International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 8, August 2012)
Modelling Of Brushless DC Motor Drive Using Sensored
And Sensorless Control(back EMF zero crossing etection)
Preetha Philip1, Dr. Meenakshy K2
1
M.Tech Student, 2Associate Professor, Dept. of Electrical Engg. Govt. Engineering College, Thrissur
II. MATHEMATICAL MODEL OF BLDCM
Abstract— This paper describes the modelling and
hardware implementation of brushless DC motor drive based
on sensored and sensorless control (back Emf zero crossing
detection) algorithm. The dynamic equations of the motor are
modelled in MATLAB/SIMULINK. In addition to this, speed
PI controller block, current hysteresis controller block,
current reference block, inverter block and commutation logic
block, are modeled and the entire drive is simulated. For
sensored control, commutation logic is obtained from rotor
position detection, and for sensorless control, it is obtained
from back EMF zero crossing detection. A TMS320F28035
based sensored and sensorless BLDC drive system has been
implemented using high voltage digital motor controller kit.
Fig.2.1 shows a dynamic equivalent circuit of the
BLDC motor. For this model, the stator phase voltage
equations in the stator reference frame of the BLDC Motor
are given as in Eq. (2.1)-(2.5). The following assumptions
are made:1) the three phase windings are symmetrical, 2)
magnetic saturation is neglected, 3) hysteresis and eddy
current losses is not considered, and 4) the inherent
resistance of each of the motor windings is R ,the selfinductance is L, and the mutual inductance is M.
Keywords- BLDC, Back EMF zero crossing detection,
MATLAB, Sensored control, Sensorless control, modelling
and simulation.
I. INTRODUCTION
Household appliances are expected to be one of fastestgrowing end-product market for electric motor drivers
(EMDs) over the next few years. The major appliances
include cloth washers, room air conditioners, refrigerators,
vacuum cleaners, freezers, etc. These appliances have
traditionally relied on classic electric motor technologies
such as DC motors, single phase AC induction motors,
including split phase, capacitor-start, capacitor–run types,
and universal motors. These motors typically are operated
at constant-speed directly from main AC power without
regarding the efficiency. Consumers now demand for lower
energy costs, better performance, reduced acoustic noise,
and more convenient features. The traditional technologies
cannot meet these demands. Permanent magnet brushless
dc (PM BLDC) motors are becoming more and more
popular in various applications owing to their superior
controllability and performance.
The modelling and simulation analysis for BLDCM
based on computer engineering can effectively shorten
development cycle of position control of BLDCM drive
and evaluate rationality of the control algorithm imposed
on the system, which provides a good foundation and
method for system design and verifying novel control
strategy.
Fig 2.1 Dynamic equalent circuit
(2.1)
Where, Ua, Ub and Uc are the phase voltage of threephase windings, ia, ib and ic are the phase current, and ea,
eb and ec are the back EMF.
) 1
0° r 120°
6 r1 120° r 180°
1
180° r 300°
6 r 21 300° r 360°
Electrical power of motor can be calculated using Eq.
(2.2)
P=
+
+
(2.2)
(
Electromagnetic torque can also be expressed as Eq.
(2.3). Speed is derived from rotor position Өr as in Eq.
(2.4).
153
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 8, August 2012)
+
TABLE 3.1
Back-EMFs modeled as a normalized
function of rotor position
(2.3)
(2.4)
Theta_elec
=
(2.5)
From the above equations, BLDC motor can be
modeled.
0 – 60
III. IMPLEMENTATION OF SIMULATION MODEL IN
MATLAB/SIMULINK
60 – 120
0
0
According to the mathematical model given above, the
complete motor drive is simulated in MATLAB/
SIMULINK environment. A double-loop control scheme is
used in this system, where the outer loop is speed loop with
PI controller and the inner loop is current loop with
hysteresis controller. The entire drive is divided into
several functional blocks, which includes BLDCM body
block, speed PI controller block, current hysteresis
controller block, current reference block, inverter block and
commutation logic block. By the logical combination of
these blocks, the simulation model of BLDCM drive is
implemented.
A. Body Block
The body block of BLDCM is the core part of simulation
model for the total control system, which includes rotor
speed and torque calculation, as well as solution of the back
EMF waveform. The piecewise linear method is selected to
produce the trapezoidal back EMF waveform, which
divides one period of 0°-360° into six commutation stages.
Each running stage can be expressed by a section of line, as
shown in table 3.1. According to the signals of rotor
position and speed at any time, the running station of each
stage will be determined. Fig 3.1 shows the body block of
BLDC motor modeled in SIMULINK.
1
0
0
1
0
0
0
-1
0
0
-1
0
0
240 –300
300 –360
-1
1
0
120 –180
180 –240
-1
1
1
-1
Fig 3.1The body block of BLDCM
154
-1
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Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 8, August 2012)
B. Current Hysteresis Controller Block
The aim of this block is to achieve hysteresis current
control, in which input signals are three phase reference
currents and actual currents, and output signals act as the
control signals of inverter, as shown in Fig. 3.2.
TABLE 3.2
Relationship between reference current and rotor position
theta
Iar
Ibr
Icr
Is
-Is
0
Is
0
- Is
0
Is
-Is
- Is
Is
0
- Is
0
Is
0
- Is
Is
Fig 3.2 Current hysteresis controller block
C. Speed PI Controller Block
The speed control uses PI regulator. Its integral term has
the effects of accumulation, memorization and delay, which
enables PI controller to remove static error. The block
diagram of speed PI controller is shown in Fig.3.3. The
Saturation block limits the amplitude of three phase
reference current output to the demanding range.
Fig 3.3 Speed PI controller block
D. Current Reference Block
The action of the current reference block is to produce
three-phase reference currents depending on the signal of
current amplitude, Is, and the position signal. The output of
this block is given to the current hysteresis controller.
 Sensored Control: The rotor position is sensed for each
600, and correspondingly, reference current is generated.
Table 3.2 shows relation between the rotor position and
the three-phase reference current and Fig.3.4 shows the
switching sequence.
Fig 3.4 Reference current generation using sensored control
Fig 3.5 shows the entire BLDC
implemented in MATLAB/SIMULINK.
155
motor
drive
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Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 8, August 2012)
Back EMF zero crossing detection circuit output gives
signals similar to hall sensor signals. Thus they can be
effectively used for generating appropriate reference
current .Figure 3.7 illustrates the same.
Fig 3.7 Line voltage Eac, Phase voltage Ea, hall sensor outputs
IV. RESULTS OF MODELLING
Simulation results obtained from modelling the BLDC
motor drive using rotor position detection and by Back
EMF zero crossing detection is shown below.
A. Rotor Position Detection Technique
Plot of theta Vs. Time:
Fig 4.1 Rotor position Vs time
Fig 3.5 Reference current generation using rotor position detection
Back EMF waveforms:
Figure 4.2 shows the back EMF waveforms obtained at a
reference speed 3000 rpm at no-load using rotor position
detection. The waveforms obtained are 120 flat topped
trapezoidal, as expected from the motor model.
 Sensorless control (Back EMF zero crossing detection):
Back EMF zero crossing detection is used to generate
reference current. The output of this block is given to
current hysteresis controller block to determine the
control signals of the inverter block.
Fig 3.6 Reference current generation using back EMF zero crossing
detection algorithm
Fig 4.2 Back EMF waveform
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Torque Vs. time (for a step load of 0.15 Nm at 0.2s):
Figure 4.6 shows the plot of torque Vs. time.
Phase currents:
Figure 4.3 shows the phase current waveforms at no
load.
Fig 4.6 Torque Vs. time graph for a step load of 0.15 Nm
B. Back EMF Zero Crossing Detection Technique
Back EMF waveforms:
Figure 4.7 shows the back EMF waveforms obtained at a
reference speed of 3000 rpm, at no-load. The waveforms
obtained are 120 flat topped trapezoidal, as expected from
the motor model.
Fig 4.3 Phase currents at no-load
Speed- time plot:
The speed Vs. time graph is shown in figure 4.4.The
motor reaches the reference speed at 0.05 s.
Fig 4.4 Speed Vs time plot
Fig 4.7 Back EMF waveforms
Phase currents (for a step load of 0.15 Nm at 0.2s):
Figure 4.5 shows the waveforms of the three phase
currents when a load of 0.15Nm is applied at 0.2 s
Phase currents:
Figure 4.8 shows the phase current waveforms at no
load.
Fig 4.8 Phase currents at no-load
Fig 4.5 Phase currents for a step load of 0.15 Nm
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Speed- time plot:
The speed Vs. time graph is shown in figure 4.9.The
motor reaches the reference speed at 0.05 s
V. HARDWARE IMPLEMENTATION AND RESULTS
For validating the simulation studies, hardware has to be
set up for the proposed methods. Circuit implementation
consists of two sections, the control circuit and the power
circuit. Control circuit comprises of the microcontroller
TMS320F28035, which acts as Commutation sequencer,
regulated DC power supply for microcontroller and driver
circuit. Power circuit comprises of a 160V DC supply,
three phase bridge inverter and BLDC motor. A High
Voltage Digital Motor Control kit, TMDSHVMTRPFCKIT
is used to implement the hardware of sensored and
sensorless control of brushless DC motor.
A. Hardware Implementation Of Sensored Control
Circuit overview:
The figure 5.1 shows the schematic diagram of the
experimental set up of BLDC motor drive with sensored
control.
Fig 4.9 Speed Vs time plot
Phase currents (for a step load torque of 0.15 Nm at 0.2s):
Figure 4.10 shows the waveforms of the three phase
currents when a load of 0.15Nm is applied at 0.2 s.
Fig 4.10 Phase currents for a step load of 0.15 Nm
The parameters of the motor used for modelling are
given in Table 3.3
TABLE 3.3
The parameters of BLDC motor
Stator resistance (Rs)
11 ohm
Stator inductance (Ls)
33.5mH
Back EMF constant
37.8V/Krpm
Torque constant
43.4 oz-in/A
No-load current
0.2 A
Fig 5.1 Schematic diagram of experimental setup (sensored control)
Flow chart:
Program mainly consists of two loops, the main loop and
the ISR loop. In the main loop, all the peripherals used in
BLDCM control, are initialized. The ISR loop is executed
when the enable flag is set high. The flow chart for the
sensored control is shown in figure 5.2.
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3L 3H
 Back EMF waveform (obtained in ccs4 at a speed of 746
rpm)
Fig 5.2 Flow chart for sensored control
 MOD 6 counter output (obtained in ccs4 at a speed of
746 rpm)
Hardware results for sensored control:
 Gate pulses: 1L 1H
2L 2H
 Hall sensor outputs
HALL A
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HALL B
B. Hardware Implementation Of Sensorless Control (Back
EMF Zero Crossing Algorithm)
Circuit overview: The figure 5.3 shows the schematic
diagram of the experimental set up of BLDC motor drive
with sensorless control.
HALL C
 Back EMF waveform Ea( obtained at a speed of 2400
rpm)
Back EMF waveform Ea
Fig.5.3 Schematic diagram of experimental setup for sensorless
control
Flow chart: Program mainly consists of two loops, the
main loop and the ISR loop. In the main loop, all the
peripherals used in BLDCM control, are initialized. The
ISR loop is executed when the enable flag is set high. The
flow chart for the sensorless control is shown in figure 5.4
Back EMF waveform Eb
Fig 5.4 Flow chart for sensorless control
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Hardware results for sensorless control:
 Gate pulses:
1L 1H
Eb
Ec
2L 2H
VI. CONCLUSION
Based on the mathematical model of the BLDCM, the
modelling and simulation, for the specified motor is
presented in this paper. The simulation results satisfy the
theoretical analysis. The control system is found to operate
stably and has the fairly good dynamic and static
characteristics. Using this simulation model built for
BLDCM, advanced control algorithms can be verified
conveniently. Through the modularization design, a lot of
time can be saved and the design efficiency can also be
improved significantly.
3L 3H
REFERENCES
 Back EMF waveform (obtained at reference speed- 2400
rpm)
Ea
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