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International Journal of Advanced Engineering Research and Technology (IJAERT) Volume 4 Issue 1, January 2016, ISSN No.: 2348 – 8190
4
www.ijaert.org
Speed Control of PMBLDC motor using Fuzzy Logic Controller with
Sensorless Technique
Mohammad Zaid1, Mohammad Ayyub
2
1,2Department of Electrical Engineering, Zakir Hussain College of Engineering & Technology, Aligarh Muslim
University – Uttar Pradesh, India
Abstract Recent advances in the field of power electronics have
made PMBLDC motors very popular. They are being
used in host of applications because they posses
certain desirable features as compared to brushed DC
motor and servo motors. This paper presents speed
control of PMBLDC motor using Fuzzy logic
controller with sensorless operation of motor. The
simulation is carried out in MATLAB/SIMULINK
platform. The simulation result compares the
performance of Fuzzy Logic Controller with PI
controller.
Keywords: Fuzzy logic controller, PMBLDC motor, PI
controller, DC motor.
I. INTRODUCTION The first electronically commutated brushless DC
motor was developed with the help of Hall elements
in1962 [11], since then tremendous development has
been made in the field of power electronics and
permanent magnet materials. Today PMBLDC motor
is used in many applications from aerospace,
automobile industry to household appliances. The
PMBLDC motor posses certain desirable features such
as high efficiency, high power factor, lower
maintenance, precise and accurate control and high
power density. The PMBLDC motor generally has a
trapezoidal back emf which is different as compared
with PMSM which has a sinusoidal back EMF. The
PMBLDC motor is developed on the basis of brushed
DC motors, but unlike brushed DC motors the
commutation is electronically controlled and Hall
sensors are used for sensing the rotor position. The
output of Hall sensors are used for generation of
switching signals for the inverter. Hall sensors are
costly and less reliable especially in space application.
Due to these reasons various sensorless techniques
have been developed. Each of the sensorless
techniques employed have their own advantages and
disadvantages. These sensorless techniques are used to
detect the rotor position of the motor indirectly. Most
popular and widely used technique is back emf
detection using line voltage difference method.
Actually in any sensorless scheme we need to identify
exact commutation instants for the generation of
virtual Hall signals, in the scheme using difference of
line voltage the difference of two line voltages gives
the back emf of any one phase. The zero crossing
instants of that phase emf waveform gives the
approximate commutation instants of the current of
that phase. The zero crossing instants need to be phase
shifted to get the exact commutation point. A low pass
filter generally introduces the delay required for the
operation. Most of the back emf detection techniques
suffer from serious drawback that at low speeds it is
difficult to detect the back emf, hence some starting
methods needs to be employed before motor
accelerates to minimum threshold speed. Another
improved method for detection of rotor position is the
utilization of third harmonic component in the EMF
waveform of the motor. The voltage between the
artificial neutral and motor neutral gives the third
harmonic voltage component which contains the
information about the zero crossing instants of back
EMFs of the three phases. It can be shown that [9] this
voltage between the two neutrals is numerically equal
to mean of three EMFs. Zero crossings of third
harmonic voltage when properly processed
corresponds to exact commutation instants which is
needed for proper switching of inverter. In most of the
cases motor neutral is not accessible hence midpoint of
DC link can also be used for generation of third
harmonic voltage [9], but this signal is more noisy as
compared to the previous signal obtained between the
two neutrals.
In this paper we have employed sensorless technique
based on the line voltage difference method. We have
also used Fuzzy logic based controller for speed
control of motor. For comparison we have used a PI
controller and then fuzzy logic based controller. The
problem with conventional controllers comes when
either plant structure is unknown or if known is so
complex that design of controller by classical approach
would be impractical and cumbersome. The other
problem comes when model of a system is highly non
linear or rate of parameter change of plant is extremely
high. Fuzzy controllers perform very well in the
situations described above because by using FLC we
need not to know the plant structure and also by time
needed for design of controller may be significantly
shortened. However performance improvement using
FLC will depend on tuning and choosing a appropriate
rule base for FLC.
International Journal of Advanced Engineering Research and Technology (IJAERT) Volume 4 Issue 1, January 2016, ISSN No.: 2348 – 8190
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II. SYSTEM CONFIGURATION Consider a star connected PMBLDC motor whose
stator is star connected. The motor stator is fed by a
three phase inverter which is operated in 1200
mode.
Only two phase conduct at a time and third phase is
floating. The switches are triggered utilizing the exact
rotor position of the motor .Figure 1 shows the overall
system configuration of the drive system. The speed
controller used can be a PI controller or a Fuzzy logic
controller. The control loop has outer speed controller
and inner current controller. Table 1 gives details of
PMBLDC motor specifications.
Fig.1 Overall PMBLDC motor drive
Table 1 The PMBLDC motor specifications
III. BACK EMF ZERO CROSSING
ESTIMATION In this method the zero crossing point of back emf is
estimated using the difference in line voltage.Zero
crossing points will give us the virtual hall signals
needed for the proper switching of the inverter
switches. Consider the voltage of phase a of the motor
with respect to neutral point as
Van= Ria + (L-M) ia +Ea (1)
Similar equations can be written for phase b and c .
Vbn= Rib + (L-M) ib +Eb (2)
Vcn= Ric + (L-M) ic +Ec (3)
From these equations line to line voltages can be found
Vab = R(ia-ib) + L (ia-ib) +ean-ebn (4)
Vbc= R(ib-ic) + L (ib-ic) +ebn-ecn (5)
Vca=R(ic-ia) +L (ic-ia) +ecn-ean (6)
Now to find the difference in line voltage subtract
equation five from four. No neutral point is required
for estimation of line voltages.
Vabbc= R(ia-2ib +ic) + L (ia-2ib+ic) + ean -2ebn+ecn (7)
Now consider a situation in which phase a and phase c
is conducting and phase b is open. In this situation ean
= -ecn. Therefore, in that interval (7) may be simplified
as
Vabbc= ean-2ebn+ecn = -2ebn (8)
The above result shows that the difference in line
voltage Vabbc gives the inverted and magnified
waveform of back emf of phase b. Similarly Vbcca and
Vcaab gives the inverted and magnified back emf wave
forms of phase c and a. The above derivation shows
that zero crossing of back emf can be estimated
indirectly by proper processing of three stator voltages.
A low pass filter is generally used for removing the
high frequency components present in the derived back
emf waveform. The other advantage we get by using
low pass filter is that sufficient amount of delay is
produced which gives exact commutation instants for
the generation of virtual hall signal.
IV. IMPLEMENTATION OF FUZZY
LOGIC BASED SPEED CONTROLLER The FLC scheme observes the pattern of the speed
loop error and correspondingly updates the output of
the controller to match the actual speed with the
reference speed. The triangular membership function
with 5 linguistic variables and 25 rules are used in the
FLC design. We have chosen a linear rule base which
is widely accepted with triangular membership
functions. All membership functions (MF’s) for
controller inputs, i.e., error (e) and change of error
(Δe) incremental change in controller output Δu for PI-
type FLC are defined on common interval [-1,1]. Each
of the rules of FLC is characterized with an IF part
called antecedent and then part called consequent. We
have taken three scaling factors namely Ke, Kce and
Kdu. These scaling factors are very important for
tuning of FLC because once membership functions
along with rule base are defined they cannot be
changed every time. Hence to get the optimal response
we have to tune these scaling factors until we get the
Parameters Symbol Value Units
Resistance R 2.875 Ohms
Inductance L 2.7 mH
Back-emf-
constant
ke 0.42 V/rad/s
Torque
constant
kt 0.042 N-m/A
Viscous
Damping
B 0.000089 N-
m/(rad/s)
Rotor
Inertia
J 0.0005 Kg-m2
Number of
Poles
P 4 -
International Journal of Advanced Engineering Research and Technology (IJAERT) Volume 4 Issue 1, January 2016, ISSN No.: 2348 – 8190
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desired response. However every Fuzzy controller
design should tend to solve a control problem with a
minimal number of Fuzzy sets. If by succeeding to
solve a problem with a 5*5 Fuzzy rule base rather than
a 7*7 Fuzzy rule base, the processing of 25 instead of
49 rules will save a lot of computing time.
We have chosen 25 rule base system. Also it may seem
that a larger number of Fuzzy sets will result in a better
designed controller, practical experience has proven
that the number of Fuzzy sets involved is not so
important. The 25 rules along with their meaning used
in Table 2 gives Fuzzy inference system. Table 3 gives
meaning of linguistic variables of Fuzzy inference
system.
Table 2: Rule table for Fuzzy inference system
Table 3: Meaning of linguistic variables in Fuzzy
inference system
NVB Negative very big
NB Negative big
NM Negative medium
NS Negative small
Z Zero
PS Positive small
PM Positive medium
PB Positive big
PVB Positive very big
e Speed error
ce Change in speed error
Above rule base in words can be defined as “IF e is
NB and ce NB then Δu(output change) is NVB”.
Figure 2 and 3 shows the membership functions of
error and change in error in speed. Figure 4 shows the
overall design of Fuzzy logic controller with scaling
factors.
Fig.2 Membership function for input variable “e”
Fig.3 Membership function for input variable “ce”
Fig.4 Fuzzy Logic based speed controller
Figure 5 and 6 shows the membership function of
output variable and relationship between input and
output variables.
Fig.5 Membership function for input variable “e”
Fig.6 Surface showing relationship between e, ce and
Δu based on rule base
International Journal of Advanced Engineering Research and Technology (IJAERT) Volume 4 Issue 1, January 2016, ISSN No.: 2348 – 8190
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Figure 7 shows the modelling of back emf waveform
using look up tables.
Fig.7 Modelling of back emf’s
V. SIMULATION RESULTS AND
DISCUSSION
The performance of the developed PMBLDC motor is
simulated in Simulink. Simulation results of motor
speed, current and emf along with PWM signals are
obtained. Figure 8 shows Simulink based model of
PMBLDC motor drive system.
Fig. 8 PMBLDC motor model with PI and FLC based
speed controller
The motor is first started with sensors and is then
switched over to sensorless control at 200ms. The
main problem in this method is detecting the actual
zero crossing because of the spikes present in the
voltage, hence an appropriate filter design is necessary.
The other problem is to determine the instant when the
control is shifted from sensor control to sensorless
control, practically this is done by first exciting two
phases out of three for a predetermined duration called
prepositioning time, which may be fixed on the inertia
of motor and its load capability. At the end of the
predetermined period motor have moved from an
unknown position to a predetermined position. Figure
9 shows the line voltage difference Vabbc which gives
zero crossing for back EMF of phase a. Figure 10
shows the zero crossing estimated by difference in line
voltage method. Filtering helps in acquiring accurate
commutation instants. Exact commutation instant will
be 30 degree phase shifted from zero crossing point
The exact commutation instants are being shown in
figure 11. A low pass second order filter with cut off
frequency of 24 Hertz is being used for filtering. From
the above figure it can concluded that zero crossing
estimated by difference of line voltage is the real
commutation instant which we require for generation
of virtual hall signal. Figure 12 and 13 gives
comparison between real hall signal originally
generated by sensors and virtual hall signals generated
by detecting exact commutation instants, both signals
should exactly match for satisfactory operation of
motor in sensorless control.
Fig.9 Line Voltage difference Vabbc
Fig. 10 Estimation of ZCP of phase b from line voltage
difference Vabbc
International Journal of Advanced Engineering Research and Technology (IJAERT) Volume 4 Issue 1, January 2016, ISSN No.: 2348 – 8190
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Fig. 11 Estimation of ZCP of phase b from filtered line
voltage difference Vabbc
Fig.12 Virtual hall signal b
Fig.13 Real hall signal b
Figure 14 shows the motor position in radians in
sensorless control.
Fig.14 Rotor position in radians
The performance of PI controller with sensorless
control is evaluated in this section. Load torque is
applied at 0.2 seconds. From figure 15 and 16 it can be
seen that there is a significant reduction in set point
speed with application of load torque. Speed is reduced
to 194 rad/s from set point speed of 200 rad/s. Motor
speed again reaches set point speed after significant
delay of 0.3 seconds.
Fig. 15 Speed response with PI controller (Tl=1Nm)
Fig. 16 Speed response with PI controller (Tl=1Nm)
Fuzzy Logic controller with sensorless control is
employed here. The load torque of 1Nm is applied at
t=0.2 second, similar to what we have done with PI
controller .The speed response in figure 17 shows that
there is almost no reduction in speed of the motor
when load torque is applied at t=0.2 second which
shows the superiority of fuzzy logic controller if
properly tuned over PI controller. It can be seen from
figure 18 that the reduction in speed after application
of load torque is less than 1 rad/s, and motor gets back
to set point speed almost instantaneously. This is great
improvement over PI controller which takes almost 0.3
seconds to get back at same speed reference for same
amount of load torque applied. Figure 19 shows the
speed response of motor using fuzzy logic controller
when step change in reference speed is made .
Fig. 17 Speed response with FLC (Tl=1Nm)
International Journal of Advanced Engineering Research and Technology (IJAERT) Volume 4 Issue 1, January 2016, ISSN No.: 2348 – 8190
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Fig. 18 Speed response with PI controller (Tl=1Nm)
Fig.19 Set point speed increased from 200 rad/s to 300
rad/s with FLC.
The trapezoidal waveform of back emf of phase a and
current of phase a is shown in figure 20 and 21.
Fig.20 Back emf phase a
Fig.21 current phase a
VI. CONCLUSION A detailed Simulink model of PMBLDC motor with
and without Hall sensors has been developed and its
speed is controlled by using both Fuzzy logic and PI
controller Motor is found to be running smoothly in
sensorless operation and all the waveforms i.e. motor
phase currents, back Emf, rotor position has been
obtained from Simulink model. Speed control using
both Fuzzy controller and PI controller has been done.
The use of Fuzzy controller has generally reduced the
rise time and settling time of the speed response of the
motor. Hence a tuned Fuzzy controller has
outperformed conventional PI controller. However the
main advantage of using Hall sensors is that motor
design remains simple, and no extra circuitry is
needed.
REFERENCES [1] George K. I. Mann, Bao-Gang Hu and G. Gosine
“Analysis of Direct Action Fuzzy PID Controller
Structures”, IEEE TRANSACTIONS ON SYSTEMS, MAN,
AND CYBERNETICS—PART B: CYBERNETICS, VOL. 29,
NO. 3, JUNE 1999.
[2] Rajani K. Mudi and Nikhil R. Pal, “A Robust Self-
Tuning Scheme for PI- and PD-Type Fuzzy Controllers”,
IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 7, NO.
1, FEBRUARY 1999.
[3] Ming-Fa Tsai, Tran Phu Quy, Bo-Feng Wu, and Chung-
Shi Tseng ,” Model Construction and Verification of a
BLDC Motor Using MATLAB/SIMULINK and FPGA
Control,”IEEE Conference Publications Singapore,2011.
[4] E.Kaliappan, C.Chellamuthu, Modeling, simulation and
experimental analysis of permanent magnet brushless DC
motors for sensorless operation” Archives of Electrical
Engg.Vol.61,2012
[5]. Paul P. Acarnley and John F. Watson, Review of
Position sensorless operation of Brushless Permanent
Magnet machines, IEEE Transactions on Industrial
Electronics, VOL. 53, NO. 2, APRIL 2006.
[6]. Kim D.K., Lee K.W., Kwon B.I., Commutation torque
ripple reduction in a position sensorless brushless DC motor
drive. IEEE Trans. Power Electron. 21(6): 1762 1768
(2006).
[7] Aakanksha Girolkar and G. Bhuvaneswari, Control of
PMBLDC Motor Using Third harmonic back emf sensing
with zigzag transformer, IEEE Conference Publications
,2013.
[8] J.C Moriera, Indirect Sensing of rotor flux position of
permanent magnet AC motor operation over a wide speed
range; IEEE Trans. Ind. Appl., vol. 32,no.6,pp 1394-
1401,Nov/Dec 1996.
[9] J.P.Johnson, M.Ehsani and Yilcan Guzelgunler, “Review
of Sensorless Methods For Brushless DC”, IA Conference,
1999. Thirty Fourth IAS Annual Meeting Conference
Record of the 1999 IEEE, Vol.1, October 1999, pp. 143-
150.
[10] N. Matsui, “Sensorless permanent magnet brushless DC
and synchronous drives”, in Proc. Electro motion 3,1996,
pp. 172-180.
[11] Chang Liang Xia, Permanent Magnet Brushless DC
Motor Drives and Controls, Wiley Press, Beijing, 2012.
[12] Chetan K. Lad, R. Chudamani, Sensorless Brushless
DC Motor Drive based on Commutation instants derived
from the Line Voltages and Line Voltage Differences, 2013
Annual IEEE India Conference (INDICON)
[14] J. X. Shen, Member, Z. Q. Zhu, Sensorless Flux-
Weakening Control of Permanent-Magnet Brushless
Machines Using Third Harmonic Back EMF, IEEE
TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL.
38, NO. 4, NOVEMBER/DECEMBER 2004.