Sensorless Drive of Permanent Magnet Brushless
DC Motor with 180 Degree Commutation
Boyang Hu, Student Member, IEEE and Swamidoss Sathiakumar, Member, IEEE
School of Electrical and Information Engineering
The University of Sydney
Sydney, NSW, Australia
E-mail: boyang@ee.usyd.edu.au
Abstract—The three-phase wye connected permanent magnet
brushless dc motor is conventionally driven by 120 degree
commutation. Two phases are conducting current and the
other one is always floating without any torque produced in
each conduction interval. Rather than the conventional 120
degree drive, all three phases of 180 degree commutation are
expected to conduct current in all sectors, which results in
more power delivered from inverter side to the motor side for
the same power supply voltage. In this paper, a recently
proposed sensorless algorithm is highlighted with well
performance in low speed operation. Based on dSPACE,
comparison of different dynamic conditions between 120 and
180 degree commutation is presented and analyzed
comprehensively. Extensive experiment tests show excellent
results on dynamic performance of 180 degree commutation,
which matches the simulation results from Simulink/Matlab.
180 degree commutation is verified to work properly with the
ability to deliver more power when compared with
conventional 120 degree commutation.
Keywords—brushless dc motor; sensorless drive; low
speed;120/180 degree commutation;
I.
INTRODUCTION
Permanent magnet brushless dc motors (BLDCM) with
trapezoidal back electromotive force (EMF) are being
increasingly used in last two decades. The latest advances in
permanent magnet materials, solid-state devices and microelectronics have contributed to new energy efficient electric
drives for BLDCM drive [1]. The Advantages of BLDC
motor are with higher efficiency, higher power to weight
ratio, higher torque to current ratio, faster dynamic response,
less maintenance, better power factor and better output
power per unit mass and volume, rather than conventional
motors. Two forms of permanent magnet AC motors are
commonly used in industrial drives, which are permanent
magnet synchronous motor(PMSM) and brushless dc
motor(BLDCM). PMSM is with sinusoidal back-EMF
waveform and BLDCM is with trapezoidal waveform. Due
to the absence of brushes and field windings, BLDCM has
many inherent advantages, compared to PMSM, such as
higher speed capability, larger application range from low
speed to high speed, higher power density and so on [2]. To
produce a constant electric torque, BLDCM is considered
c
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IEEE
with rectangular phase current energized, which is to be in
phase with back-EMF signals.
It is well known that sensors have many limitations in
less accessible location environment. It is necessary to
eliminate the unreliable and costly position sensors by using
sensorless methods. The previous sensorless methods for
brushless dc motors are reviewed in the literature [3]-[8]. In
summary, sensorless methods are to find the accurate rotor
position information for energizing three phase windings by
using algebraic manipulations, back-EMF signals, sensorless
starting techniques or other novel techniques. Rotor position
estimation techniques are grouped into the following four
categories [2]:
1. Detection of back-EMF, which can be further
categorized into the following approaches:
a) Zero-crossing approach,
b) Phase locked loop technique,
c) Back-EMF integration approach
2. Detection of stator third harmonic voltage
3. Detection of conducting interval of free-wheeling
diodes connected in anti-parallel with the solid-state
switches
4. Monitoring the inductance variation of d-q axes (PMSM)
Two Main drawbacks must be considered about backEMF zero-crossing approach. First of all, when motor is at
standstill or very low speed operation, back-EMF is not
possible to be obtained. The other disadvantage is that zerocrossing instant is with 30 degree shift from the commutation
instant. Refer to Fig. 1, there is always a 30 electrical degree
shift between the back-EMF zero-crossing instant and the
commutation instant. In the case of dynamic performance
when motor speed is variable during this offset time, position
would not be accurately estimated. To solve these two
problems, a novel sensorless speed and position estimation
method [9] is recently proposed, which is successfully
presented in theory and simulation, however, due to very
limited experiment results, dynamic conditions are still not
shown properly.
BLDCM is conventional driven with 120-degree
commutation, which is two phases “on” and the other phase
floating, which is shown in Fig. 2. Due to the reason that
torque production is almost directly proportional to the
106
phase current [10], the floating phase doesn’t produce any
torque. As shown in Fig. 3, all the three phase are “on” in
each conduction intervals of 180-degree. The 180-degree
commutation can generate larger output torque than 120degree for the same given power supply, which has been
investigated in [11] and [12].
In this paper, a novel 180-degree sensorless system is
proposed based on the sensorless algorithm [9]. The speed
and position are obtained based on the estimated back-EMF
signals which are calculated by simply measuring the threephase currents and three-stator terminal voltages. The
proposed 180-degree sensorless system works well in both
directions. PWM mode is applied for the proposed 180degree sensorless system with satisfactory implementation
results. The comparisons between the conventional 120degree and the proposed 180-degree sensorless system are
fully addressed. The validity of the proposed system is
verified through both simulation and implementation.
II.
PRINCIPLE OF OPERATION
A. Switch Sequences
Figure 1: Three phase back-EMF and activation phase voltage of 120degree commutation.
For the conventional 120-degree sensorless commutation
of BLDCM, the winding without phase current in each
conduction interval can be considered as a sensor for backEFM detection. However, for the 180-degree commutation,
due to all the three phases conduct current all the time in
each conduction intervals without floating, there are no
back-EMF available in stator terminals. The conventional
back-EMF detection methods cannot be applied to 180degree commutation. The speed and position can be
estimated from the estimated back-EMFs, which are
calculated by simply sensing the terminal voltages and
phase currents.
Even though the sensorless drive with 180-degree
commutation works properly in theory and simulation
environment [12], experimental implementation has never
been successfully addressed. Experiment verification of
BLDCM sensorless drive with 180-degree commutation is
of great significance.
A
B
1) Sensor-based Analysis
As shown in Fig. 4, permanent magnet BLDCM is
typically driven by six switches MOSFET inverter. T1, T3
and T5 are the high side transistors. T2, T4 and T6 are the
low side transistors. Hall sensors are traditionally used for
detecting the rotor position. The switching sequences are
determined based on the hall sensor signals. To run the
motor continuously and smoothly, next commutation switch
sequence is used for the current conduction interval.
Permanent magnet rotor is attracted to move to the next
sector. Installation of hall sensors and motor three phases
are described in Fig. 5. Based on the hall sensor signals,
rotor position is simply obtained, which is shown in Fig. 6.
According to the current position, the next switching
sequences can be summarized into table 1.
Figure 4: Three-phase six switches inverter and BLDCM
C
Figure 2: Conduction interval of 120-degree commutation.
Figure 3: Conduction interval of 180 degree commutation.
Figure 5: Hall sensor installation with three phases of U, V, W
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Equation (1) shows the mathematical model of BLDCM,
where the Vabc are three-phase voltages. Rabc are the threestator resistances. I abc represent the three-phase currents.
Labc are the value of the stator inductance per phase. M is
mutual inductance between each two phases and
Eabc represent the back-EMF in the respective three phases.
Figure 6: Position of current conduction interval
Sensor signals are the same for both 120 and 180 degree
commutation, and the driven pattern is shown in table 1.
Table 1: Switch sequences of 120 and 180 degree commutation
Switch Sequences
120 degree commutation
Polarities
A B C
180 degree commutation
Transistor
“on”
Polarities
A B C
ªVa º ª Ra
«V » = « 0
« b» «
«¬Vc »¼ «¬ 0
0
Rb
0
0 º ª Ia º
ª La M M º ª I a º ª Ea º
d«
»
«
»
0 » « I b » + « M Lb M »» «« Ib »» + «« Eb »» (1)
dt
«¬ M M Lc »¼ «¬ Ic »¼ «¬ Ec »¼
Rc »¼ «¬ Ic »¼
ª
« trape θ
( r)
«
ª Ea º
«
P
« E » = − ψ × ω trape § θ − 2π
r «
¨ r
« b»
2
3
©
«
¬« Ec ¼»
«
4π
§
«trape ¨ θ r −
3
©
¬
º
»
»
ªYa º
P
·»
« »
¸ » = − ψ × «Yb »
2
¹»
¬«Yc ¼»
·»
¸»
¹¼
Intervals
(degree)
Transistor
“on”
0 - 60
T1, T6
+
0 -
T1,T4,T5
+
- +
60 - 120
T3, T6
0
+ -
T1,T4,T6
+
- -
120 - 180
T3, T2
-
+ 0
T1,T3,T6
+
+ -
180-240
T5, T2
-
0
+
T2,T3,T6
-
+ -
240-300
T5, T4
0
-
+
T2,T3,T5
-
+ +
The three-phase back-EMF signals are given in the
Equation (2), where trape(θ r ) represents a piecewise linear
and periodic signal with the period 2π and the magnitude 1.
ψ represents the magnitude of flux linkage and ωr is rotor
300-360
T1, T4
+
- 0
T2,T4,T5
-
- +
speed. As shown in Equation (2), the Yabc are the signals
(2)
with speed information. The Yabc are given by Equation (3).
2) Sensorless Algorithm
Sensorless drive of 180-degree operation is simulated in
[12], as well as the modeling of the BLDCM. In this section,
the sensorless algorithm [9] is used.
The theory of this sensorless algorithm is illustrated in
Fig. 7. The main principle is to estimate the speed and
position by sensing the three-phase terminal voltage and
current signals to obtain the estimated back-EMF through
machine equations. Yabc signals are trapezoidal waveforms
with speed information. The estimated speed is the
maximum value of the absolute values of Yabc signals. The
position signal is obtained from the look up table of [9].
trape(θ r ) takes the extreme value of ±1 for any given value
of θ r . The magnitude of rotor speed can be simply obtained
by Equation (4).
ªYa º ª Ea º
«Y » = « E »
« b» « b»
«¬Yc »¼ «¬ Ec »¼
ª
« trape θ
( r)
«
«
2π
( − P 2 )ψ = ωr «trape §¨ θ r −
3
©
«
«
4π
§
«trape ¨ θ r −
3
©
¬
ωr = max ( Ya , Yb , Yc
Figure 7: Sensorless algorithm
108
)
º
»
»
·»
¸»
¹»
·»
¸»
¹¼
(3)
(4)
3) Pulse Width Modulation (PWM) Mode Operation
In order to control the speed, torque, and the power
applied to the BLDCM, PWM signals are commonly used.
Due to the chopping frequency is fixed, acoustic and
electromagnetic noise are relatively easy to filter [10]. Hard
chopping technology is to modulate both high and low side
of switches at the same time. In order to minimize the chance
of short circuit, soft chopping is implemented in this paper,
which is only used to modulate the three switches of the high
side of inverter. Theory of soft chopping technology is
shown in Fig. 8. “d” is value of duty cycle from 0 to 1.
2010 IEEE Conference on Robotics, Automation and Mechatronics
PWM signals are generated by comparing the duty cycle
with a periodic double side triangular waveform with the
magnitude from 0 to 1. The frequency of the double side
triangular waveform is the PWM modulation frequency. The
modulated activation phase voltage signals of both 120degree and 180-degree commutation are shown in Fig. 9.
20
15
10
5
0
-5
-10
-15
-20
0
0.05
0.1
0.15 0.2
0.25
0.3
0.35
0.4
0.45
0.5
Time (s)
Figure 10: Phase current and terminal voltage of BLDCM 120-degree
sensorless commutation
Figure 8: PWM soft chopping
Figure 9: Modulated phase voltage of 120 and 180 degree commutation
III.
SIMULATION ANALYSIS
The 120 and 180 degree sensorless systems are simulated
in Simulink/Matlab environment. The BLDCM parameters
are shown in table 2. Simulation results of phase current,
terminal voltage, estimated back-EMF, estimated speed and
position of 120 and 180 degree commutation are shown
respectively in this section.
Figure 11: Phase current and terminal voltage of BLDCM 180-degree
sensorless commutation
Table 2: Table of motor parameters
Motor parameters
Pole pairs
1
Friction Coefficient (B)
0
Stator Resistance (R)
5.85
Ω
Stator Inductance (L)
0.966
mh
(ψ )
0.115
Wb
3
gcm 2
Flux Linkage
Inertia of Rotor
(J)
Figure 12˖Estimated back- EMF, estimated speed and estimated position
signals of the proposed180-degree sensorless system.
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IV.
EXPERIMENT RESULTS
A. Sensorless of 120 and 180-degree commutation
A 20W BLDCM with manufacturer type-number EC22200118 is used in experiment. Tests are implemented based
on the dSPACE DS1104 controller board. This controller
board is appropriate for motion control applications and fully
programmable from Simulink/Matlab, which can efficiently
generate and download the code to the dSPACE boards.
Current transducer LEM HY 5-P and voltage transducer
LEM LV 25-P are used to accurately sense the phase current
and terminal voltage signals for sensorless algorithm.
DMC550 is a digital motor controller designed for BLDCM
with both sensor and sensorless based drive from Taxas
Instruments. Fig.13 and Fig.14 show the implementation
results of phase current and stator terminal voltage of the
sensorless 120-degree commutation respectively. The phase
conducts current for 120 electrical degrees and floats for the
other 60 electrical degrees. The back-EMF is available when
the phase is floating, which is described in Fig.14.
Figure 16: Terminal voltage of 180-degree sensorless commutation.
Figure 17: Estimated position of clockwise direction of 180-degree
sensorless commutation.
Figure 18: Estimated position of counter-clockwise direction of 180-degree
sensorless commutation.
Figure 13: phase current of 120-degree sensorless commutation.
An incremental encoder is used to obtain the actual speed
signal, which is solely used for the comparison and not for
the control purposes. Fig.19 describes the actual speed of
the 180-degree sensorless commutation. The estimated
speed is shown in Fig20. The proposed sensorless algorithm
works satisfactorily to estimate the rotor speed and energize
the motor stator windings.
Figure 14: Terminal voltage of 120-degree sensorless commutation.
The experimental results of the proposed 180-degree phase
current and stator terminal voltage are shown in Fig.15 and
Fig.16. It can be seen that the phase of the sensorless 180degree commutation conducts current in each conduction
intervals. The stator terminal connects to either the positive
or the negative of the dc power supply, which results in no
back-EMF appeared at the stator terminals. The estimated
position signals of the proposed 180-degree sensorless
system are satisfactorily shown in two opposite directions in
Fig.17 and Fig18.
Figure 19: Actual speed of 180-degree sensorless commutation.
Figure 20: Estimated speed of 180-degree sensorless commutation.
Figure 15: Phase current of 180-degree sensorless commutation.
110
In order to present the validity with speed, position and
torque control of the proposed 180-degree sensorless system,
it is necessary to demonstrate the implementation with
PWM operation. Fig.21 and Fig.22 describes the phase
2010 IEEE Conference on Robotics, Automation and Mechatronics
current and stator terminal voltage of the 120-degree
sensorless commutation, which are for the comparison
purpose. The PWM results of the phase current and stator
terminal voltage are successfully shown in Fig23 and Fig.24
respectively.
Figure 21: Phase current of 120-degree sensorless commutation (PWM).
V.
CONCLUSION
In this paper, a novel 180-degree sensorless commutation
system of BLDCM is proposed and verified to work
properly through both the simulation and implementation.
The simulation is carried out in the Simulink/Matlab and the
experiments are implemented through the dSPACE DS1104
controller board. The conventional 120-degree and the
proposed 180-degree sensorless commutation systems are
compared with satisfactory simulation and experimental
results. The proposed 180-degree sensorless commutation
system is able to work successfully in both directions with
accurate speed and position estimations. Finally, the
proposed 180-degree sensorless commutation system is
discussed to deliver more power from the inverter side to
the BLDCM side for the same given power supply voltage.
Since the generated torque of the BLDCM only depends on
the value of the phase current, the proposed 180-degree
sensorless system is able to generate more torque than the
conventional 120-degree system with the same dc supply.
REFERENCES
Figure 22: Terminal voltage of 120-degree sensorless commutation (PWM).
[1]
Figure 23: Phase current of 180-degree sensorless commutation (PWM).
Figure 24: Terminal voltage of 180-degree sensorless commutation (PWM).
B. Discussion
The validity of the proposed 180-degree sensorless
commutation system shows well performance on both
directions with accurate speed and position estimations. The
PWM operation is also applicable for the proposed system,
which provides the validity of speed control, position
control and torque control. Due to the three stator resistors
are allocated as one is in series with the parallel connection
of the other two resistors, the overall phase to phase
resistance is less than the value of 120-degree. The phase
current of 180-degree is larger than that of 120-degree
commutation under the same power supply voltage, which
results in more power is delivered from inverter side to the
motor side.
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