A Simplified Speed Control Of Induction Motor based on a Low Cost FPGA

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 7, No. 4, August 2017, pp. 1760~1769
ISSN: 2088-8708, DOI: 10.11591/ijece.v7i4.pp1760-1769  1760
Journal homepage: http://iaesjournal.com/online/index.php/IJECE
A Simplified Speed Control Of Induction Motor based on a Low
Cost FPGA
Lotfi Charaabi, Ibtihel Jaziri
Departement of Electrical Engineering, L.S.E-ENIT, université Tunis El Manar BP 37 EL Belvédère,
1002 Tunis, Tunisia
Article Info ABSTRACT
Article history:
Received Jan 1, 2017
Revised Mar 16, 2017
Accepted Mar 30, 2017
This paper investigates the development of a simplified speed control of
induction motor based on indirect field oriented control (FOC). An original
PI-P controller is designed to obtain good performances for speed tracking.
Controller coefficients are carried out with analytic approach. The algorithm
is implemented using a low cost Field Programmable Gate Array (FPGA).
The implementation is followed by an efficient design methodology that
offers considerable design advantages. The main advantage is the design of
reusable and reconfigurable hardware modules for the control of electrical
systems. Experimental results carried on a prototyping platform are given to
illustrate the efficiency and the benefits of the proposed approach.
Keyword:
Design efficiency
FOC
FPGA
Induction machine
PI controller Copyright © 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Lotfi Charaabi,
Departement of Electrical Engineering,
L.S.E-ENIT, université Tunis El Manar BP 37 EL Belvédère,
1002 Tunis, Tunisia.
Email:lotfi.charaabi@enit.rnu.tn
1. INTRODUCTION
The Field Oriented Control (FOC) or vector control has seen rapid expansion in recent years. The
FOC can be used to vary the speed of an induction motor over a wide range. It was initially developed by
Blaschke in the beginning of 1970s [1]. The FOC can be implemented in two ways Indirect and Direct
control scheme. The technique described in this work is based on indirect FOC because there is no direct
access to the rotor currents. Indirect vector control of the rotor currents is accomplished using the following
data:
a. Rotor mechanical velocity
b. Instantaneous stator phase currents
c. Rotor electrical time constant
The motor must be equipped with stator currents sensors and a rotor velocity feedback device.
Traditional indirect vector control consists of the ten blocks [2], [3]:
a. Clarke forward transform block
b. Park forward and inverse transform block
c. Rotor flux angle estimator block
d. Three PI controller blocks
e. Field weakening block
f. SVM block
This paper presents a simplified speed control of induction Motor which consists of only six blocks:
a. Clarke inverse transform block
b. Park inverse transform block

IJECE ISSN: 2088-8708 
A Simplified speed Control Of Induction motor based on a low cost FPGA (Lotfi Charaabi)
1761
c. Rotor flux angle estimator block
d. One PI-P controller block
e. Field weakening block
f. Hysteresis block
Microprocessors and Digital signal Processors (DSP) based solutions are available for digital AC
motor control applications like DSPIC family from Microchip [4], TMS320C24x family from Texas
Instruments [5] and STM32 family from STMicroelectronics [6]. Nevertheless, hardware solutions such as
FPGAs have already been used with success in AC motor control and drive applications such as pulse width
modulation (PWM) [7], [8], Direct Torque Control of induction motor [9-11] and FOC [12], [13] drives.
In this paper, a simplified speed control of an induction motor based a low cost FPGA is proposed.
The FPGA implementation is outlined by an efficient design methodology which is based on modularity and
reusability concepts [14], [15].
The major benefit for using FPGA is the achievement of the digital control algorithm within a few µ
second [16]. The calculation time, including the A/D conversion time of 2.4 µs, for the proposed FPGA
based controller is only equal to 3.135 µs. So, for a 20 KHz power converter, the digital control feedback can
be approximated quite closely to an analogue one because the effects of sampling and delay in the feedback
loop are small compared to the process time scale improving therefore the performances of the control.
The first section will detail the simplified speed control strategy of an induction motor. This strategy
is based on indirect FOC. The second section will present the hardware architecture design based FPGA.
Finally, in a third section, some experimental results carried on a prototyping platform will be shown for the
validation of the developed control system.
2. SIMPLIFIED SPEED CONTROL STRATEGY
2.1. Principle of the Proposed Control Strategy
The well-known discrete-time model of a squirrel-cage induction motor in the dq reference frame is
used for this study. The voltage, the stator flux linkage and the electromagnetic torque Equations expressed in
the rotor reference frame (d-q coordinates, with d-axis linked to the inductor) are:
𝑢 = (𝑅 + 𝑅 ) 𝑖 + 𝜎𝐿 − (𝜔 𝜎𝐿 𝑖 + 𝑅 𝜓 )… (1)
𝑢 = (𝑅 + 𝑅 ) 𝑖 + 𝜎𝐿 + (𝜔 𝜎𝐿 𝑖 + 𝜔 𝜓 )... (2)
𝑢 = = 𝑅 𝑖 + − (𝜔 − 𝜔 )𝜓 (3)
𝑢 = = 𝑅 𝑖 + − (𝜔 − 𝜔 )𝜓 (4)
𝜓 = 𝐿 𝑖 + 𝐿 𝑖 (5)
𝜓 = 𝐿 𝑖 + 𝐿 𝑖 (6)
𝜓 = 𝐿 𝑖 + 𝐿 𝑖 (7)
𝜓 = 𝐿 𝑖 + 𝐿 𝑖 (8)
= (𝜓 𝑖 − 𝜓 𝑖 ) (9)
(𝜔 − 𝜔 ) = 𝜔 (10)
+ 𝜔 = − (11)
Where Rs is the stator resistance, Rr is the rotor resistance, Lm the stator/rotor mutual inductance, Ls
and Lr the stator-rotor inductances, p the number of pole pairs, ωe the electrical velocity, ωr is the angular
velocity of the rotor, ωsl is the slip velocity, usd and usq the d-q components of the stator voltage, isd and isq
the d-q components of the stator current, urd and urq the d-q components of the rotor voltage, ird and irq the d-

 ISSN: 2088-8708
IJECE Vol. 7, No. 4, August 2017 : 1760 – 1769
1762
q components of the rotor current, ψsd and ψsq the d-q components of the stator flux linkage , ψrd and ψrq the
d-q components of the rotor flux linkage and Te the electromagnetic torque. The rotor flux is allowed to be
aligned with the d-axis so that
𝜓 = (12)
This constraint can be represented by the vector diagram in Figure 1.
Figure 1. Induction machine vector diagram with ψrq set to zero
Setting ψrq to zero in Equations (9), the new torque Equation becomes.
= (𝜓 𝑖 ) (13)
If Equations (3) and (7) are combined using the constraint (12), the rotor flux Equation becomes
𝜓 = 𝑖 (14)
Where s denotes the differential operator d/dt and τr the rotor time constant.
Equation (14) implies that the rotor flux depends only on the stator current.
If Equations (4) and (8) are combined using the constraint (12), the slip velocity becomes
𝜔 = − (15)
Using Equations (6) and (10) a new slip velocity Equation can be defined
𝜔 = (16)
So, the slip angle is estimated by the following relation:
= ∫ 𝑖 + (17)
Where θsl0 is the initial slip angle which can be set to zero
Equation (10) gives
= + = ∫ 𝑖 + (18)
Using Equations (2), (6) and (15), the q-component stator voltage usq can be expressed with isd, isq
and ψrd
𝑢 = (𝑅 + 2𝑅 ) 𝑖 + 𝜎𝐿 + (𝜎𝐿 𝜔 𝑖 ) (19)
Stator frame
Roto
r
d-axis
q-axis
ω
r
ω
e
ω
e
θsl
θeθr
ψr
is
isq
isd

IJECE ISSN: 2088-8708 
1763
For this control strategy, the d-component stator current isd is imposed to obtain the nominal torque.
Subsequently, by Equation (14), the d-component of the rotor flux linkage ψrd becomes constant in steady-
state. Then, controlling isd implies controlling the torque. The related control scheme is shown in Figure 2.
Figure 2. Principle of the control strategy
2.2. PI-P Controller Design
The PI-P regulator is introduced into the control scheme in order to achieve a second order system
with a damping coefficient ζ=0.7.
The dynamic model of the speed induction motor drive is significantly simplified, and can be
reasonably represented by the block diagram shown in Figure 3. τ represents the time constant for the desired
current isq
Figure 3. The block diagram of the PI-P regulator with the process
Figure 4. P regulator associated with the process
The goal of the P regulator is to obtain a second order system with real poles in closed loop. In order
to simplify the calculation we neglect the viscous friction coefficient f. Figure 4 shows the simplified block
diagram of the P regulator with the process.
IM
(d,q)
(a,b,c)
Hys
t
isd
*
isq
*
isa
*
isb
*
isc
*
c1
c2
c3
θe
isa
isb
isc
θr= +
PI-P
+ -
=
4
1
2
35
1. PI-P controller block
2. Angle and speed estimator block
3. Dq-to-abc transform block
4. Hysteresis controller block
5. Field weakening block
ωr
*
+
-
+
+
-
+
-
1
+
PI
regulator
P
regulator
+
-
P
regulator
1

 ISSN: 2088-8708
1764
The closed loop transfer function
( ) =
( )
( )
= (20)
The P coefficient kv is selected to obtain a double real pole called ωn
= (21)
Then, the transfer function becomes
( ) =
( )( )
(22)
Where ωn=1/2τ
The PI regulator is introduced before the P regulator in order to compensate the real pole ωn and to
obtain a second order system in closed loop
To compensate the real pole ωn, PI coefficients must obeys this rule
= 𝜔 (23)
Using Equation (23), the global closed loop transfer function becomes
( ) =
( )
( )
= (24)
Then, for a desired damping coefficient ζ, kp is expressed by the following Equation
= (25)
3. ARCHITECTURE DESIGN
The purpose of this section is to develop a discrete-time and an optimized architecture based FPGA
for the control algorithm. The most used discretization method is based on Forward shift approximation [17].
The shift form approximation is given by
= (26)
Where T is the sampling period.
As shown in Figure 2, the control algorithm is divided into four modules. The description of the
different modules is detailed below.
PI-P controller block: This module generates the digital values of the stator component references
isq* through the rotor angular velocity error. The discretization of the PI-P algorithm using the Forward shift
approximation gives
{
( ) = 𝜔 ( ) − 𝜔 ( )
𝑢( ) = ( ) + 𝑖( )
𝑖( ) = 𝑖( − 1) + ( )
𝑖 ( ) = (𝑢( ) − 𝜔 ( ))
(27)
Where Kp, Ki and Kv depends on kp, ki, kv and T
The data flow graph (DFG) corresponding to the PI-P algorithm is presented in Figure 5

IJECE ISSN: 2088-8708 
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Figure 5. (a) DFG of the PI-P controller, (b) DFG of the speed and angle estimator
Angle and speed estimator block: This module generates the rotor velocity ωr and the electrical
angle θe through the rotor angle θr. The rotor angle is provided by an absolute coder.
The discretization of Equation (18) provides the discrete-time Equation of the electrical angle
estimator:
( ) = ( − 1) + 𝑖 ( ) + ( ) (28)
Where =
The rotor velocity is obtained from the rotor angle using the following Equation:
𝜔 ( ) =
( ) ( )
(29)
Where ( − ) is the rotor angle at instant + . Figure 5 shows the DFG of the estimator
dq-to-abc transform block: This module contains the dq-to-abc transformation. It generates the digital values
of the stator current references isa*, isb* and isc*. Equation (30) shows a matrix representation of this module
𝑖 ( ) =
[
√
−
√ √
−
√
−
√ ]
[
( ) − ( )
( ) ( )
] [
𝑖
𝑖 ] (30)
Using trigonometric formula, Equation (30) leads to the Equation (31)
{
𝑖 = √ ( ( + ) 𝑖 + ( + ) 𝑖 )
𝑖 = √ ( ( + ) 𝑖 + ( + ) 𝑖 )
𝑖 = −𝑖 −𝑖
(31)
-
ωr(k)ω*
r(k)
i(k-1)
u(k)
e(k)
isq(k)
Kp Ki
i(k)
+
+
Kv
-
Z-1
+
isq(k)
ωr(k)
θe (k-1)
A 1
+
-
θr (k)
θe (k)
Z-d
1/ΔT
Z-1
(a)
(b)

 ISSN: 2088-8708
1766
Figure 6 shows the DFG corresponding to the dq-to-abc transformation module.
Figure 6. DFG of the dq-to-abc transformation estimator
Hysteresis controller block: This module contains three identical hysteresis controllers. It generates
the switching states c1, c2 and c3 via the comparison of the stator current references to the measured stator
currents.
4. Experimental Set-up
For this project, the used FPGA target is a XC2s100 from Xilinx Inc. The FPGA based hardware
control system includes the speed controller, an AD converter interface and a serial interface in one FPGA
chip. Figure 7 shows the corresponding implemented architecture.
Figure 7. FPGA based hardware control system
The serial interface module provides a serial communication between the host PC and FPGA. The
control unit is started at each rising edge of the sampling frequency Fs. It activates firstly the AD and coder
interface which starts the AD conversion process. AD conversion of the stator currents takes 2.4µs. When the
conversion process is finished, the AD interface module read converted data and treats them to generate the
digital values of the measured stator currents isa[n], isb[n] and isc[n]. Then, the control unit activates the speed
controller module. This module allows the generation of the switching states c1[n], c2[n] and c3[n]of the VSI.
The computation time, including the AD conversion time, from the AD converter stator currents acquisition
θ[n]
π/2 11π/
6
π
+ + +
Sin Sin Sin Sinisd[n] isq[n]
x x x x
+ +
xx
isa[n] isc[n]
+
π/
3
2 3
+
-
0
isb[n]
2 3
Serial
interfac
AD
Interface
isa[n
]isb[n
]isc[n
]
Control Unit
ωr
(n)
AD
isa isb
AD
Control
Clock
40MHz
DIV
Start
Read
FPGA
c1[nc2[n]c3[n]
Tx
Rx
Fs
θr
FOC
controller
Coder
Interface

IJECE ISSN: 2088-8708 
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to the switching states generation is equal to 3.135 µs. By comparison, the used dead time of the used VSI is
about 3.3 µs. So the computation time is almost negligible and the digital control feedback can be
approximated to an analog one.
To test the FPGA based controller, a test bed for the control of an induction machine was
assembled. Figure 8 shows the prototyping platform.
Figure 8. Prototyping platform (a) Control system (b) General view
The test bed is composed of a 0.75 Kw induction motor provided with a 1024 points encoder,
current sensors and a controlled load for load torque generation. The VSI module includes a three phase
IGBT based inverter, a 2200 µF capacitance and a three phase diode rectifier. An AD conversion circuit
board is used to convert the measured currents and an inverter interface circuit board allows the voltage level
adaptation of the switching states for the control of the inverter.
Figure 9. (a)Stator current isa for speed step input from 200 rad/s to 50 rad/s(Band width=0%Isn , and
Fs=10KHz) (b)Stator current isa for speed step input from 20 rad/s to 200 rad/s(Band width=0%Isn , and
Fs=10K Hz)
During experimentation, the DC voltage source E of the three phase inverter is set to 400V.
Figure 9 presents the experimental results of the stator current isa for an hysteresis controller band width
equal to 0% of the rated line current, a sampling frequency Fs equal to 10KHz and different values of the
speed input.
Figure 10 presents the speed response of the system for ramp input. It shows the speed response
after a torque load perturbation. The speed response is provided by the serial interface to a host PC.
Experimental results shown in Figure 9 and Figure 10 give proof that the control system satisfy the
basic requirements of the control strategy and validate therefore the good functionality of the system. The
same experiment has been done in the literature [20] with the indirect FOC which gave similar performances.
Table 1 shows the variation of the time response for the indirect FOC and the simplified indirect FOC.
Table 1. Variation of settling time, maximum overshoot with indirect FOC
Controller Indirect FOC Simplified indirect FOC
Rise time 1.9 s 2 s
Maximum overshoot in (%) 12.6 2.3
(a)
FPGA
AD
converters
VSI
interface
board
(b)
VSI
IM
Host
PC
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-100
-80
-60
-40
-20
0
20
40
60
80
100
t (s)
isa(%)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-100
-80
-60
-40
-20
0
20
40
60
80
100
t (s)
isa(%)
(a) (b)

 ISSN: 2088-8708
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Figure 10. (a) Speed response of ramp as function of time (b) Speed response for 200 rad/s reference input
without and with torque load
5. CONCLUSION
This paper presents the implementation on a FPGA of a simplified speed control for induction
machine. The control algorithm is based on indirect FOC. It uses only six blocks instead of ten blocks. A PI-
P regulator is designed to obtain good performances for speed tracking. The algorithm was implemented on a
low cost FPGA. The implementation has rigorously followed an efficient design methodology. This
methodology was used with success for the speed control of induction machine using FPGA based controller
and it can be considered as a part of a process whose target is the creation of a specific electrical system
library of optimized reusable modules which will ensure a great flexibility for the design development.
ACKNOWLEDGEMENTS
This paper was supported by the Tunisian Ministry of High Education and Research: UR-LSE-
ENIT-03/UR/ES05
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Patterns”, Application Report SPRA524, 1999 Texas Instruments Incorporated.
0 1 2 3 4 5 6 7 8
-50
0
50
100
150
200
t(s)
speed(rad/s)
(a)
1. 1. 1. 2 2. 2. 2.
192
194
196
198
200
202
204
speed(rad/s)
Without load With load
t(s)
(b)
1.96 1.97 1.98 1.9 2 2.01 2.02 2.03 2.04
196.5
197
197.5
198
198.5
199
199.5
200
200.5
201
250

IJECE ISSN: 2088-8708 
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APPENDIX
Induction Machine Parameters
1 KW, 230V, 50 Hz, 3 Phases, Y connection, 2 poles
Stator resistance = 7.2 Ω Rotor resistance = 1.35 Ω
Stator inductance = 0.28 H Rotor inductance = 0.075 H Mutual inductance = 0,118 H
BIOGRAPHIES OF AUTHORS
Lotfi Charaabi received the B.S degree and the M.S degree in Electrical Engineering from the
Engineering school of Tunisia, in 2002 and the Ph.D. from the department of Automatic Control
systems and Computer Engineering, university of Cachan French in 2006. Since 2009, he has
been actively cooperating in industrial project related to motor control algorithm design and
implementation. He is member of the Research laboratory LSE of the Tunisian engineering
school.
Ibtihel Jaziri received the B.S degree in Industrial electronic Engineering from the Engineering
school of Sousse, in 2010. She is currently working toward the Ph.D. degree with the Université
de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, Laboratoire des Systèmes Electriques
(LSE – LR11ES15), Tunis, Tunisia. Her main research interests include Co-design methodology
for motor control, design and implementation of motor control algorithms.

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