A New Cost Effective Sensorless Commutation

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A New Cost Effective Sensorless
Commutation Method for Brushless DC Motors
Without Phase Shift Circuit and Neutral Voltage
Dec, 2008
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OUTLINE

• 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.
• 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 (H1H3),
• and the switching signals (S1S6) 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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• 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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• 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 H1H3 ).
• Consequently, the circuit needed in the proposed
  approach is much simplercompared with that needed
  in the conventional circuit shown in Fig. 8(b).

• 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
• 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

• 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 .

• Fig. 14. (a) Duty ratio 10.

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Lagging 14.4 in 50 full-speed.

• Fig. 14. (a) Duty ratio 50.

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lagging 22.8 in full speed.

• 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
• The neutral voltage is not required in the
  proposed method, only the three motor terminal
  voltages need to be detected.
• Elimination of the fixed phase shift circuit
• 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
• 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
• 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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