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CHAPTER 3
SENSORLESS CONTROL OF BLDC MOTOR DRIVE
3.1
INTRODUCTION
BLDC motor drives are increasingly being used in a variety of
applications, ranging from low power applications like fan and disk drives, to
large industrial automotive and aerospace applications. A BLDC motor
requires an inverter and rotor position sensor to perform electronic
commutation, which is not self-commutating. The three phase inverter is
controlled by the rotor position information obtained from the position
sensors.
The position sensors, such as resolvers, absolute position encoders
and hall sensors increase the cost and size of the motor. These sensors are
temperature sensitive. Absolute position sensors are generally used for speeds
below 600rev/min. Resolvers need special external circuits to obtain the
correct position information. In some compact applications like computer
hard disk drives, it may not be possible to mount any position sensor to the
motor. Also, in motors rated below 1W, the power consumed by the position
sensor can substantially reduce the motor efficiency. Owing to these
limitations, the sensorless operation of the motor drive is receiving wide
attention.
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In the literature, a number of sensorless control techniques have
been reported for the operation of BLDC motor drives. The techniques
available in the literature are based on the sensing of the back emf, terminal
voltage, flux linkage variation and freewheeling diode conduction in the open
phase.
Among these sensorless control techniques, the back emf based
detection method is widely used for low cost applications, because of its
simplicity. Since this research work is focused only on the study of AI
controller techniques for the BLDC motor drives used for low power
applications, the sensorless control technique based on the back emf zero
cross detection has been selected. This chapter discusses the extension of the
simplified simulation model developed for the BLDC motor drive with hall
sensors for obtaining a sensorless operation.
3.2
SENSORLESS CONTROL OF THE BLDC MOTOR DRIVE
A three phase star connected BLDC motor driven by a three phase
inverter using six step commutations has been considered. The commutation
time is determined every sixty electrical degrees, by detecting the back emf
zero crossing point of the floating phase. Figure 3.1 shows the block diagram
of the simple sensorless control technique for the BLDC motor drive.
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Figure 3.1
Block diagram of the simple sensorless control technique for
BLDC motor drive
As discussed in the previous Chapter, a BLDC motor is normally
operated in two phases in the ON mode leaving the third phase open. This is
available for measurement of the back emf. Figure 3.2 gives the flowchart of
the steps involved in the sensorless control of the BLDC motor drive. It
consists of alignment, sensorless starting and transition from the starting to
the sensorless running.
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Figure 3.2 Flow chart of the simple sensorless control
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In this work a virtual hall signal is generated based on the detected
back emf zero crossing points. At any instant, only one of the phases is open,
and this open phase voltage is used to generate the position information of the
rotor. Let us consider an instant where phases A and B are in conduction,
whereas phase C is in open state, as shown in Figure 3.3. The zero crossing
instant of this voltage resembles the position signal generated from the hall
sensor. The transition from one state to the other is without any delay.
Figure 3.3 shows the zero crossing of the back emf waveform for the ideal
case.
Figure 3.3 Zero crossing of back emf waveform (ideal)
3.3
STARTING
The sensorless control technique based on the back emf has been
widely used for low cost applications. However, the ZCP of the back emf
cannot be obtained when the BLDC motor is standstill or operating at nearly
zero speed. Therefore, a special starting arrangement is needed for the smooth
starting and reliable transfer to sensorless control. One of the most commonly
used starting methods is,
“align and go”. In this method, the rotor of the
BLDC motor drive is aligned to the specified position by energizing any two
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phases of the stator winding and then accelerating the rotor speed according to
the commutation sequence until the ZCP of the back emf is detected. The
motor is started according to the procedure explained in the flow chart, shown
in Figure 3.2. The motor is started in the open loop mode and switched on to
the sensorless mode, as the rotor reaches the minimum speed of 50 rpm.
3.4
PWM CONTROL OF BLDC MOTOR DRIVE
The PWM can be applied to the top or bottom switches, or to both.
The three phase winding of the BLDC motor drive is shown in Figure 3.4. In
this work, the zero crossing of the back emf is detected from the terminal
voltage of the floating phase.
Figure 3.4 Three phase winding of the BLDC motor Drive
Let, va -
terminal voltage of the phase connected to the positive
dc-link rail during the PWM control period.
vb - terminal voltage of the phase connected to the negative
dc-link rail, and
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vc - terminal voltage of the floating phase. The back emf is
detected from the terminal voltage of the floating phase.
The following equations are involved in the detection of the back
emf zero crossing points.
ia ib
and
ic 0
(3.1)
By applying Kirchhoff’s voltage law, the expression for the center
tap voltage is derived as given in equation (3.2) and (3.3)
di ·
§
vn va ¨iars Ls a ea
dt ¹̧
©
di ·
§
vn vb ¨iars Ls a eb
dt ¹̧
©
(3.2)
(3.3)
The open phase voltage is expressed in equation (3.4)
vc
v n ec
( 3 .4 )
From equation (3.2) to (3.4), an expression for vn is arrived at as
given in equation (3.5)
§ v a v b · § e a eb ·
¨
¨
© 2 ¹̧ © 2 ¹̧
On substituting equation (3.5) in equation (3.4)
vn
§ va vb · § ea eb ·
¨
ec
¨
© 2 ¹̧ © 2 ¹̧
From the Figure 2.2, it can be seen that
vc
e a eb
ec
( 3 .5 )
( 3 .6 )
( 3 .7 )
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Equation 3.6 is rearranged and expressed as given in Equation (3.8)
vc
§ va vb ·
ec
¨
2
©
¹̧
(3 .8 )
The terminal voltage of the floating phase depends on the voltages
applied to the phase connected to the positive dc-link rail, and the negative dc
link rail during the PWM period. The terminal voltage of the floating phase
has both the rising edge and falling edge.
(a)
Figure 3.5 (Continued)
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(b)
Figure 3.5
Calculation of terminal voltage during rising edge (a) ON
period (b) OFF period
The terminal voltage of the floating phase is analyzed during the
PWM “ON” or “OFF” period. Figure 3.5 shows the calculation of the
terminal voltage of the floating phase for the rising edge during PWM “ON”
and “OFF” periods. In the “PWM ON” period, the positive phase is connected
to the positive dc-link rail and the negative phase is connected to the negative
dc-link rail. The terminal voltage of the floating phase C is given as
vc
§ v DC
¨
¨ 2
©
·
¸ ec
¸
¹
(3 .9 )
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The zero crossing point of the back emf is detected when vc
becomes
v DC
2
as given in equation (3.10)
§ v DC
¨
¨ 2
©
vc
·
¸
¸
¹
(3.10)
And during the PWM “OFF” period, both the positive and negative
phases are connected to the negative dc-link rail. Then the terminal voltage of
the floating phase, i.e., phase c, is given by
vc
ec
( 3 . 11 )
Similarly, the terminal voltage of the floating phase for the case of
the falling edge is derived as given in equations (3.12) to (3.14). Figure 3.6
shows the calculation of the terminal voltage of the floating phase for the
falling edge during PWM “ON” and PWM “OFF” periods.
Figure 3.6 (a) (Continued)
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(a)
(b)
Figure 3.6
Calculation of terminal voltage during falling edge (a) ON
period (b) OFF period
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·
¸ ec
¸
¹
§ v DC
¨
¨ 2
©
vc
( 3 . 12 )
The zero crossing point of the back emf is detected as
vc
§ v DC
¨
¨ 2
©
·
¸
¸
¹
(3 .13 )
And during the PWM “OFF” period, both the positive and the
negative phases are connected to the negative dc-link rail. Then the terminal
voltage of the floating phase C, is given by Equation (3.14)
vc
ec
( 3 . 14 )
Therefore, the condition for the zero crossing detection of the back
emf is decided by the PWM control technique, and the status of the PWM. In
the detection of the back emf zero crossing point, two reference voltages were
used to facilitate the BLDC motor drive to operate at low speed and high
speed duty range.
For the duty ratio of less than 50%, zero volt is assumed as the
reference voltage, and for a duty ratio more than 50%, 0.5 volt is assumed as
the reference voltage.
The following equations are derived to detect the zero crossing
instant of the back emf during the PWM on period.
where, t1 and t2 are the time instants of the voltages, V1 and V2
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The time instant of the zero crossing point can be determined as
follows,
tZ
t1 t 2 t1
(V V 1 )
v 2 v1
( 3 . 15 )
During the “PWM On period” the reference voltage is 0.5 volt dc.
The following equations are derived to detect the zero crossing instant of the
back emf during the PWM On period.
§ v1 V
¨¨
© t1 t z
· § V 2 V1
¸¸ ¨¨
¹ © t 2 t1
·
¸¸
¹
( 3 . 16 )
The time instant of the zero crossing point can be determined as follows,
tZ
where,
t1 t 2 t1
(V V 1 )
v 2 v1
( 3 . 17 )
t Z is the time instant of the zero crossing point of back emf.
Equations (3.15) and (3.17) show that the time instants obtained
from the rising and falling edge is the same.
3.5
SIMPLIFIED SIMULATION MODEL OF THE BLDC
MOTOR DRIVE
WITH
SENSORLESS
CONTROL
TECHNIQUE
The simulation model of the BLDC motor drive consists of a
controller block, back emf zero cross detection block, the inverter and motor
block, as shown in Figure 3.7. The simplified simulation model developed for
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the BLDC motor drive with hall sensors has been extended to obtain the
sensorless model. In this model the hall sensors are replaced by a sensorless
estimation block.
Figure 3.7
Model of the BLDC motor drive with back emf zero cross
detection technique
The inverter and switching logic sequence are implemented using
an S-function builder as discussed in the previous chapter. The output voltage
of the inverter depends on the DC source voltage, rotor position signal, phase
current and the back emf. The sensorless control technique is based on the
calculation of the zero crossing points of the back emf waveform. The input to
this block is the back emf and the output of this block is the calculated virtual
hall signals. The motor is operated in the open loop mode during starting and
a change over to the sensorless mode takes place at 0.25 seconds.
3.6
SIMULATION STUDIES
The position information obtained from the sensorless technique
was compared with that obtained from the hall sensors, as shown in
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Figure 3.8. The comparison shows that the signal derived from the back emf
zero crossing point matches with the signals provided by the hall sensors,
with a small deviation at the alignment and starting. This shows that the
sensorless model developed will be useful in the design of the study of the
controllers for the BLDC motor drive. The closed loop speed response of the
BLDC motor drive with the sensorless control technique is shown in
Figure 3.9. Figure 3.10 shows the speed response of the BLDC motor for the
load torque of 0.5 Nm, applied at 2 seconds.
Figure 3.8
Comparison of the position signal obtained from hall sensor
and the sensorless technique
Figure 3.9 Speed response of the BLDC motor drive
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Figure 3.10 Speed response during loading
Figures 3.11 and 3.12 show the phase A, back emf and phase
current waveforms. The alignment of the rotor lasts for 0.05 seconds.
Subsequently, the starting mode lasts for 0.25 seconds. Changeover occurs at
0.25 seconds, wherein the operation is changed to the running mode. Figure
3.13 shows the measured phase C voltage, with respect to the ground and
commutation signal. The commutation signals obtained from the sensorless
circuit and the hall sensors are closely matched.
Figure 3.11 Back emf waveform with a zoomed view
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Figure 3.12 Phase -A current waveform with the zoomed view
Figure 3.13 Terminal voltage and commutation signal
3.7
HARDWARE IMPLEMENTATION AND TEST RESULTS
The experimental setup consists of the BLDC motor with the
variable mechanical load, Digital signal processor, inverter and the back emf
detection circuit. The parameters of the motor used in this study are listed in
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Table
2.1.
The
sensorless
technique
is
implemented
using
the
TMS320LF2407A digital signal processor of the Texas instruments. The
BLDC motor is driven by a three phase MOSFET inverter module. The
terminal voltage of the floating phase is sampled at 20 kHz frequency to
detect the zero crossing points of the back emf waveform.
The LF2407 DSP senses the current and position signal of the
drive, to generate the corresponding gating signals. The LF2407 consists of
three capture units to detect the rising and the falling edges of the back emf
waveform. Hence, for every 60 degree electrical, one capture unit interrupt is
generated. The input channel ADCIN0 is used to sense the dc current, and the
output pins PWM1 to PWM6 are used to supply the gating signals to the
inverter. The DAC module of the LF2407 evaluation board is used to display
the system variables through an oscilloscope.
An algorithm was developed, which includes the prepositioning and
generation of the PWM signals, regulation of the speed and current response,
measurement of the current and DAC output. The switching states of the
inverter are controlled using the ACTR register. The motor drive is started in
the open loop mode until the minimum speed is achieved, and then it runs in
the sensorless mode. The alignment of the rotor lasts for 0.005 seconds.
Subsequently, the starting mode lasts for 0.025 seconds and the changeover to
the running mode occurs at 0.025 seconds. Figure 3.14 shows the Voltage
and phase current waveforms obtained from the sensorless technique. The
experimental results obtained from the sensorless technique for 10%, 40%
and 55% duty ratios are shown in Figure 3.14. The current is in phase with the
voltage waveform for the entire speed range. Figure 3.15 shows the similar
results obtained from the sensorless technique available in the literature, as
reported by Yen-shin Lai (2008). The results were very closely matched,
confirming the accuracy of the sensorless technique.
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(a) Duty= 10%
(b) Duty= 35%
(d) Duty=55%
Figure 3.14 Voltage and phase current waveforms
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Figure 3.15 Voltage and phase current waveform as reported by Yen –
Shin Lai, (2008) for a duty of 55%
With a view to verifing the calculated time instants of the ZCP of the back
emf waveform, the commutation instants obtained from the sensorless
technique are compared with those obtained from the hall sensors. Figure 3.16
(a) shows the commutation instants obtained from the sensorless technique
and hall sensors, and Figure 3.16 (b) shows the responses available in the
literature.
(a)
Figure 3.16 (continued)
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(b)
Figure 3.16 Waveforms of Voltage and commutation signals (a)
sensorless technique (b) reported by (Yen- Shin Lai, 2008)
Figure 3.17 shows the experimental results of the voltage and the generated
PWM waveforms for the top and bottom switches for the duty- 15%, 25% and
95%. The results clearly indicate that the sensorless technique works well
from the low duty to the high duty range.
(a) Duty= 15%
Figure 3.17 (Continued)
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(b) Duty= 25%
(c) Duty =75%
Figure 3.17 Waveforms of Voltage and PWM control signal
The snap shot of the experimental set up used in the sensorless
BLDC motor drive is given in Figure 3.18.
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Figure 3.18 Snap shot of the experimental setup
3.8
CONCLUSION
The simplified simulation model developed for the BLDC motor
drive discussed in chapter Two, has been extended to obtain a sensorless
operation. The sensorless technique based on the back emf zero cross
detection technique was implemented with an experimental setup, and the
performance of the BLDC motor drive was compared with that of the
simulation model and also with the waveforms available in the literature. The
experimental results confirm that, this model can be used to study and design
an AI controller for the BLDC motor drive.