Implementation of Type-2 Fuzzy Logic Controller in PMSM Drives Using DSP

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 9, No. 3, September 2018, pp. 1098~1105
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v9.i3.pp1098-1105  1098
Journal homepage: http://iaescore.com/journals/index.php/IJPEDS
Implementation of Type-2 Fuzzy Logic Controller in PMSM
Drives Using DSP
S. Wahsh1
, Y. Ahmed2
, E. Abo Elzahab3
1,2
Department of Power Electronics and Energy Conversion, Electronics Research Institute, Giza, Egypt
3
Department of Electrical Power and Machines, Cairo University, Giza, Egypt
Article Info ABSTRACT
Article history:
Received Oct 30, 2017
Revised Apr 24, 2018
Accepted Aug 6, 2018
This paper presents interval type-2 fuzzy logic (IT2FL) controller applied on
a direct torque controlled (DTC) permanent magnet synchronous motor
(PMSM), using digital signal processing (DSP). The simulation of PMSM
with space vector pulse widths modulation (SVPWM) inverter presented
under several operating condition. To verify the simulation results a hard
ware setup is prepared and tested at several operating conditions using
dspace 1102 DSP model. The experimental and simulation results are in
agreement, the torque dynamic response is very rapid and the system
achieves the steady state in a very short time.
Keyword:
Direct torque control
Fuzzy logic controller
Fuzzy type-2
PMSM
Space vector modulation Copyright © 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
S. Wahsh,
Department of Power Electronics and Energy Conversion,
Electronics Research Institute,
33 El-Tahrirst., Dokki, Giza, Egypt
Email: wahsh@eri.sci.eg
1. INTRODUCTION
Fuzzy logic systems (FLS) have been successfully applied to control complex or ill-defined
processes whose mathematical models are difficult to obtain. The ability of converting linguistic descriptions
into automatic control strategy has made it a practical and promising alternative to the classical control
scheme for achieving control of complex nonlinear systems.
The concept of type-2 fuzzy sets was initially proposed by Zadeh as an extension of typical fuzzy
sets (called type-1). Mendel and Karnik developed a complete theory of IT2FL systems. Recently, T2FLSs
have attracted more attention in many literatures and special issue of IEEE Transactions on Fuzzy systems.
A decentralized adaptive controller based on type-2 fuzzy systems has been presented by [1], the controller
used to maintains the tracking errors in PMSM based on field oriented control. An adaptive
IT2FLCcontroller is proposed in [2] for PMSM drives, Type-2 fuzzy logic system combined with adaptive
control to achieve accurate control system which able to track the refence speed in a system with higher
uncertainties.
IT2FL systems are more complex than type-1, the major difference being the present of type-2 is
their antecedent and consequent sets. IT2FL systems result better performance than type-1 fuzzy logic
systems on the applications of function approximation, modeling and control [2]-[8]. The wide ranges of
applications of type-2 FLS have shown that it provide good solutions, especially in the presence of
uncertainties as
a. Uncertainties in inputs to the FLC which translate to uncertainties in the antecedent Membership
Functions (MFs).
b. Uncertainties in control outputs which translate to uncertainties in the consequent MFs of the FLC.

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Implementation of Type-2 Fuzzy Logic Controller in PMSM Drives Using DSP (S. Wahsh)
1099
c. Linguistic uncertainties as the meaning of words that are used in the antecedent and consequent
linguistic labels can be uncertain-words mean different things to different people.
In the mid 1980’s the direct torque control (DTC) was introduced for induction motor by Takahashi
et al. In the 1990’s, DTC for permanent magnet synchronous motor (PMSM) was developed. Compared with
field oriented control, the DTC has many advantages such as less machine parameter dependence, simpler
implementation and quicker dynamic torque response. There is no current controller needed in DTC, because
it selects the voltage space vectors according to the errors of flux linkage and torque. DTC has some
drawbacks, such as the high torque and flux ripples. Due to sophisticated and large computational of vector
control DTC recognized as a viable solution to achieve these requirements and reduce the complexity of
vector control.
In this article, DTC technique used to control the speed of the PMSM, the speed controller is
represented by IT2FL, the torque and flux regulators are represented by conventional PI controllers. The
controller’s parameters are adjusted for minium traking error, the system implemented and tested at different
operating conditions using DSP.
2. PMSM MATHEMATICAL MODEL AND DIRECT TORQUE CONTROL PRINCIPLE
The stator flux linkage vector ψs and rotor flux linkage ψm can be drawn in the rotor reference
frame (d-q), stator reference frame (ds-qs) and stationary reference frame(α-β) as shownin Figure 1[9]-[12].
(1)
(2)
(3)
(4)
(5)
Where vd, and vq are the d-q axis voltages, id and iq are the d-q axis stator currents, Ld and Lq, are
the d-q axis inductances, , and , are the d-q axis stator flux linkages, is the stator resistance per
phase, the rotor speed and , is the stator flux linkage due to the rotor magnets. By transforming the
rotor reference flux component ψd, ψq and current id, iq to the stator reference flux component ψds, ψqs and
current component ids, iqs with the transformation (6) and (7), torque (5) can be transformed as in (8).
Figure 1. The stator and rotor flux linkages in different reference frame
(6)
and (7)

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 9, No. 3, September 2018 : 1098 – 1105
1100
(8)
(9)
(10)
Equation (10) shows that to increase torque, δ should be increased; to increase δ stator flux should
turn faster than rotor flux by the selection of optimum voltage vector according to difference between the
reference and actual values of torque and flux.
3. SPACE VECTOR MODULATION
The main advantages of the space vector modulation (SVM) are: A 15% increase in DC link voltage
utilization compared with the sine-triangle technique. Lower harmonic content, particularly at high
modulation indices compared with the sine-triangle technique [11].
The voltage-vector space is divided up into six sectors in the vector space as shown in voltage-
vector space in Figure 2. In one sampling interval, the output voltage vector can be written as
(11)
Where t0, t1,………., t7 are the turn-on time of the vectors ,….., , t0, t1,….., t7≥0, ,
and Ts is the switching time. However, in order to reduce the number of switching actions and make full use
of active turn-on time for space vectors, the vector U is commonly split into the two nearest adjacent voltage
vectors and zero vectors U0 and U7 in an arbitrary sector. For example, in sector I, in one sampling interval,
vector U can be expressed as:
(12)
Figure 2. Voltage vector space
4. INTERVAL TYPE -2 FUZZY LOGIC SYSTEM
In order to represent an IT2F set, we use two membership functions called upper membership
(UMF) and lower membership (LMF) [13]-[18]. Uncertainty of the primary membership grade of a type-2

1101
MF consist a bounded region that called footprint of uncertainty (FOU) which models the uncertainties in the
shape and position of the type-1 fuzzy set. Shown in Figure 3.
An UMF and a LMF are two type-1 MFs that are bounds for the FOU of an interval type-2 MF. The
UMF is a subset that has the maximum membership grade of the FOU, and the LMF is a subset that has the
minimum membership grade of the FOU Figure 4.
Figure 3. Block diagram of a PMSM drive with
DTC-SVM system Figure 4.Membership Function of Fuzzy type-2
A IT2FLS consists of four basic elements Figure 5: the type-2 fuzzyfier, the fuzzy rule-base, the
inference engine, and the type-2 type reduction/defuzzifier. The IT2FL system works as follows, the crisp
inputs from the input sensors are first fuzzified into input type-2 fuzzy sets. The input type-2 fuzzy sets then
activate the inference engine and the rule base to produce output type-2 fuzzy sets. The type-2 FLC rules will
remain the same as in a type-1 FLC but the antecedents and/or the consequents will be represented by IT2F
sets. The inference engine combines the fired rules and gives a mapping from input type-2 fuzzy sets to
output type-2 fuzzy sets. The type-2 fuzzy outputs of the inference engine are then processed by the type-
reducer which combines the output sets and performs a calculation which leads to type-1 fuzzy sets called the
type-reduced sets. After the type-reduction process, the type-reduced sets are defuzzified to obtain crisp
outputs that are sent to the actuators [14]-[16].
Figure 5. Configuration of a fuzzy type-2 logic system
It has been argued that using IT2F sets to represent the inputs and/or outputs of FLCs has many
advantages when compared to type-1 fuzzy sets; we summaries some of these advantages as follows:
1. As the type-2 fuzzy set membership functions are themselves fuzzy and contain a footprint of
uncertainty, they can model and handle the linguistic and numerical uncertainties associated with the
inputs and outputs of the FLC. Therefore, FLCs that are based on type-2 fuzzy sets will have the
potential to produce a better performance than type-1 FLCs when dealing with uncertainties.
2. Using type-2 fuzzy sets to represent the FLC inputs and outputs will result in the reduction of the FLC
rule base when compared to using type-1 fuzzy sets as the uncertainty represented in the footprint of
uncertainty in type-2 fuzzy sets lets us cover the same range as type-1 fuzzy sets with a smaller number
of labels. The rule reduction will be greater as the number of the FLC inputs increases.
3. Each input and output will be represented by a large number of type-1 fuzzy sets which are embedded
in the type-2 fuzzy sets. The use of such a large number of type-1 fuzzy sets to describe the input and
output variables allows for a detailed description of the analytical control surface as the addition of the
extra levels of classification gives a much smoother control surface and response.
4. It has been shown that the extra degrees of freedom provided by the footprint of uncertainty enables a
type-2 FLC to produce outputs that cannot be achieved by type-1 FLCs with the same number of
membership.

 ISSN: 2088-8694
1102
A standard approach for speed control in drives is the use of a PI controller. Recent developments in
artificial intelligence based control have brought in to focus a possibility of replacing a PI controller with a
fuzzy logic (FL).
The membership functions for input and output variables for the PI-type fuzzy type-2 are speed
error (E), change of speed error (ΔE), and change of torque as output (ΔT).
5. EXPERIMENTAL DRIVE CONFIGURATION
The laboratory set-up built for experimental tests of the PMSM drive system consists of the
following main parts:
1. PMSM BeckhoffAM 247 Series with resolver.
2. Beckhoof AX2513 series digital servo amplifier.
3. DSP (DSPACE DS1102) model.
4. PC Pentium 2, 32MB of RAM, 1GB of ROM with Windows and DSP Processor.
5. PC Pentium 4, CPU 3 GHz, 1GB of RAM with Windows XP and Beckhoff Motor software.
6. MCRT 48200V digital torque transducer.
7. Tektronix digital storage oscilloscope TPS2024 model.
8. Dc generator and resistive load
The overall system as shown in Figure 6 consists of the PMSM with built in resolver and shaft
encoder in order to measure the motor position, another component in the system is the BECKHOFF digital
servo amplifier which drive the motor using space vector PWM technique, also, there are output group of
sensors to measure the actual motor currents, voltage, and torque. This system is controlled using DSP
implemented in computer system using Matlab software.
6. SIMULATION AND EXPERIMENTAL RESULTS
There are many control strategies for DTC PMSM drives. Fuzzy typ-1 was used in control of DTC
PMSM drives and now we apply IT2FLS. IT2FL controller is used for speed loop, torque and flux loops
controllers are of conventional PI controller type [19]-[23]. The system is modeled with MATLAB
SIMULINK using PMSM data in appendix (A), with switching time Ts=0.0002sec. Figure 7 shows the speed
response at 2000 rpm reference speed, while Figure 8 shows the load torque response (TL) at load step
change from 0.55 NM to 1.1 N.M at 1 sec time, Figure 9.shows the current response. Motor torque and
reference torque is shown in Figure 10.
Figure 6. Laboratory Set-up

1103
(a)Simulation (b) Experimental
Figure 7. Speed Response
(a)Simulation
(b) Experimental
Figure 8. Torque Response
(a)Simulation (b) Experimental
Figure 9. Three phase Current Response
7. CONCLUSION
This paper presents modeling, simulation and implementation of a speed control in PMSM drive
based on DTC technique. IT2FL utilized as a speed controller, since it provides additional degrees of
freedom and handles systems uncertainties. The drive system has been simulated and tested using MATLAB
SIMULINK. Simulation and experimental are presented under different operating conditions. A hardware
setup is implemented and tested using dspace 1102 DSP board. The results show that the system operation
more smooth and reaches steady state faster when using fuzzy type-2 with the same number of memberships
as compared to conventional fuzzy. The system reaches steady state in 700 ms, 1.5% speed overshot, 1.35%
speed ripples and zero steady state speed error experimentally. The results show good agreement between
simulation and test results.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
500
1000
1500
2000
2500
3000
time-(sec)
wr-(rpm)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-2
-1
0
1
2
3
4
5
6
7
8
9
time-(sec)
Torque-(N.M)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-8
-6
-4
-2
0
2
4
6
8
time-(sec)
3ph
current-(A)

 ISSN: 2088-8694
1104
APPENDIXES
Appendix 1. PMSM Parameters
Data Value
Rated speed 3000 rpm
Rated torque 2.2 N.M
p 6
R 11.0 ohm
Ld 25mH
Lq 25mH
J 1.6Kg-cm2
.
Ym 0.295 Wb
Vdc 350.0 volt
Ts 0.0002 sec
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BIOGRAPHIES OF AUTHORS
Prof. S. WAHSH received his B.Sc. degree in Electrical Engineering from
AinShamsUniversity, Cairo, in June 1967. In 1973 he joined the National Research Center
(NRC) as a researcher. He received his Ph.D. in Electric Drives from Budapest Technical
University, Hungary in January 1980.Since 1980 he has been working as an assistant
professor in the Electronics Research Institute (ERI). From 1984 till 1998 he was head of
Power Electronics and Energy Conversion Dept., ERI. In 1990 he became a professor of
Power Electronics in ERI. He has authored more than a hundred thirty articles in the field
of modeling, analysis and control of DC, IM, SRM and PMSM. Furthermore, he has
supervised several M Sc and PhD thesis. He has also managed several projects as principal
investigator. Prof. Wahsh works part time in various Egyptian universities. He also is
acting as member in evaluating committee of university staff. He was a visiting professor
for various foreign universities. He has done a considerable amount of consulting
engineering work in Industrial Electronics .His major field of interest includes Power
Electronics, Electric Drives, Motion Control and Electrical/Hybrid Vehicles.
Dr. Yasser obtained his B.SC from Tanta university faculty of engineering, electrical power
and machine department 1999 He works at Electronics Research Institute (ERI).in Power
Electronics and energy conversion department since 2001. Dr. Yaser obtained his Msc and
PhD from Cairo University at 2006 and 2014. His major interest are :Electrical drives
control, Electric and hybrid electric vehicles modeling, simulation, and control. Modeling
and simulation of electrical systems.
Prof.Abou El-Zahab, born at 1948. He obtained his B.Sc. (Very Good with honors), M.Sc.
Electrical Engineering, Cairo University, Egypt at 1970, 1974and Ph.D. University of Paul
Sabatier, France, 1979.He appointed Teaching Assistant, 1970, Assistant Prof. 1985, and
Prof. Electrical Power and Machines Department, Cairo University 1990. He works as
visiting Professor, University of Calgary, Canada 1991, 1992, United Arab Emirates
University, UAE 1997 and 1999. Prof. Abou El-Zahab works part-time at Interdisciplinary
Engineering Program, American University in Cairo, and Professor, Petroleum Engineering
Department, 2004, 2009. His consulting engineering includes (member of Electrical
Engineering Consulting Group), Design of Lighting and Electrical Distribution System in
different industrial, commercial and institutional projects, registered: Professional
Engineer, Egypt. Principal member in the Egyptian Society and Egyptian Syndicate of
Engineers. He won prize for graduate studies research, Cairo University 1998 and 2004.

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