Energy and Power Engineering, 2013, 5, 363-371
http://dx.doi.org/10.4236/epe.2013.55037 Published Online July 2013 (http://www.scirp.org/journal/epe)
DSP Based Simulator for Speed Control of the
Synchronous Reluctance Motor Using
Hysteresis Current Controller
Abdel-Karim Daud1, Basim Alsayid2
1Electrical and Computer Engineering Department, Palestine Polytechnic University (PPU), Hebron, Palestine
2Electrical Engineering Department, Palestine Technical University (PTU), Tulkarm, Palestine
Received May 12, 2013; revised June 13, 2013; accepted June 20, 2013
Copyright © 2013 Abdel-Karim Daud, Basim Alsayid. This is an open access article distributed under the Creative Commons Attri-
bution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
ABSTRACT
This paper presents the field oriented vector control scheme for synchronous reluctance motor (SRM) drives, where
current controller followed by hysteresis comparator is used. The test motor has a star-connected wound stator and a
segmental rotor of the multiple barrier type with an external incremental encoder to sense rotor position. The magnetic
characteristics of this motor are described using 2D finite element method, which is used firstly for rotor design of SRM.
The field oriented vector control, that regulates the speed of the SRM, is provided by a quadrature axis current com-
mand developed by the speed controller. The simulation includes all realistic components of the system. This enables
the calculation of currents and voltages in different parts of the voltage source inverter (VSI) and motor under transient
and steady state conditions. Implementation has been done in MATLAB/Simulink. A study of hysteresis control scheme
associated with current controllers has been made. Experimental results of the SRM control using TMS320F24X DSP
board are presented. The speed of the SRM is successfully controlled in the constant torque region. Experimental results
of closed loop speed control of the SRM are given to verify the proposed scheme.
Keywords: Field Oriented Control; 2D Finite Element Method; SRM; Hysteresis Current Controller; DSP;
MATLAB/Simulink
1. Introduction
Synchronous reluctance motor (SRM) has recently at-
tracted the efforts of a number of researchers and is
gaining favor as a possible alternative for ac drives [1-4].
Since the converter fed SRM does not need a starting
cage, an optimized rotor for synchronous performance
can be designed. The simple and rugged structure allows
high speed drives to be readily attained while the copper
and iron losses confined into the stator allow the motor to
be operated with high electric and magnetic loads with
advantage on the torque/weight ratio. A drawback of
these drives resides in the need of synchronization with
the rotor position [5-7]. The complicated coupled nonlin-
ear dynamic performance of SRM can be significantly
improved using vector control theory [4,8-16] where
torque and flux can be controlled separately. Simulations
have helped the process of developing new systems in-
cluding motor drives, by reducing cost and time.
Simulation tools have the capabilities of performing
dynamic simulations of motor drives in a visual envi-
ronment so as to facilitate the development of new sys-
tems [14,17,18].
In this work, the simulation of a field oriented con-
trolled SRM drive system is developed using MAT-
LAB/Simulink.
The motor has a segmental rotor of the multiple barrier
type with an external incremental encoder to sense rotor
position. The simulation circuit will include all realistic
components of the drive system. This enables the calcu-
lation of currents and voltages in different parts of the
inverter and motor under transient and steady state con-
ditions. A closed loop control system with a PI controller
in the speed loop has been designed to operate in con-
stant torque region. A study of hysteresis control scheme
associated with current controller has been made. Simu-
lation results are given for the speed range in constant
torque region of motor operation. Finally, the experi-
mental verification obtained by using the DSP based
C
opyright © 2013 SciRes. EPE

A.-K. DAUD, B. ALSAYID 364
vector control is presented.
2. Prototype Rotor Design
2.1. Rotor Types
Almost all of the important parameters of the synchro-
nous reluctance motor depend on the synchronous in-
ductance ratio or saliency ratio,
 = Lq/Ld. The main
classes of rotor design aimed at maximizing
 are trans-
versely and axially laminated multiple barrier rotors as
shown in Figures 1 and 2, respectively. In all cases the
objective is to achieve a high Lq by providing, essentially,
flux guides for q-axis flux; and low Ld by providing flux
barriers to d-axis flux.
In respect to axially laminated rotor, a transverse lami-
nated one has many advantages such as simplicity in the
mechanical construction, lower manufacturing cost and
rotor skewing possibility. On the contrary it has a quite
large level of torque ripple due to the stator slots and
rotor flux barriers that produce a non sinusoidal air-gap
permeance variation.
2.2. Direct Finite Element Design
A two-dimensional finite element method is used to de-
sign the rotor and to analyze the magnetic characteristics
of the motor by taking into account the non-linearity and
saturation phenomena. The solutions of the magnetic field
with different rotor displacements and phase excitations
Figure 1. Transversely laminated multiple-barrier rotors.
Figure 2. Axially laminated multiple-barrier rotor.
are obtained. The magnetic field characteristics are de-
scribed over the entire area of the motor in terms of
magnetic vector potentials.
The result of magnetic flux calculation is shown in
Figure 3 for only 1/6 of the machine due to symmetry
considerations. The achievable saliency ratio is limited
by two factors: the d-axis permeance cannot be zero and
the laminations are subject to saturation in the q-axis.
Figure 4 shows the cross-sectional view of the pro-
posed reluctance motor. It is a three-phase six-pole motor,
with 4 barriers per pole. The stator is the same as that of
the PM synchronous motor. The rotor cores are laminated
in the rotor shaft direction. Magnetic reluctance in the
d-axis is large and in the q-axis is small. There is a narrow
connection ring in the fringe of the rotor and narrow con-
nection bars from the centre to the fringe in the d-axis.
They are necessary for mechanical stability of the rotor.
The rotor design is based on maximising torque. Fig-
ure 4 shows more detail of the rotor construction indi-
cating two key variables, Wiron and Wair, corresponding to
the width of each rotor segment and of the width of the
air gap between segments respectively. The sum of the
n*(Wiron + Wair) is chosen so as to always equal the width
Figure 3. Stator and rotor fluxes (MTC45).
Figure 4. Cross-sectional view of the proposed SRM.

A.-K. DAUD, B. ALSAYID 365
of one stator tooth (Wt) in order to limit, as much as pos-
sible, pulsating fluxes (torque ripple)in the stator teeth. In
practice, values of n = 1, 2 and 3 were investigated.
For purposes of comparison between different geome-
tries it is useful to define the ratio Kw = Wair/Wiron. Clearly,
when Kw = 0, the rotor is assumed to be completely made
of iron (no saliency). When Kw = 1 the rotor is con-
structed of lamination segments in which the air space
and lamination segments are equal. FEA for n = 1, 2 and
3 gave maximum torque for Kw = 1 and n = 3, in which
Wair = Wiron = 1.86 mm.
2.3. Torque and Torque Ripple
Three-phase motor currents have been considered to
supply the stator expressed by Equation(1) and the re-
sulting stator flux forms an electrical angle of 45° (15°
mechanical) with q-axis, which gives a maximum torque
curve (MTC45) (see Figure 3).

122sin
122sin 12
122sin 240
a
b
c
I
I
I








106 A
00 A
106 A




(1)
where
 = 120˚ is the electrical angle corresponding to
stator flux at 45° electric degrees from rotor flux, 122 A
is maximum current for half stator slot. The same normal
B-H characteristic is computed for stator and rotor mag-
netic material. With FEA a value of 4.2 Nm of Torque
has been calculated, it was the best value for different
values of electrical angle between stator and rotor fluxes,
which was verified experimentally. The torque ripple
results from the non-sinusoidal air-gap permeance func-
tion for the stator slots and rotor flux barriers; its estima-
tion requires an accurate FEA with different stator-rotor
relative positions. A few significant rotor positions,
among infinite ones, have been considered in order to
predict the torque ripple with a good accuracy.
Five rotations have been considered, each rotation of 1
mechanical degree or 3 electrical degrees, which corre-
spond to a half stator tooth pitch.
The results of calculated torque for each position are
obtained in Figure 5. It shows the torque ripple for a
rotation of an electrical angle of 15° (equal to a me-
chanical angle of 5°, six-pole motor). This is the angle of
skewing of the rotor adopted to reduce torque ripple.
The main dimensions of the test motor are shown in
Table 1. It is a 6-pole sinusoidal synchronous reluctance
motor (SRM). It has a star-connected wound stator, a
segmental rotor of the multiple barrier type (see Figure 6)
and external incremental encoder to sense rotor position.
3. SRM Drive System
The well-known d-q model of AC machines is widely
Figure 5. Torque ripple.
Figure 6. Cross section of the synchronous reluctance ma-
chine.
Table 1. SRM parameters.
Name Symbol Value
Rated voltage Vn 220 V
Rated torque Tn 5 Nm
Rated current In 14.9 A
Rated speed nn 1000 RPM
Maximum speed nmax 6000 RPM
Number of pole pairs P 3
Stator resistance Rs 0.3 Ω
q-axis Inductance Lq 0.009 H
d-axis Inductance Ld 0.004 H
Motor Inertia J 0.0755 kgm2

A.-K. DAUD, B. ALSAYID 366
used for simulation purposes. Based on the assumption
that the stator windings are sinusoidally distributed, the
d-q model is a powerful tool for dynamic simulation of
most AC machines including the reluctance synchronous
machine.
The d-q reference frame equations describing the mo-
tor are:
10
1
0
q
q q
d
d
v
v
L


 


 

 


d
d
d
r
qq
q
dd
q
rdd
L R
LL L
ii
ii L tR
LL





 


 

 




(2)
where id and iq are the d and q axis stator currents, Ld and
Lq are the stator phase d-axis and q-axis winding self in-
ductance respectively; R is the stator winding resistance;
r is the rotor electrical speed; vd and vq are the stator
voltages expressed in the dqreference frame. The inverter
frequency is related as follows
s
r
P

  (3)
where P is the number of pole pairs.
The electromagnetic torque equation is given by

edqdq
LLii
3
2
TP (4)
For maximum torque per ampere id = iq, therefore the
currents id and iq can be obtained from Equation (5) as
follows:

3
2
e
dq
T
PL L
d
i (5)
The equation of the motor dynamics is

dd
eLr r
TT tBJw (6)
TL stands for external load torque. B represents the
damping coefficient and J is the moment of inertia of the
rotor. The Equations (2), (4) and (6) constitute the whole
control model of the SRM. A system configuration of a
vector-controlled SRM drive system is shown in Figure
7.
The dynamic d q modeling is used for the study of
motor during transient and steady state. It is done by
converting the dqo variables to three phase currents by
using inverse Parks transformation [16-18].
SRM is fed form a voltage source inverter (VSI) with
current control. The control is performed by regulating
the flow of current through the stator of the motor. Cur-
rent controllers are used to generate gate signals for the
inverter. Proper selection of the inverter devices and se-
lection of the control technique will guarantee the effi-
ciency of the drive.
In the vector control scheme, torque control can be
carried out by suitable regulation of the stator current
vector; this implies that accurate speed control depends
on how well the current vector is regulated. In high-per-
formance vector drives, a current-control loop, with a
considerably high bandwidth, is necessary to ensure ac-
curate current tracking, to shorten the transient period as
much as possible and to force the voltage source inverter
(VSI) to equivalently act as a current source amplifier
within the current loop bandwidth. In this work, a hys-
teresis-band current controlled VSI is used. This control-
ler will generate the reference currents with the inverter
within a range which is fixed by the width of the band
gap. In this controller the desired current of a given phase
Figure 7. SRM vector-controlled drive system.

A.-K. DAUD, B. ALSAYID 367
(a,b and c) is summed with the negative of the
measured current (ia, ib and ic). When the current error
exceeds a predefined hysteresis band, the upper switch in
the half-bridge is turned off and the lower switch is
turned on. As the current error goes below the hysteresis
band, the opposite switching takes place. The principle of
hysteresis band current control is illustrated in Figure 8
[4,16].
iii
Speed controller calculates the difference between the
reference speed (  *) and the actual speed (  ) producing
an error, which is fed to the PI controller. PI controllers
are used widely for motion control systems. Speed con-
trol of motors mainly consist of two loops the inner loop
for current (band hysteresis current controller) and the
outer loop for speed (speed controller) as shown in Fig-
ure 7. The order of the loops is due to their response,
how fast they can be changed. This requires a current
loop at least 10 times faster than the speed loop. An in-
cremental encoder is used as a position sensor.
Control loops in the actual drive system, shown in Fig-
ure 7, are implemented in software on Texas Instruments
(TMS320F24X) processor and executed with a cycle
period of 70s. The flow chart of this program is shown
in Figure 9.
At switching on, the program initializes the hardware
registers, I/O ports are then pre-set to their initial states,
the inverter, ADC converters, position sensor (optical
encoder) and software variables. Then it initializes the
speed calculation and hysteresis regulators. The system
now completes all initializations and starts the main pro-
gram which requires a computational time of 70s of
period cycle.
The main program will first calculate actual speed of
the motor (
 ), read reference speed (  *) and actual cur-
rents (ia, ib and ic) from ADCs. Errors are then saved and
new errors are calculated. Speed regulator is realized by
a discrete PI.
Figure 8. Hysteresis current controller.
Figure 9. System flow diagram.
Calculation of q i

and d in the rotating reference
frame is done. Then it will read position from the en-
coder. Based on rotor position, three-phase reference
currents (a
i
i

, b i

and c i

) in the stationary reference frame
are calculated. This is followed by the execution of cur-
rents loop and resulting controlled signals are sent to the
inverter. Write DAC and wait end cycle are finally exe-
cuted.
4. Simulation in Simulink
The SRM drive simulation was built in several steps like
dqo variables transformation to abc phase, calculation
torque and speed, control circuit, inverter and SRM. The
dqo variables transformation to abc phase is built using
the reverse Parks transformation. For simulation purpose
the voltages are the inputs and the current are output.
Using all the drive system blocks, the complete system
block has been developed as shown in Figure 10. The
system built in Simulink for a SRM drive system has
been tested with the Hysteresis current control method at

A.-K. DAUD, B. ALSAYID 368
we (rad/s)
vb c (V )
v
+
-
vb c
theta
idqsr i*abc
stationary dq
to ab c
ISP
Beta
iq
id
rotating idq 45
i*q
i*d
the
idqsr
rotatin g dq to
stationary dq
Discrete,
T
s = 1e-005 s
.
pow ergui
pi output
1.3
load torque
PI
iqr
iqdsr1
pi/4
idr
ia bc real
i*abc reference
iabc
iref
va
vb
vc
hysteresi s current
controll er
e rro r
in
x
X-Y Signal Scope
iabcreal
To Workspace2
speed
To Workspace
Te
Workspace3To
iabcreferenc
e
To Workspace1
T e (N.m)
m
A
B
C
Tm
Synchronous Reluctance
Ma chin e wi th zero
magnetic flux
Step1
Step
0
Speed Ref1
157
Speed Ref
3
3
?
Doubl e cli ck here for more in fo
<Elect romagnet ic t orque Te (N* m )>
<Rot or speed wm (rad/ s)>
<Rot or angle thet am (rad)>
Figure 10. Synchronous reluctance motor drive system in Simulink.
30
the constant torque region of operation.
The motor parameters used for simulation are given in
Table 1. Figure11 shows the real three phase currents
drawn by the motor as a result of the hysteresis current
control. The currents are obtained using Park’s reverse
transformation. It is clear that the current is non-sinu-
soidal at the starting and becomes sinusoidal when the
motor reaches the controller command speed at steady
state.
Figure 12 shows a variation of the speed with time.
The steady state speed is the same as that of the com-
manded reference speed. Figure 13 shows the developed
torque of the motor. The starting torque is the rated
torque. The steady state torque is about 1.3 Nm.
Figure 14 shows the real three phase currents drawn
by the motor as a result of the hysteresis current control,
when the motor changes its speed from 1000 rpm to
−1000 rpm with a load torque of 1.3 Nm. It is clear that
the currents are inversed due to the speed variation from
1000 to −1000 rpm. The speed performance is shown in
Figure 15 for this case. The steady state speed is the
same as that of the commanded reference speed.
Figure 16 shows the developed torque of the motor for
the speed variation from 1000 to −1000 rpm. The starting
torque is the rated torque (5 Nm). The steady state
torque is about 1.3 Nm in positive and negative opera-
tion of the motor.
5. Experimental Results
A DSP based PC board integrated system (TMS320F24X
DSP board), is used for vector control of SRM drive [14].
The schematic diagram of the hardware implementation
is shown in Figure 17. Feedback signals to the controller
board are the actual motor currents and the rotor position
angle. The currents are measured by the Hall-effect
transducers. The currents are then buffered and fed to the
A/D ports of the controller board. The motor shaft posi-
00.5 1.0 1.5 2
-30
-20
-10
0
10
20
time (s)
iabc (A)
Figure 11. Actual phase currents with hysteresis control at
1000 rpm with 1.3 N·m.
120
00.5 1.01.52
0
20
40
60
80
100
time (s)
speed (rad/s)
Figure 12. Dynamic performance for a step variation of the
reference speed from 0 to 1000 rpm (  = 105 rad/s) with a
torque load of 1.3 N·m.
6
00.5 1.0 1.52
0
1
2
3
4
5
torque (Nm)
time
(
s
)
Figure 13. Developed torque for a step variation of the ref-
erence speed from 0 to 1000 rpm (1.3 N·m load torque).

A.-K. DAUD, B. ALSAYID 369
00.5 1.01.5 2.0 2.53
-30
-20
-10
0
10
20
30
time
(
s
)
iabc (A)
ia
ib
ic
Figure 14. Inversion of actual phase currents due to a step
variation of a speed from 1000 rpm to −1000 rpm with a
torque load of 1.3 N·m.
00.5 1.0 1.5 2.0 2.53
-150
-100
-50
0
50
100
150
time (s)
speed (rad/s)
Figure 15. Dynamic performance for a step variation of the
speed from 1000 rpm to −1000 rpm (  = −105 rad/s) with a
torque load of 1 N·m.
00.5 1.0 1.5 2.0 2.5 3.0
-6
-4
-2
0
2
4
6
time (s)
torque (Nm)
Figure 16. Developed torque with hysteresis control for a
step variation of the speed from 1000 rpm to −1000 rpm (1
N·m load torque).
tion is measured by an optical incremental encoder in-
stalled at the motor shaft. The commutating signals for
the drive pulses have also been generated by the hystere-
sis controller. The control algorithm has been imple-
mented via the controller board using assembly language
programming.
A series of experiments has been carried out to evalu-
ate the performances of the proposed vector controlled
SRM drive system. Different sample results are pre-
sented in the following figures. Figure 18 demonstrates
the actual phase current ia wave form at speed 1500 rpm
for a load of 2 Nm.
The experimental evaluation of speed with load as pa-
rameter of DSP based SRM drive is shown in Figure 19.
It shows the step speed response of 1000 rpm of the pro-
posed system for a load of 1.3 Nm.
In Figure 20, the behaviour of the current of phase A
is shown during the inversion of speed from 1000 RPM
to −1000 rpm with load torque of 2 Nm. Figure 21
shows the response of the drive to a step variation of the
reference speed from 1000 to −1000 rpm with a load
Figure 17. The hardware schematic of experimental system.
Figure 18. Actual phase current ia wave form at 1500 rpm
for a load of 2 N·m.

A.-K. DAUD, B. ALSAYID 370
Figure 19. Experimental speed responses of SRM drive for
step variation from 0 to 1000 rpm with load torque of 1.3
N·m.
Figure 20. Inversion of actual speed and actual phase cur-
rent ia wave forms due to a step variation of the reference
speed from 1000 rpm to −1000 rpm (load Torque of 2 N·m).
Figure 21. Dynamic performance for a step variation of the
reference speed from 1000 rpm to −1000 rpm (load torque
of 1 N·m).
torque of 1 Nm.
6. Conclusions
A rotor for a reluctance motor has been designed using
2D finite element method. The maximum torque has
been found to be 4.2 Nm. The results obtained by FEA
seem to be valid because, after the construction of the
rotor, experimental results show that the maximum
torque is about 4.2 Nm and the torque ripple with posi-
tion is very closed to the results obtained by FEA.
A MATLAB/SIMULINK simulation model has been
proposed for closed loop speed control with internal cur-
rent loop using hysteresis controllers. The experimental
results show that the proposed field oriented vector con-
trolled SRM drive can handle the effects of step change
in reference speed and parameter variations. The overall
system performances are quite good in terms of dynamic,
transient and steady-state responses.
Simulation and experimental results show that the pro-
posed control scheme guarantees stable and robust re-
sponse of the SRM drive, under a wide range of operat-
ing conditions. Subsequently, it can be utilized in high
performance motion control applications.
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