Research Journal of Applied Sciences, Engineering and Technology 3(4): 284-289, 2011
ISSN: 2040-7467
© Maxwell Scientific Organization, 2011
Received: February 14, 2011
Accepted: March 15, 2011
Published: April 20, 2011
Modelling and Simulation of Closed Loop Controlled Buck Converter
Fed Pmbldc Drive System
1
S. Prakash and 2R. Dhanasekaran
1
Research Scholar, E.E.E Department, SathyabamaUniveristy, Chennai, Tamilnadu, India
2
Syed Ammal Engineering College, Ramanathapuram, Tamilnadu, India
Abstract: Permanent Magnet Brushless DC Motor (PMBLDC) is one of the best electrical drives that has
increasing popularity, due to their high efficiency, reliability, good dynamic response and very low
maintenance. This makes the interest of modeling an ideal PMBLDC motor and it’s associated Drive System
in simple and lucid manner. In this paper the drive system is proposed with a buck converter topology. It has
the advantages of reduced switching losses, low inductor power loss, reduced ripple by using a pi-filter, which
in turn makes the DC link voltage to be stable. The modeling and simulation of the PMBLDC motor is done
using the software package MATLAB/SIMULINK. The operation principle of the buck converter is analyzed
and the simulation results are presented in this paper to verify the theoretical analysis.
Key words: Converter, drive, filters, Permanent Magnet Brushless DC Motor (PMBLDC)
electronic commutation is used. Having the armature on
the stator makes it easy to conduct heat away from the
windings, and if desired, having cooling arrangement for
the armature windings is much easier as compared to a
DC motor. A BLDC is a modified PMSM with the
modification being that the back-emf is trapezoidal
instead of being sinusoidal as in the case of PMSM (Luk
and Lee, 1994). The position of the rotor can be sensed by
hall effect position sensors, namely Hall_A, Hall_B, and
Hall_C, each having a lag of 120º w.r.t the earlier one.
Three Hall position sensors are used to determine the
position of the rotor field. Model of a BLDC motor Since
a BLDC motor is easy to control, it is the motor of choice
in many applications requiring precise control of speed
(AtefSalehOthman and Al-Mashakbeh, 2009), (ByoungKukLee et al., 2001). The BLDC motor model is
explained as, the electromagnetic torque, Tem is linearly
proportional to the armature current ia. i.e., Tem = KT ia,
where KT is the torque constant.
The back-emf in a BLDC motor is linearly
proportional to the rotational speed of the shaft. The backemf is proportional to the speed of the motor and its
direction is given by Flemings right hand rule.
Considering that in a magnetic field of intensity B, a
conductor of length l on the edge of rotor of radius r is
rotating at an angular velocity of radians per second. Then
the speed of the conductor is given by:
INTRODUCTION
Permanent magnet brushless DC (BLDC) motor is
increasingly used in automotive, industrial, and household
products because of its high efficiency, high torque, ease
of control, and lower maintenance (Krishnan, 2003;
Krishnan and Shiyoung, 1997). A BLDC motor is
designed to utilize the trapezoidal back EMF with square
wave currents to generate the constant torque. A
conventional BLDC motor drive is generally implemented
via a six-switch, three phase inverter (Rahul et al., 2003)
and three Hall-effect position sensors that provide six
commutation points for each electrical cycle. Cost
minimization is the key factor in an especially fractional
horse-power BLDC motor drive for Home applications. It
is usually achieved by elimination of the drive
components such as power switches and sensors.
Therefore effective algorithms should be designed for the
desired performance and the relevant drive system which
in turn controls the motor for all its defined applications
with high efficiency, as well as good in maintaining the
speed for variable torque. The mathematical modeling of
DC to DC converter is given by (Luo, and Ye, 2005;
Muo, 2004). The objective of the preset work is to model
and simulate buck converter fed PMBLDC drive.
PMBLDC motor: The brushless DC motor is actually a
permanent magnet AC motor whose torque-current
characteristics mimic the DC motor. Instead of
commutating the armature current using brushes,
vel = T x r
Corresponding Author: S. Prakash, Research Scholar, E.E.E Department, SathyabamaUniveristy, Chennai, Tamilnadu, India
284
Res. J. Appl. Sci. Eng. Technol., 3(4): 284-289, 2011
The emf e generated in that conductor is given by:
⎛ v a ⎞ ⎛ Ra
⎜ ⎟ ⎜
⎜ vb ⎟ = ⎜ 0
⎜ ⎟ ⎜
⎝ vc ⎠ ⎝ 0
e = T rBl
Conventionally the number of conductors in an electrical
machine is given by Z, and if the number of conductors in
series is Z/2, the series back-emf is given by e as:
⎛ Lp
⎜
⎜M
⎜
⎝M
e = T mrBl (Z/2)
In terms of the magnetic flux:
d
dt
Lba
Lb
Lbc
d
dt
⎛ i a ⎞ ⎛ ea ⎞
⎜ ⎟ ⎜ ⎟
⎜ i b ⎟ + ⎜ eb ⎟
⎜ ⎟ ⎜ ⎟
⎝ i c ⎠ ⎝ ec ⎠
0
Rb
0
0 ⎞ ⎛ ia ⎞
⎟⎜ ⎟
0 ⎟ ⎜ ib ⎟ +
⎟⎜ ⎟
Rc ⎠ ⎝ ic ⎠
0
Lp − M
0
⎞ ⎛ ia ⎞ ⎛ ea ⎞
⎟ d ⎜ ⎟⎜ ⎟
⎟ dt ⎜ ib ⎟ ⎜ eb ⎟
⎟ ⎜ ⎟⎜ ⎟
Lp − M ⎠ ⎝ ic ⎠ ⎝ ec ⎠
0
0
Rearranging the equations, we have obtained equations in
a form suitable for simulation. PMBLDC motor with new
power converter topology is given by Krishnan and
Shiyoung (1997). Four switch three phase brushless motor
for low cost commercial applications is given by Lee
(2003). The above literature does not deal with Modelling
and Simulation of Buck Converter fed PMBLDC drive.
This study proposes buck converter for PMBLDC Drive.
Considering all the three phases following equations are
used to model the two pole three phase BLDC motor.
⎡⎛ La
⎢⎜
⎢⎜ Lab
⎢⎜⎝ Lac
⎣
M
⎛ Lp − M
⎜
⎜ 0
⎜
⎝ 0
ia+ib+ic = 0
ia+ib = - ic
0 ⎞ ⎛ ia ⎞
⎟⎜ ⎟
0 ⎟ ⎜ ib ⎟ +
⎟⎜ ⎟
Rc ⎠ ⎝ ic ⎠
0
M⎞
⎟
M⎟
⎟
Lp⎠
M
Lp
⎛ va ⎞ ⎛ Ra
⎜ ⎟ ⎜
⎜ vb ⎟ = ⎜ 0
⎜ ⎟ ⎜
⎝ vc ⎠ ⎝ 0
where, KE is the back emf constant.
The model of a BLDC consisting of three phases is
explained by means of equations, since there is no neutral
used, the sum of the three phase currents must add upto
zero, i.e.,
0
Rb
0
0 ⎞ ⎛ ia ⎞
⎟⎜ ⎟
0 ⎟ ⎜ ib ⎟ +
⎟⎜ ⎟
Rc ⎠ ⎝ i c ⎠
From above two equations we get:
e = Ke Tm
⎛ va ⎞ ⎛ Ra
⎜ ⎟ ⎜
⎜ vb ⎟ = ⎜ 0
⎜ ⎟ ⎜
⎝ vc ⎠ ⎝ 0
0
Rb
Lca ⎞ ⎛ ia ⎞ ⎤ ⎛ ea ⎞
⎟⎜ ⎟⎥ ⎜ ⎟
Lcb ⎟ ⎜ ib ⎟ ⎥ + ⎜ eb ⎟
⎟⎜ ⎟ ⎜ ⎟
Lc ⎠ ⎝ ic ⎠ ⎥⎦ ⎝ ec ⎠
SIMULATION RESULTS
Closed loop system is simulated using Matlab
Simulink. The Simulink model of closed loop controlled
buck converter inverter fed PMBLDC drive which shown
in Fig. 1a. Here 48V DC is stepped down to 24V DC
using a buck converter. The output of buck converter is
filtered using pi-filter. The output of the pi-filter is applied
to the three phase inverter, the inverter produces three
phase voltage required by the PMBLDC motor. The
technical specifications of the drive systems are as
follows:
If the permanent magnet inducing the rotor field ios in the
shape of an arc, it requires that the inductances be
independent of the rotor position, hence:
La = Lb = Lc = Lp
Considering the symmetry of the above matrix in addition
to independence w.r.t the rotor position:
Input voltage: 48 V DC
Buck output voltage: 24 V DC
Pulse width to Buck MOSFET: 0.5 duty cycle (50%)
Toff : 50%
Pulse width (33%) to Inverter MOSFET: 120° mode of
operation.
Lab = Lba = Lbc = Lcb = Lca = Lac = M
Above equation reduces to:
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Res. J. Appl. Sci. Eng. Technol., 3(4): 284-289, 2011
Voltage
Fig. 1a: Simulink diagram of closed loop system
Time
Fig. 1b: Triggering pulses
Parameters of BLDC motor:
The inverter is a MOSFET bridge:
Stator resistance Rs
: 2.8750 ohms
Stator Inductance Ls
: 8.5e-3 Henrys
Flux induced by magnets
: 0.175 Weber's
Back EMF Flat area
: 120 degrees
Inertia
: 0.8x10G3
Friction factor
: 1x10G3
Pole pairs
: 4
Stator windings are connected in star to an internal neutral
point.
The actual speed is measured and it is compared with
the reference speed, the error is given to the PI Controller,
the output of the PI controller is one of the inputs to the
comparator. The other input is high frequency triangular
wave. The output of the comparator controls the pulse
width applied to the buck MOSFET. The pulses given to
the MOSFETS 1, 3 and 5 are shown in Fig. 1b.
286
Voltage
Res. J. Appl. Sci. Eng. Technol., 3(4): 284-289, 2011
Time
Voltage
Fig. 1c: DC input voltage
Time
Current
Fig. 1d: Phase voltages of inverter
Time
Fig. 1e: Output currents of inverter
287
Voltage
Res. J. Appl. Sci. Eng. Technol., 3(4): 284-289, 2011
Time
Speed
Fig. 1f: Back EMF waveforms
Time
Fig. 1g: Rotor speed in rpm
D.C. input voltage is shown in Fig. 1c and its value
is 48 volts. Phase voltages of the three phase inverter are
shown in Fig. 1d. The voltages are displaced by 120º.
Three phase currents drawn by the motor are shown in
Fig. 1e. The back emfs in the three phases are shown in
Fig. 1f. The response of speed is shown in Fig. 1g. The
speed settles at 130 rpm, which is equal to the set value.
Fig. 1c: DC input voltage
reduce the input voltage to the required value. Pi-filter is
proposed at the output of the buck converter to reduce the
ripple. This drive system has advantages like reduced
number of switches and improved response. The scope of
this paper is modeling and simulation of closed loop
controlled PMBLDC drive system. The hardware
implementation is yet to be done. The contribution of
authors is the development of new simulink model for
buck converter fed PMBLDC motor drive.
CONCLUSION
ACKNOWLEDGMENT
Closed loop controlled PMBLDC drive system is
modeled and simulated using MATLAB/SIMULINK and
the results are presented. Buck converter is proposed to
The experiment was conducted in power electronics
laboratory, Sathyabama University. The authors would
288
Res. J. Appl. Sci. Eng. Technol., 3(4): 284-289, 2011
like to thank Head of the Department, Electrical
Department, Sathyabama University for providing the
facilities.
Luk, P.C.K. and C.K. Lee, 1994. Efficient modeling for
a brushless DC motor Drive. 20th International
conference on Industrial Electronics, Control and
Instrumentation, IECON'94, 1: 188-191.
Luo, F.L. and H. Ye, 2005. Energy Factor and
Mathematical modeling for power dc-dc converters.
Proc. Inst. Elect. Eng., 152(2): 191-198.
Muo, E.L., 2004. Mathematical modelling for power dcdc converters. IEEE International Conference.
Powercon’04, Singapore, pp: 323-328.
Rahul, K., S.M. Madani, H. Masoud and A.T. Hamid,
2003. A low cost BLDC motor drive using buckboost converter for residential and commercial
Applications. IEEE International Conference on
Electric Machines and Drives, IEMDC’03, 2:
1251-1257.
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