inductance (H)
is the magnetizing inductance (H)
is the load torque (N.m)
is the inertia of motor (Kg.m2)
is the friction coefficient (N.m.s/rad)
A. Speed Control of Induction Motors
Speed control of induction motor can be classified to
two methods. The first method is cold scalar control. The
second method is cold vector control. Scalar control involves
only magnitude of the control variables with no concern for
the coupling effects between these variables. Conversely
vector control involves adjusting the magnitude and phase
alignment of the vector qualities of the motor [19]. Scalar
control such as the constant Volts/Hertz method when applied
to an AC induction motor is relatively simple to implement
but gives a sluggish response because of the inherent coupling
effect due to torque and flux being function of current and
frequency. In this paper we use the scalar control method.
B. Fuzzy Logic Controller (FLC)
In the last few years, fuzzy logic has met a growing
interest in many motor control applications due to its nonlinearity handling features and independence of the plant
modeling. The fuzzy controller (FLC) operates in a
knowledge-based way, and its knowledge relies on a set of
linguistic if-then rules, like a human operator. The controller
architecture includes some rules which describe the casual
relationship between two normalized input voltages and an
output one. These are:
-Error (e), that is the speed error,
Fig. 3. Triangular membership functions for input variables e and Δe
Fig. 4 and Table 1 show the proposed membership
functions for output variable and the control rules. The
inference strategy used in this system is the Mamdani
algorithm, and the center-of-area/gravity method is used
as the defuzzification strategy
704
IV. SIMULATION RESULTS
The simulation results of five-phase nine level
inverter fed five-phase induction motor is done using
MATLAB SIMULINK. 6 N.m load torque has been
applied to the motor during the simulation. The motor
parameters are Lm = 0.2576 H, Lls = Llr = 0.2786 H, rs
=4.87 ohm, rr = 4.87 ohm, P = 4 pole, J = 0.009 Kg.m2,
and B = 0.005 N.m.s/rad The simulation results of
voltage, current, motor speed and torque presented when
the speed reference increased from 1000 rpm to 1450 rpm.
We find the frequency change from 33.33 HZ at 1000 rpm
to 48.33 Hz at 1450 rpm and the voltage increase from
146.6 V to 212.5 V. This mean that the flux is maintain
constant (V/f = constant). Fig.6. Show the simulation
results for five-phase system with PI and FLC.
Fig. 4. Triangular membership functions for output variable
PB
PM
PS
Z
NS
NM
NB
e
PB
NB
NB
NB
NB
NM
NS
Z
PM
NB
NB
NB
NM
NS
Z
PS
PS
NB
NB
NM
NS
Z
PS
PM
Z
NB
NM
NS
Z
PS
PM
PB
NS
NM
NS
Z
PS
PM
PB
PB
NM
e
V a
0
-500
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0
0.05
0.1
0.15
0.2
0.25
Time (sec)
0.3
0.35
0.4
0.45
0.5
V b
500
0
-500
V c
500
0
-500
500
NS
Z
Z
PS
PS
PM
PM
PB
PB
PB
PB
PB
PB
0
-500
PB
500
V e
NB
500
V d
Δe
Table 1. Linguistic Rule Table
0
-500
Output phases voltage of five-phase nine-level inverter
10
8
6
p h a s e s c u rre n t (A )
4
2
0
-2
-4
-6
-8
Fig. 5. Block diagram of scalar control of five-phase induction motor using PI
and FLC
-10
0
0.05
0.1
0.15
0.2
0.25
Time(sec)
0.3
0.35
Phases current (PI controller)
705
0.4
0.45
0.5
10
8
6
p h a s e s c u rre n t (A )
4
2
0
-2
-4
-6
-8
-10
0
0.05
0.1
0.15
0.2
0.25
Time (sec)
0.3
0.35
0.4
0.45
0.5
Phases current (FLC controller)
Fig. 6 the simulation results for five-phase induction motor using PI and
fuzzy logic control
V. CONCLUSIONS:
The five-phase nine level voltages are applied to
a five-phase induction motor and dynamic behavior of the
induction motor has been examined under V/f control. A
FLC that improve the performance of the scalar induction
motor drives has been proposed. The simulation results
show that using the proposed technique of the voltage con
be controlled in a wide range.
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