A New Cost Effective Sensorless Commutation
Method for Brushless DC Motors Without
Phase Shift Circuit and Neutral Voltage
Dec, 2008
高等伺服控制報告
授課老師： 王明賢 教授
學 生 ： 楊智淵
南台科大電機系
OUTLINE
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ABSTRACT
I. INTRODUCTION
II. MATHEMATICAL MODELS OF EACH COMMUTATION STATE
III. PROPOSED ZCP DETECTION APPROACH BY AVERAGE LINE
TO LINE VOLTAGE
IV. ANALYSIS OF THE COMMUTATION ERROR
V. EXPERIMENTAL EVALUATION
VI. CONCLUSION
REFERENCES
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Abstract

This paper presents the analysis, design, and implementation of a high
performance and cost effective sensorless control scheme for the
extensively used brushless dc motors.

In an effort to decrease cost and increase ease of implementation, the
commutation signals are obtained without the motor neutral voltage,
multistage analog filters, A/D converters, or the complex digital phase
shift (delay) circuits which are indispensable in the conventional
sensorless control algorithms.

In the proposed method, instead of detecting the zero crossing point of
the nonexcited motor back electromagnetic force (EMF) or the average
motor terminal to neutral voltage, the commutation signals are
extracted directly from the specific average line to line voltages with
simple RC circuits and comparators.
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In contrast to conventional methods, the neutral voltage is not needed;
therefore, the commutation signals are insensitive to the common mode
noise. Moreover, the complex phase shift circuit can be eliminated.

Due to its inherent low cost, the proposed control algorithm is
particularly suitable for cost sensitive products such as air purifiers,
air blowers, cooling fans, and related home appliances.

Theoretical analysis and experiments are conducted over a wide
operating speed range and different back EMF waveforms to justify
the effectiveness of the proposed method.
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I. INTRODUCTION

DURING the last two decades, a lot of research on sensorless control
techniques for brushless dc motors (BLDCMs) have been conducted. This
research can be divided into four categories.

Detection of the zero crossing point (ZCP) of the motor terminal
to neutral voltage with a precise phase shift circuit.

Back electromagnetic force (EMF) integration method.

Sensing of the third harmonic of the back EMF.

Detection of freewheeling diode conduction and related extended
strategies .
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The neutral voltage is required for comparison with the non-conducted
back EMF or the average terminal voltage, in which it will introduce a high
common-mode noise.
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Since the zero crossing points of the conventional back EMF method are
inherently leading 30 electric degrees of the ideal commutation points, a
precise velocity estimator and a phase shift circuit (algorithm) are needed
to process the zero crossing signals so that accurate commutation points
can be determined.
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
Instead of detecting the motor terminal to neutral voltage, the
estimated commutation signals are extracted directly from the
specific average line to line voltage of a BLDCM using simple
single-stage low pass filters and low cost comparators.

That is, the estimated commutation signals are well in phase
with the ideal commutation points. Unlike conventional
solutions, the proposed method does not require additional
virtual motor neutral voltage, complex phase shift circuits, or
precise speed estimators.
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II. MATHEMATICAL MODELS OF EACH
COMMUTATION STATE

Fig. 1 shows the equivalent circuit of a BLDCM and the
inverter topology.
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Fig. 2 illustrates the relationship
among the back EMF waveform of an
ideal BLDCM, the armature current,
the commutation signals (H1–H3),
and the switching signals (S1–S6) for
the inverter.

According to the polarity of the
armature current as illustrated in Fig. 2,
the terminal voltage of each phase can
be divided into three sub-sections, i.e.,
positive, negative, and nonconducted.
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10
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Fig. 3 illustrates the equivalent
circuits of each commutation
state for phase-“a ” over one
electric cycle, and the same
results can be obtained for the
other two phases.
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States I and II: Armature Current is Positive:
Fig. 3(a) and (b) illustrate the equivalent circuit of the commutation states (I
and II) where the armature current is positive. If the conduction voltage
caused by the power switches and the diodes is negligible, then the terminal
voltage can be obtained according to the switching status of the power
switch S1
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States IV and V: Armature Current is Negative:
Fig. 3(c) and (d) illustrate the equivalent circuit of the commutation states
(IV and V) where the armature current is negative. Since the switch S2 is
turned on, the motor terminal is connected to the power ground. Therefore,
the terminal voltage will be kept low despite the switching status of the
upper legs
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States III and VI: Armature is Open (Nonconducted):
Fig. 3(e) and (f) illustrate the equivalent circuit of the commutation
states (III and VI) where the armature is open. Since the armature is
disconnected from the voltage source, the terminal voltage can be
expressed as the summation of the armature back EMF and the neutral
voltage
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If the switch of the upper leg is conducted (e.g., S3 is on), the neutral
voltage can be expressed as
According to (6) and (7), the neutral voltage can be written as
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If the switch of the upper leg is not conducted (e.g., S3 is off), the neutral
voltage can be expressed as
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17
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Substituting (14) into (8) and (11), the motor neutral voltage can be
rewritten as
Substituting (12) and (13) into (5), the terminal voltage of a BLDCM which
has an ideal trapezoidal back EMF waveform can be expressed as
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Equation (18) represents the case where the back EMF waveform is
perfectly sinusoidal
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Note that each motor
terminal is placed between
the upper diodes, which are
connected to the dc source,
and the lower diodes of the
inverter, which are
connected to the ground. It
can be expected that the
maximum and minimum
terminal voltages will be
fixed between Vdc and 0.
Fig. 4 shows the measured
terminal voltage and the
corresponding switching
signals. It is found that the
waveforms are in
accordance with the
theoretical analysis.
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III. PROPOSED ZCP DETECTION APPROACH BY
AVERAGE LINE TO LINE VOLTAGE

The major problem of the conventional back EMF sensing techniques is
that they require noisy motor neutral voltage and a fixed phase shift circuit.

Since the noisy motor neutral voltage will introduce the common mode
noise into the sensorless circuit, a low pass filter is indispensable.

On the other hand, the fixed phase shift function over a wide speed range is
hard to implement with analog circuits.

In order to cope with the aforementioned problems, the proposed method
extracts the commutation points directly from the motor terminal voltages
with simple comparators and a single stage low pass filter.
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
If the terminal voltages are expressed in the average form (i.e., duty ratio),
the switching states in (3), (4), (17), and (18) can beeliminated. The
terminal voltages are rewritten as follows.
States I and II: Armature Current is Positive:
States III and VI: Armature is Open (Nonconducted):
States III and VI: Armature is Open (Nonconducted):
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According to (19)–(21), the ideal average terminal voltages for all three
phases with different duty ratios are illustrated in Fig. 5.
Fig. 5. Ideal average terminal voltages under different duty ratios.
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
The measured instantaneous (upper trace) and average (lower trace)
terminal voltages as the duty ratio is increased from 10%,to 50%, to 100%
are shown in Fig. 6.
Fig. 6. Measured instantaneous (first trace) and average
(second trace) terminal voltages under different duty ratios. (a)
Duty ratio = 10%. (b) Duty ratio = 50%. (c) Duty ratio = 100%.
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
According to the average terminal voltage derived in (19)–(21), the average
line to line voltage Vac can be expressed
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Equation (23) reveals that the zero
crossing points of the average line to
line voltage will occur at 30 and 210
electric degrees.

According to (22) and (23), Fig. 7
shows the phase relationship among
the ideal back EMF, the average
terminal voltage, and the average line
to line voltage of phase “a ” and
phase “c .”

It is clear to see that the average line
to line voltage Vac lags 30 electric
degrees compared with the back
EMFea , namely the zero crossing
points of the line to line voltage are
in phase with the ideal commutation
signals.
Fig. 7. Phase relationship among the back EMF,
the average terminal voltage,and the average
line to line voltage.
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
Table (I) summarizes the three specific line to line voltages for the
proposed sensorless commutation approach.
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• Fig. 8(a) illustrates the practical circuit for implementing the proposed
approach to obtain the commutation signals (namely the virtual Hall effect
signals H1~H3 ).
• Consequently, the circuit needed in the proposed approach is much
simplercompared with that needed in the conventional circuit shown in Fig.
8(b).
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Fig. 8. Proposed and conventional sensorless commutation circuits. (a)
Proposed cost effective sensorless commutation circuit. (b) Conventional
sensorlesscommutation circuit.
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IV. ANALYSIS OF THE COMMUTATION
ERROR

A. Phase Delay by the Low Pass Filter and the Armature Impedance
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B. Voltage Spikes by the Residual Current
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A. Phase Delay by the Low Pass Filter and the
Armature Impedance

The phase delay angles caused by the input low pass filter and the armature
impedance shown in Fig. 9(a) and (b) can be expressed as
Since the 30 (or 90 ) phase shift circuit shown in Fig. 8(b) is not required in the
proposed approach, the corner frequency fc of the input low pass filter can be easily
determined by the maximum motor speed RPMmax and the switching frequency fs ,
in which the value of fc can be chosen as
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
The phase delay caused by the armature impedance
can be neglected in most small to mid-sized
BLDCMs due to the fact that the value of the
resistance is usually much larger than the inductance.
The current loop compensator can be used to
overcome the delay caused by the armature
impedance, however, it is not needed in most home
appliance applications since it is only required in very
high speed applications.
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B. Voltage Spikes by the Residual Current
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The voltage spikes shown in Figs. 4 and 6 are created by the residual
current when the armature current is blocked by the power switches. The
voltage spike is the main cause for the commutation error in the
conventional back EMF integration method and the window-captured back
EMF method (detecting back EMF during the silent period) .
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Fig. 9. Illustration of various
commutation errors.
(a) Low pass filter.
(b) Armature impedance.
(c) Effect of the voltage spike.
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V. EXPERIMENTAL EVALUATION

Fig. 10 shows the block diagram
of the proposed sensorless control
method. The system can be
divided into several subblocks,
including a velocity command
generator, an open loop starting
process, a line to line voltage
based virtual Hall effect signal
circuit, an electric commutation
table, and a PWM generator.
Fig. 10. Block diagram of the overall system.
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Fig. 11. Structure of the employed
BLDCMs. (a) Type I (segmented
magnet), trapezoidal back EMF. (b)
Type II (ring magnet), sinusoidal back
EMF.
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Fig. 12. Measured back EMF waveforms of employed BLDCMs.
(a) Type Imotor. (b) Type II motor.
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Fig. 13. Measured commutation signals under different duty ratios and back EMF waveforms
(from top to bottom: average terminal voltage V a, average terminal voltage Vc , average
line to line voltage Vac , estimated commutation signal, signal from Hall effect sensor). (a)
Duty ratio = 10%, type I motor. (b) Duty ratio= 50%, type I motor. (c) Duty ratio = 100%,
type I motor. (d) Duty ratio = 10%, type II motor.
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It can be seen that the signal
from the conventional
solution strongly depends on
the operating speed; the
mismatch angle is leading
21.8 in 10% full-speed .
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Fig. 14. (a) Duty ratio = 10%.
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Lagging 14.4 in 50%
full-speed.
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Fig. 14. (a) Duty ratio = 50%.
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lagging 22.8 in full speed.
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Fig. 14. (a) Duty ratio = 100%.
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
The large commutation error is mainly caused by the multistage filters;
thereforea speed dependent phase compensation algorithm is usually
indispensable. Compared with the conventional solution, the proposed
method is not only easier to design and implement, but also exhibits better
performance.
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VI. CONCLUSION

Unlike conventional back EMF based sensorless commutation methods
which focus on detection of the ZCP of the motor terminal to neutral
voltage, a novel sensorless commutation method based on the average line
to line voltage is proposed in this study. Both theoretical analysis and
experimental results verify that satisfactory performance can be achieved
with the proposed sensorless commutation method. Compared with the
conventional solutions, the proposed method has several advantages,
including the following.
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
Elimination of the motor neutral voltage:
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Elimination of the fixed phase shift circuit:

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Since the amplitude of the line to line voltage is significantly larger than the phase
voltage, even a small back EMF can be effectively detected. Namely, a lower open loop
starting speed can be achieved.
Insensitive to the back EMF waveform:

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The proposed specific average line to line voltage inherently lags 30 electric degrees
compared with the phase back EMF. Moreover, experimental results have revealed that
thephase relationship is insensitive to operating speed and load conditions.
Low starting speed:


The neutral voltage is not required in the proposed method, only the three motor terminal
voltages need to be detected.
Compared with the third-harmonic detection method, the proposed method can be used
for a BLDCM with nonideally trapezoidal or sinusoidal back EMF waveforms, since
most BLDCMs do not have ideal back EMF waveforms.
Cost effective:

Because the speed estimation algorithm and the complex phase shift circuits are not
required, the costly digital signal processor controller is not needed. Using a simple
starting process, the proposed method can be easily interfaced with the low cost
commercial Hall effect sensor based commutation ICs. Consequently, the proposed
method is particularly suitable for cost sensitive applications such as home appliances
and related computer peripherals.
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REFERENCES
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