CHAPTER
9
Brushless Dc Motors
9.1
Introduction
The dc motor is widely used because of its merits, namely, (i) ease of variation
of speed and (ii) the linear speed–torque characteristics in its range of operation
except in the high-torque region. Its main drawback is the commutator, which
makes it bulky and costly, and this imposes limitations on the design. Its field
poles are situated on the stator, making the field stationary. Though the armature
conductors carry alternating currents, the commutator and brushes are so arranged
that the spatial distribution of the armature current direction as well as armature
magnetomotive force (mmf) remain constant for all speeds. The stator field and
armature mmf waves interact to provide a steady torque at any permissible speed.
To obtain sparkless commutation, the brushes are placed in the neutral axis, thus
giving a displacement of 90◦ between the field and armature mmf waves.
Ac motors are preferred in applications where the commutator is undesirable,
but there are still some areas in which they cannot replace dc motors. This gave the
impetus for the development of the brushless dc motor, which is a combination
of (a) an ac machine, (b) a solid-state inverter, (c) electronic control circuitry,
and (d) a rotor position sensor. These modules constitute a drive system that
provides a linear speed–torque characteristic similar to that of the conventional
dc motor. The construction of this ac motor is the same as that of a self-controlled
synchronous machine with a permanent magnet rotor. Here, the inverter is the
power converter, with the ac machine connected at its output. The frequency of
the inverter is changed in proportion to the speed of the ac motor so that the
armature and the rotor mmf waves revolve at the same speed. This results in the
production of a steady torque at all speeds as in a dc motor. The three components,
namely, the rotor position sensor, the electronic control circuitry, and the inverter,
perform the same function as the brushes and the commutator in a dc motor. A
slight difference between the brushless dc motor and the conventional dc motor
is that the former need not operate at a displacement of 90◦ between the field and
armature mmf waves, as it is free from the problem of sparking. This displacement
is usually set at a suitable value so that the performance requirements are satisfied.
732
Brushless Dc Motors
Brushless dc motors are suited for applications requiring high starting torque,
good efficiency at low speeds, and continuous speed variation from standstill to
full speed. With its low torque ripple, it is a strong contender for high-performance
servo drives used in the machine tool industry as well as those employed in
robotics.
After going through this chapter the reader should
• understand the principle of the brushless dc motor,
• know the constructional features of the electronic commutator, which is the
heart of the brushless dc motor,
• get acquainted with the various types of sensors used with the electronic
commutator,
• become familiar with the mechanism of torque production in the sinusoidaltype two-phase, brushless dc motor and also in the three-phase, half- and
full-wave configurations,
• know the method of implementation of the closed-loop control of a brushless
dc drive,
• get acquainted with the different types of current controllers that can be used
in the closed-loop scheme,
• become familiar with the recent developments in this field, and
• know how the performance of the brushless dc motor differs from those of
the three conventional motors, namely, the dc motor, the induction motor,
and the brushless synchronous motor.
Brushless dc motors are suited for applications requiring high starting torque,
good efficiency at low speeds, and continuous speed variation from standstill to
full speed. With its low torque ripple, it is a strong contender for high-performance
servo drives used in the machine tool industry as well as those employed in
robotics.
9.2
Sinusoidal and Trapezoidal Brushless Dc Motors
A distinction is made in the industry between the following two types of brushless
motors. The self-controlled synchronous machine with a standard permanent
magnet rotor, whose air gap flux distribution and back emf waveform are both
sinusoidal, is called a sinusoidal brushless dc machine. On the other hand, the
term brushless dc motor is usually assigned to a self-synchronous machine,
in which these two waveforms are trapezoidal in nature. These two types of
brushless dc motors have the following common features: the drive characteristics
and the control methods are the same, and in both cases the motor must be
energized with controlled currents that are synchronized with the rotor position.
They, however, differ in the following aspects of construction and operation. The
standard synchronous motor requires sinusoidal current excitation, whereas the
trapezoidal brushless dc machine is supplied with a square-wave or quasi-square
wave current. The rotor position sensor for the trapezoidal brushless dc motor
usually consists of simple position detectors such as magnetic position sensors,
733
Electronic Commutator
Hall effect devices, or optical position sensors. By sensing the rotor magnetic
field, these sensors determine the phase-switching points. On the other hand,
more precise position information has to be given to the sinusoidal brushless dc
motor, so that the resulting armature mmf waveforms are accurately positioned.
The trapezoidal brushless dc motor will henceforth be called the brushless dc
motor.
9.3
Electronic Commutator
The most important part of a brushless dc motor is the electronic commutator, in
which the following events take place. The signals from the rotor position sensor
act on the electronic control circuitry and the resulting output signals operate
appropriate switches in the inverter circuit. The development of the brushless dc
motor is explained below. In a dc motor, the stator contains salient poles, and
sometimes the interpoles also, which are energized by a field coil. The rotor,
usually called the armature, carries a current which is supplied by an external
dc source. The rotor currents have to be switched periodically in order to keep
the two fields as nearly perpendicular to each other as possible for maintaining
unidirectional torque between the rotor and stator. In a conventional dc motor, this
switching is done with the help of the mechanical commutator and the brushes.
Figures 9.1(a) and (b), respectively, show a two-segment commutator for a twopole machine and the connection of the coil sides to the commutator segments.
The external dc supply is connected to these segments through fixed brushes.
Figure 9.2 shows the waveform of the torque, as a function of the electrical
position, for this simple two-commutator segment. It is seen that the torque is
unidirectional but pulsating in nature.
+
S
N
–
(a)
+
Brushes
–
(b)
Fig. 9.1 Connection of (a) a two-segment commutator and (b) coil sides
The electrical angles are measured with respect to the neutral axis. Maximum
torque occurs when the coil sides are situated at the centres of the north and south
poles, respectively. Now, if the number of coil sides, and hence the number of
commutator segments, is doubled, as shown in Fig. 9.3(a), the torque waveform
will become fairly smoother [Fig. 9.3(b)]. The mean torque in this case can be
calculated to be 0.9 times the maximum torque.
It is possible to design a dc motor in which the rotor has permanent magnet
poles and the stator current is switched. However, in this case the brushes have
734
Brushless Dc Motors
Torque
Tmax
90
180
270
360
Angular position
(electrical degrees)
Fig. 9.2 Torque vs angular position curve for a two-segment commutator
+
N
S
Torque
–
(a)
Tmax
0.9Tmax
0
90
180
270
(b)
360
Angular position
(electrical degrees)
Fig. 9.3 (a) Four-segment commutator; (b) its torque vs angular position curve
to rotate at the same speed as the rotor to maintain unidirectional torque. Though
such a rotor–stator combination may not give optimum performance, as in the
conventional machine, it can be advantageously used in electronic commutator
circuits. This is because with a stationary commutator it is easier to operate the
electronic devices that are used as switches. The spread out of a typical inverted
dc machine with coils and switches is shown in Fig. 9.4. The stator flux can be
controlled as required, by means of the switches connected to the positive or
negative buses, at the appropriate moments.
Electronic Commutator
N
735
S
Positive rail
Negative rail
Fig. 9.4 Switching circuit for an electronic commutator
This inverted machine will have a rotor of the salient-pole type. Hence, the field
flux constitutes the major portion of the air gap flux, and the effect of armature
reaction can be neglected.
Though the circuit of Fig. 9.4 has been used in some electronic commutator
motors, its drawback is that it employs a large number of switching devices
and is hence expensive. It is stated above that a four-coil-side armature (stator)
which is accompanied with a four-segment commutator gives a fairly high mean
torque and will be optimum from the point of view of the number of commutator
segments, because it gives a fairly smooth torque function with minimum number
of switches. Figure 9.5(a) shows one such four-segment electronic commutator,
which is meant to be used with a two-phase ac synchronous motor having windings
A and B. The switch positions that give appropriate polarities for the windings
are given in Fig. 9.5(b).
Sw4
–
Switch
A
+
Position
Sw1
Sw3
B¢
B
Sw1 Sw2 Sw3 Sw4
¥
1
¥
2
A¢
¥
3
Sw2
(a)
4
¥
(b)
Fig. 9.5 (a) Four-segment electronic commutator (b) table of electronic switching
Figure 9.6 shows the implementation of the electronic commutator for a
two-phase ac motor. With the p-n-p and n-p-n transistors playing the roles
736
Brushless Dc Motors
of switches, the base signals for the transistors of Fig. 9.6 are obtained from
a magnetic rotor position sensor as shown in Fig. 9.7(a), or from a Hall sensor as
shown in Fig. 9.7(b) (Mazda 1990).
Rotor
Q Q¢ Q2 Q¢2 Q3 Q¢3 Q4 Q¢4
position 1 1
Sw1
Sw2
Sw3
Sw4
Sw5
Sw6
Sw7
Sw8
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
´
4
´
´
´
3
1
2
Q1
Q¢1
Q2
Q¢2
Q3
Q¢3
Q4
Q¢4
+
–
Fig. 9.6 Detailed circuitry of electronic switching for a four-segment commutator
In Fig. 9.7(a), the auxiliary rotor that is associated with the magnetic position
sensor is attached to the main rotor and revolves in a four-pole stator yoke. A
sensing coil is wound around each of these poles, which correspond to each of
the four switching points of a four-segment motor, and this feeds the respective
stator winding switch. A high-frequency oscillator supplies the two coils placed
at diametrically opposite ends of the yoke, and is arranged to produce signals of
opposite phases. It can be seen that a voltage will be induced in only those coils
which are under the rotor poles, so that the system produces rotor position signals.
Figure 9.7(b) shows Hall generators (HGs) that are used to detect rotor position
and are widely used in many small electronic commutator motors. The robustness
of magnetic sensors as well as the lightness of optical devices are combined in
the Hall generator. The Hall effect can be stated as follows. A current Ic passed
between the two faces of a thin conductor or a semiconductor placed in a transverse
magnetic field B would result in a redistribution of the charge carried within the
device and the induction of a voltage across it in a direction perpendicular to both
the current flow and the magnetic field. This voltage, termed as the Hall voltage,
is proportional to both Ic and B.
Electronic Commutator
737
W2
W3
Auxiliary
rotor
W1
Oscillator coil
Rotor sensing
winding
Magnetic structure
W4
High-frequency
oscillator
(a)
+V
W1
TR¢ 1
TR1
R1
W3
TR¢ 3
HG1
W2
TR¢ 2
TR2
TR3
HG2
W4
TR¢ 4
HG3
TR4
HG4
R2
–V
(b)
Fig. 9.7 (a) Magnetic rotor position sensor; (b) a typical Hall sensor consisting of
Hall generators, transistors, resistors, and inductors
738
Brushless Dc Motors
Hall generators positioned at the commutator switching positions would react
with the rotor field and produce the required position signals. Employing such
sensors has the following advantages. The number of sensors can be minimal.
Second, the output from a Hall generator is of the direct current type and so
does not need rectification. A disadvantage associated with this sensor is that an
auxiliary source is required to provide the current Ic . Second, like the magnetic
sensor, some output voltage is always present due to leakage flux, and this flux
builds up in a gradual manner. Owing to their availability with high ratings,
power transistors are used here as switches. Both n-p-n and p-n-p transistors are
connected as shown in Figs 9.6 and 9.7 to facilitate the flow of current in either
direction.
9.3.1
Optical Sensors
Figure 9.8 shows the schematic diagram of a typical optical sensor. A light shield
with an aperture is connected to the rotor and revolves around a stationary light
source. Photocells placed at the four switching points detect the commutation
positions for the motor. The output signals from the light detectors, which are
usually weak, are amplified before being used for operating the stator switches.
The signals can, however, be made to rise sharply and, being unidirectional
signals, they need no rectification.
From three
other
photocells
Electronic
switches
Amplifier
Photocell
Rotor
Light
shield
Light source
Fig. 9.8 A typical optical sensor
Optical sensors, being generally less robust than magnetic systems but much
smaller and lighter, are especially suited for aerospace applications.
9.4
Torque Production
In this section, the unidirectional torque production feature in the case of a
brushless dc motor is first examined for a sinusoidally operated two-phase,
brushless motor, and then extended to the three-phase, brushless, half-wave and
full-wave configurations.
Torque Production
9.4.1
739
The Sinusoidal-type Two-phase, Brushless Dc Motor
The sinusoidal-type two-phase, brushless dc motor (Murphy & Turnbull 1988)
is just a self-controlled synchronous motor with a permanent magnet rotor, as
shown in Fig. 9.9(a). It is designed in such a way that the torques generated in the
two phases are functions, respectively, of the sine and cosine of the rotor angle
[Fig. 9.9(b)].
Phase B
iB
N
q
iA
Phase A
S
(a)
TA
q
0°
90°
180°
270°
360°
TB
q
180°
360°
Shaft angle (elec. degrees)
(b)
Fig. 9.9 (a) Schematic diagram of a two-phase, brushless dc motor; (b) torque–
position waveforms
740
Brushless Dc Motors
Thus, they are expressed as
T A = KT iA sin θ
(9.1)
T B = −KT iB cos θ
(9.2)
where iA and iB are the instantaneous phase currents and KT is the torque constant
of each of the windings.
If iA and iB are also assumed to vary sinusoidally as functions of the shaft
position θ , they can be written as
iA = Im sin θ
(9.3)
iB = −Im cos θ
(9.4)
whereas Im is the amplitude of the phase current. Therefore, the torque
contributions of the two phases are
T A = KT Im sin2 θ
(9.5)
T B = KT Im cos2 θ
(9.6)
The resultant of these two torques, which are plotted in Fig. 9.9(b), is at an angle
θ and is given by
T = T A + T B = KT Im (sin2 θ + cos2 θ )
= KT Im
(9.7)
Equation (9.7) shows that the shaft torque is proportional to the amplitude of the
current (Im ), and that it is independent of the rotor position.
9.4.2
Three-phase, Half-wave, Brushless Dc Motor
The salient features of a three-phase, half-wave, brushless dc motor are given
in Fig. 9.10(a); its supply is obtained through an uncontrolled rectifier and a dc
link. The signals from the rotor position sensors are fed into the electronic control
circuitry, which in turn provides base drive signals to the switching devices. The
stator has a star-connected winding with its star point connected to the positive
terminal of the dc link. A practical version of this type of brushless dc motor,
used for large loads, contains freewheeling diodes across the windings to provide
an alternative path for the inductive load current. The torque versus rotor angle
characteristics of the individual phases are shown in parts (i)–(iii) of Fig. 9.10(b).
These waveforms have flat top portions with widths of 120◦ and thus contribute
to the useful shaft torque. If the motor phases are energized sequentially with
rectangular current pulses for the same 120◦ intervals as the flat tops of the torque
waveform, the motor develops a steady positive torque that is independent of
the shaft position. The phase currents for positive torque production in the three
phases are also shown in parts (iv)–(vi) of Fig. 9.10(b) and for negative torque
production in parts (vii)–(ix). Each motor phase current has a conduction angle
Torque Production
A
741
Stator
iC
iA
N
C
Rotor
S
iB
B
ac supply
Q1
Q2
Q3
Inverter
Full-wave
rectifier
dc link
Rotor
position
sensor
Electronic timing and base drive
circuitry
(a)
(i)
TA
q
TB
q
TC
q
(ii)
(iii)
I
iA
(iv)
q
I
iB
(v)
q
I
iC
q
iA
(vi)
(vii)
q
iB
q
iC
(viii)
(ix)
0
60 120 180 240 300 360
q
Shaft angle (elec. degrees)
(b)
Fig. 9.10 (a) Circuit of a three-phase, half-wave, brushless dc motor; (b) idealized
waveforms giving torque vs shaft angle characteristics for A, B, C phases;
currents in A, B, C phases for positive and negative torque
742
Brushless Dc Motors
of 120 electrical degrees. The torque can be expressed as
T = KT I
(9.8)
where KT and I are, respectively, the torque constant over the flat portion of
the trapezoidal torque waveform and the flat top magnitude of any phase current
waveform. The torque characteristic shows that a reversal of the torque magnitude
is possible by delaying the transistor conduction interval by 180◦ (elec). Each
phase conducts for a duration of 120◦ , in which the torque waveform has a negative
flat top, the current direction remaining unchanged. This capability of providing
negative torque makes the brushless dc motor advantageous over the conventional
dc motor. In the latter, torque reversal is possible only with the reversal of the
polarity of the voltage as well as the direction of the armature current.
Brushless dc motors with power ratings up to 100 W are widely used.
Applications for such a power range occur in turntable drives in record players,
spindle drives for hard-disk drives used in computers, and also in computer
peripheral equipment.
The torque function can be made smoother by designing a four-phase, halfwave system with a 90◦ conduction angle. For drive capacities above 100 W, the
stored inductive energy in the motor winding becomes significant and must be
returned back to the supply through diodes. Otherwise, it leads to a destructive
breakdown of the transistors at turn-off. A practical circuit for this purpose may
consist of a half- or full-wave system with feedback diodes. The latter is described
in detail below.
9.4.3
Three-phase, Full-wave, Brushless Dc Motor
Figure 9.11 shows a motor operated with a three-phase, full-wave circuit which
employs feedback diodes for recovering inductive energy. The star-connected
winding of the motor has no neutral wire and at any particular instant there is
conduction in two of the three phases. The idealized torque versus angle curves
are shown in Figs 9.12(a)–(c) with 60◦ flat-topped intervals. These are due to the
line-to-line dc currents from A to B, B to C, and C to A. The motor will always
operate in the constant torque region if the phase currents are of the quasi-square
wave nature with amplitude I as shown in Figs 9.12(d)–(f). These phase currents
are obtained by base triggering the transistors at 60◦ intervals in the sequence
in which they are numbered in the circuit of Fig. 9.11; the conduction angle is
120◦ . Each of the transistors in this circuit is switched on in response to the rotor
position sensor. It is seen from Fig. 9.12 that each motor phase conducts for a
total of 240◦ , with 120◦ conduction each for the positive and negative currents.
Thus, the winding utilization period is double that of the half-wave motor of
Fig. 9.10(a). A steady non-pulsating torque T equal to KT I is developed in this
brushless dc motor; the torque reversal is accomplished by shifting the base drive
signals by 180◦ . These two features remain the same as in the half-wave case.
The idealized current waveforms show that the phase currents are switched
instantly from one phase to the other. In practice, however, the inductive nature
of the load will delay both the build-up as well as the collapse of the currents.
743
Torque Production
Brushless dc motor
A
Q3
Q1
Rotor
N
C
Q5
S
A
B
ac
supply
Q4
Q6
Full-wave dc
link
rectifier
Q2
B
C
Stator
dc–ac three-phase inverter
Electronic timing
and
base drive circuitry
Rotor position
sensor
Fig. 9.11 Circuit of a three-phase, full-wave, brushless dc motor
(a)
TAB
q
TBC
q
TCA
q
(b)
(c)
I
iA
q
I
iB
q
iC
120 180 240
0
60
I
300 360
(d)
(e)
(f)
q
Shaft angle (elec. degrees)
Fig. 9.12 Idealized waveforms for a three-phase, full-wave, brushless ac motor
consisting of static torque vs shaft angle characteristics T AB , T BC , and T CA
and phase currents iA , iB , and iC
744
Brushless Dc Motors
Also, the practically obtained total torque function will have a fluctuating nature
(Fig. 9.13) as against the constant characteristic [T = KT I ] of the idealized
torque (Fig. 9.12).
5
4
T
3
2
1
0
0°
60°
120°
180°
q (elec. degrees)
Fig. 9.13 A typical practical waveform of total torque vs shaft angle for the threephase, full-wave brushless dc motor
9.5
Control of Brushless Dc Drives
The preceding discussion shows that the brushless dc motor operates as an inverted
dc motor, its special features being the permanent magnet field and an electronic
commutator. The basic principles remaining the same for these two types of
motors, the circuit equations as well as the equation for the torque produced in
the case of the brushless motor also remain the same as that for a dc motor. The
applied voltage is written as
di
dθm
+ KE
(9.9)
dt
dt
where i is the motor current, R and L are the resistance and inductance per phase
of the winding, dθm /dt is the angular velocity of the rotor, and KE (dθm /dt) is the
back emf term. The expression for the torque developed by the machine becomes
v = Ri + L
d 2 θm
dθm
+ Tf + Tld
+ F
(9.10)
dt 2
dt
where KT is the torque constant, J is the total inertial constant, F is the viscous
damping coefficient, Tf is the frictional torque, and Tld is the load torque. The
constant KT is numerically equal to KE in the international system of units (SI).
As stated earlier, the rotor position sensor, electronic circuitry, and the inverter
all put together constitute the electronic commutator. In addition, the dc link
voltage and link current correspond to the armature voltage and current in the
conventional dc motor. Speed control of the brushless dc motor can be effected
by varying the dc link voltage with the help of a dc chopper or a pulse width
modulated controller. The input voltage to the electronic commutator is thereby
varied and, in turn, this voltage causes variation of the motor speed.
T = KT i = J
Control of Brushless Dc Drives
745
The inner current control loop module that serves as a torque control feature
in conventional dc drives can also be implemented in brushless dc drives by
operating the dc link in the current controlled PWM mode. A better method is
to utilize the devices used in the inverter to regulate the amplitude of the motor
current by PWM control and effect the changeover from one phase to another
as per the signals obtained from the rotor position sensor. For this purpose, the
actual current signal is obtained either from the motor leads or from the dc link.
Current feedback can also be incorporated in a conventional PWM current control
loop. Current controller IC chips are now available, their circuit consisting of six
output power transistors, a PWM current control circuit, and a Hall logic decoder.
Thermal and under-voltage protection features are incorporated in such circuits.
9.5.1
A Typical Brushless Dc Drive
Figure 9.14 shows the schematic-cum-block diagram of a typical dc brushless
drive consisting of the inner current loop and the outer speed loop. The drive
consists of a three-phase uncontrolled bridge rectifier, a dc link together with an
LC filter, and a MOSFET-based voltage source inverter.
The shaft speed of the motor is measured using a tachometer and compared
with a reference speed to give the error in speed. The latter is fed into a PID
(proportional integral and derivative) controller, which generates the torque
signals. A limiter is provided to restrict this torque to the value of the reference
torque T ∗ . In addition, it limits the winding currents to the maximum permissible
value and also provides protection to the inverter switches. The reference current
generator then takes the T ∗ signal as well as the rotor position signals and produces
the signals IR∗ , IY∗ , and IB∗ based on the output of the limiter. The hysteresis
current controller uses these signals to give out control signals that operate the
inverter switches. The net effect is that this controller forces the winding current
to remain close to the reference current signals. Two salient features of this drive
are described below.
Bridge rectifier
dc link
Three-phase
ac supply
L
T
w *r
+
we
–
wr
LC filter
T*
Inverter
Permanentmagnet
dc motor
C
iR = – (iY + iB)
I *R
Reference I *
Y
current
generator
I *B
PID
Limiter
iR iY iB
Hysteresis current controller Position
sensor
Tachometer
Fig. 9.14 A typical closed-loop brushless dc drive
746
Brushless Dc Motors
9.5.1.1 Hysteresis Current Controller With the hysteresis controller
comparing the actual current with the command signal as described earlier, if
the magnitude of the error is greater than the present tolerance value, the inverter
is switched appropriately. There is a dead band, called the hysteresis band, within
which the inverter switches do not operate. Typical single-phase reference and
actual hysteresis currents are shown in Fig. 9.15. The following discussion holds
good for a trapezoidal current waveform also. The hysteresis current controller
operates separately on each phase, Fig. 9.15 showing the current in one phase.
Hysteresis
band h
Commanded
current
Actual
current
t
Fig. 9.15 Waveforms for hysteresis control
9.5.1.2 Inverter In the three-phase inverter circuit shown in Fig. 9.16, each
output line is held at the positive dc link voltage when the MOSFETs are switched
into conduction. On the other hand, when the inductive energy flows back into the
source through feedback diodes, this line is held at the negative link voltage. For
a given phase, the device that requires to be switched depends on both the sign
+
L
D1 M3
D3 M
5
D5
C
eA
eB
R
M4
D4 M6
D 6 M2
D2
M
R
M
M1
NO
vNO
eC
R
C
L
L
M
–
Fig. 9.16 MOSFET-based six-step inverter
Control of Brushless Dc Drives
747
of the error and that of the reference current I ∗ . For a hysteresis band of width
h, the algorithm for the current control of the inverter leg having MOSFETs M1
and M4 is as follows.
•
•
•
•
If I ∗
If I ∗
If I ∗
If I ∗
> 0 and I
> 0 and I
< 0 and I
< 0 and I
> (I ∗ + h/2), turn off M1 .
< (I ∗ − h/2), turn on M1 .
> (I ∗ + h/2), turn on M4 .
< (I ∗ − h/2), turn off M4 .
These steps hold good for other inverter legs also. Thus, the hysteresis current
regulator keeps down the machine winding currents so that they lie within the
specified band. A drawback of this controller is that the switching frequency of
the hysteresis is unknown and depends on the motor parameters, namely, speed,
and also the dc bus voltage. The frequency also varies over an electrical cycle.
The ideal shapes of the induced emfs and currents in the three phases are given
in Fig. 9.17.
eA
iA
eA, iA
2p /3
0
2p
q (rad)
eB
iB
eB, iB
0
p /3
2p /3
q (rad)
eC
iC
eC , iC
p /3
0
p
2p
q (rad)
Fig. 9.17 Ideal wave shapes of induced emfs and currents
748
Brushless Dc Motors
9.6
Other Current Controllers
Apart from the hysteresis current controller, some other types of current
controllers, detailed below, can be employed in the brushless dc drive.
9.6.1
Ramp Comparison Current Control
In this method, the current error is compared with a triangular reference waveform.
When the error is greater than the instantaneous magnitude of the triangular
waveform, the control signal switches the inverter devices (MOSFETs) on. Again,
when the error magnitude is lower, the devices are switched off. Figure 9.18 shows
a typical switching voltage waveform. The switching algorithm is as follows, with
the notation I meant for the reference current.
• If I ∗ > 0 and ierror > itriangle , turn M1 on or else turn M1 off.
• If I ∗ < 0 and ierror > itriangle , turn M4 on or else turn M4 off.
With an increase in the error, the appropriate MOSFET remains in conduction for
a longer time.
Sawtooth waveform
of itriangle
ierror
t
Switching voltage
t
Fig. 9.18 Waveforms for ramp comparison current control
9.6.2
Delta Current Control
In this strategy, the actual current is compared with the reference current at fixed
sampling intervals (that is, at delta frequencies), as illustrated in Fig. 9.19. The
inverter is then operated to change the sign of the current error.
A drawback of this method is that a shoot through fault can occur when a
turn-on delay occurs in the MOSFETs. To avoid this, protection is provided by
the method of non-complementary switching. It consists of switching on only that
MOSFET which corresponds to the sign of the reference current. For the inverter
of Fig. 9.16, only the MOSFET M1 will be turned on if the reference current is
positive. The other device on the leg (M4 ) will not be turned on as long as this
condition remains.
Other Current Controllers
749
Reference current
Actual current
t
Sampling
times
Fig. 9.19 Waveforms for delta current control
9.6.3
Space Vector Current Control
This method consists of using the space vector current error, which is defined
in the case of loads with the isolated neutral, to determine the inverter gating
signals. The space current vector is defined with reference to a two-dimensional
space as the complex quantity I , where
I = I R + aI Y + a 2 I B
(9.11)
and a = ej (2π/3) .
The two axes used are the real axis, which is coincident with the axis of
the R-phase, and an axis perpendicular to the R-axis. The effect is the same as
vectorially adding the phasors. The resultant can be used to decide about the
inverter gating signals, taking into account all the current errors simultaneously.
With an earthed neutral unfaulted system, I in Eqn (9.11) will be equal to
zero, whereas it is non-zero for an isolated neutral system. Its error with respect
to the reference current signal is denoted as I , and is termed as the space vector
current error. Thus,
I = I −I
∗
∗
(9.12)
where I is the reference current vector.
If this vector I is drawn, then a line drawn parallel to the X-axis at its tip
defines one of the hysteresis boundaries (Fig. 9.20). The mirror reflection of this
line about the X-axis constitutes the second hysteresis boundary. It is shown
below that due to the absence of the neutral, the dependency between the phases
causes the space current error vector to exceed the hysteresis boundary whenever
the largest individual phase error exceeds two-thirds of the hysteresis boundary.
Apart from the space current error vector defined above, the two other variables
of interest for the following derivation are (i) the component of I in the direction
of the R-phase, namely, ( I )R , and (ii) the individual phase error in the direction
750
Brushless Dc Motors
Y-axis
Hysteresis
boundaries
IR
DI
X-axis
IB
IY
Fig. 9.20 Current vectors for space vector current control
of the R-phase, namely,
I =
The component of
I R . It can be shown that
√
1
3
( IY −
IR − ( IY + IB) + j
2
2
IB)
(9.13)
I in the R-axis direction is
1
IR − ( IY +
2
( I )R =
IB)
(9.14)
Noting that
IR +
IY +
IB = 0
(9.15)
we get,
IR = − ( IY +
IB)
(9.16)
Therefore,
( I )R =
IR +
1
3
IR =
IR
2
2
(9.17)
or
IR =
2
[( I )R ]
3
(9.18)
Similarly, for ( I )Y and ( I )B , Eqn (9.18) confirms the above proposition.
After checking the above condition simultaneously in all phases, the space
current error is used to determine the inverter gating signals. That is, after
comparing the space current error vector with the hysteresis band, the controller
applies the voltage vector which is nearest to the current error vector to the
corresponding machine winding.
9.7
Recent Trends
The design of brushless dc motors is an area towards which considerable research
and development effort has been directed. Three aspects in which progress has
been made are elaborated below.
Brushless Dc Motors Compared with Other Motors
9.7.1
751
Materials used for the Permanent Magnet
The brushless dc motor consists of a permanent magnet rotor and hence the
material used for this magnet requires special attention. Research in magnet
technology has led to the use of samarium–cobalt rare-earth material as a magnetic
material because it has a very high energy product and high coercivity. A
consequence of this is that smaller sizes of magnets can be placed on the rotor,
making the inertia of the rotor smaller compared to that of a dc brush motor of the
same capacity. Thus, dc brushless motors can have higher torque/inertia ratios as
compared to their counterparts of the same capacity.
9.7.2
Alternative Methods for Rotor Position Sensing
The rotor position sensor is one of the costlier components of the brushless motor,
and hence its elimination reduces the complexity of construction of the motor.
Using the machine terminal voltages for estimating the rotor position is one such
method that has been developed and found to give fairly accurate results.
9.7.3
Estimation of Winding Currents
Instead of direct measurement, winding currents are estimated by measuring
the dc link current and constructing an observer. The observer also utilizes
information on power device switching patterns to estimate the dc link current. At
appropriate intervals in the switching cycle, information regarding the estimated
as well as the actual dc link currents is used to correct any error in observer
estimation.
9.8
Brushless Dc Motors Compared with Other Motors
The brushless dc motor has some features that are common with each of the
following machines:
(a) the conventional brush dc motor,
(b) the inverter-driven induction motor, and
(c) the brushless sinusoidally operated synchronous motor.
To highlight its merits as well as demerits, a comparison of the brushless dc
motor with these machines is carried out below.
9.8.1
Brushless Dc Motor Versus Brush Dc Motor
The disadvantages of the mechanical commutator used with a conventional dc
motor are as follows.
(i) The commutator along with its brushes is subjected to sparking, causing
interference with electrical signals. This also leads to a reduction of its
lifespan.
(ii) The commutator is mounted on the shaft, alongside the rotor so as to permit
the brushes to be stationary. This limits the speed of the motor and also its
power output.
752
Brushless Dc Motors
(iii) It needs a high ratio of diameter to length of the armature iron, thus limiting
the machine design.
(iv) Copper, which is the material used for the commutator, softens at higher
temperatures and this feature limits the current rating of the machine.
(v) It is subject to environmental features such as dirt and moisture.
(vi) A substantial amount of heat dissipation occurs in the rotor because of the
presence of windings in it.
The brushless dc machine, on the other hand, does not have any heat-producing
elements. The ‘inside-out’ construction of the machine permits increased heat
dissipation, because the heat-generating windings are close to the stator surface,
thus facilitating natural cooling. These positive features permit higher current
ratings and greater steady-torque outputs than the traditional dc machines of
the same size. Moreover, it retains the advantages of the conventional dc
motor, namely, high starting torque and fairly high efficiency at all speeds. An
advantageous feature present in small-sized, brushless dc motors is that they
have smoother torque versus angle characteristics. This can be explained as
follows. Small-sized mechanical commutator dc motors have a smaller number
of commutator segments and consequently give a fluctuating torque versus
angle characteristic. As against this, the brushless dc motor with a four-segment
electronic commutator gives a much smoother torque function, using its switches
in an amplification mode. Any residual torque ripple can be suppressed by
closed-loop operation by means of speed feedback, which also enables the motor
to have excellent low-speed performance.
9.8.2
Brushless Dc Motor Versus Induction Motor
The brushless dc motor gives a performance similar to that of an induction motor
driven by an inverter. These two machines have similar constructional features
also, the induction motor being simpler due to the absence of rotor position
sensors. The most important difference is as follows: the frequency at which
the inverter (that is, the stator) switches operate in the brushless dc motor is
determined by the rotor speed, which is sensed by the rotor position sensors; this
rotor speed in turn depends on the winding currents. In the inverter-controlled
induction motor, the switching frequency totally relies on the frequency of the
oscillator present in the inverter. This controls the rotating field in the air gap;
the rotor merely follows this field. It can be inferred from this that the speed of
an induction motor can therefore be controlled by varying the inverter frequency.
This feature simplifies the operation of the induction motor. Other disadvantages
of the brushless dc motor are as follows.
(i) In addition to the motor leads (as in the induction motor), the leads from the
position sensor have also to be brought out, and they may be subjected to
interference from external signals.
(ii) It takes a larger starting current and this current surge may demagnetize
the permanent magnet. The current surge magnitudes are, however, less
Summary
753
significant in smaller motors which have higher impedances for their
windings.
(iii) Since the operation of the inverter that feeds an induction motor is
independent of the motor, several motors can be connected at its output.
The implementation of this feature is not feasible in a brushless dc motor.
9.8.3
Brushless Dc Motor Versus Brushless Synchronous Motor
Whereas the rotor sensing apparatus in the case of the trapezoidal brushless dc
machine consists of simple position sensing devices like the Hall effect devices,
the sinusoidal type of brushless synchronous motor needs more precise position
transducers so as to accurately synthesize the sinusoidal current waveforms. The
total torque in the latter is directly proportional to the current, but the torque
function in the brushless dc machine is slightly fluctuating. It can, however, be
improved by closed-loop control. Except for these differences, the operational
aspect of both these machines can be considered to be similar.
Summary
The brushless dc motor is an ac motor with operation similar to that of a
conventional dc motor, with the exception that the mechanical commutator in
the latter machine is replaced by an electronic commutator. This commutator
consists of a rotor position sensor, electronic switching circuitry, and an inverter.
This combination helps in the production of a unidirectional torque similar to that
in a dc motor. A three-phase, full-wave inverter gives better performance than a
half-wave circuit. In a typical closed-loop brushless dc drive, speed control is
achieved by varying the dc link voltage, whereas current can be controlled by
operating the dc link in a current controlled PWM mode.
The hysteresis as well as some other types of current controllers help in
maintaining the machine winding currents close to their specified values.
Since the rotor position sensor is a costly module, indirect methods of
estimating this position have been found to give fairly accurate results. Likewise,
indirect methods for measuring winding currents have proved to be reliable.
While the brushless dc motor gives a performance comparable to the
conventional dc motor, the cumbersome commutator of the latter can be replaced
by the more compact electronic commutator. Thus, for the same size of the
machine, the brushless motor has higher current ratings and can hence provide
greater steady-torque output.
The brushless dc drive system broadly conforms to the induction motor
drive. The two drives differ in the following feature. Whereas the speed of the
conventional induction motor drive can be controlled by varying the inverter
frequency, the signals from the rotor position sensor decide the inverter switching
instants and hence the speed of the brushless dc drive.
The brushless dc motor is superior to the brushless synchronous motor because
of the simplicity of its rotor position sensor.
754
Brushless Dc Motors
Exercises
Multiple Choice Questions
1. The construction of a brushless dc motor is identical to that of a
.
(a) brush dc motor
(b) stepper motor
(c) induction motor
(d) self-controlled synchronous motor with a permanent magnet rotor
2. The self-controlled synchronous motor is supplied with
excitation,
excitation.
whereas the brushless dc motor is supplied with
(a) sinusoidal current, sinusoidal current
(b) quasi-square wave current, sinusoidal current
(c) sinusoidal current, quasi-square wave current
(d) quasi-square wave current, quasi-square wave current
3. For optimum performance, a
electronic commutator has to be used in
a brushless dc motor.
(a) six-segment
(b) two-segment
(c) four-segment
(d) eight-segment
4. The
sensor is preferred for rotor position sensing in a brushless dc
motor.
(a) optical sensor
(b) Hall effect sensor
(c) magnetic sensor
(d) electromagnetic
5. In a three-phase, full-wave, brushless dc motor, the conduction period of the
, and each motor phase winding conducts for
.
transistors is
(a) 240◦ , 240◦
(c) 120◦ , 240◦
(b) 240◦ , 120◦
(d) 120◦ , 120◦
6. In ramp comparison current control, the output goes
when the error
exceeds the instantaneous value of the triangular waveform, whereas it goes
when the error is less than the instantaneous value.
(a) high, low
(b) low, low
(c) low, high
(d) high, high
7. The conventional brush dc machine has a limited current rating because
.
(a) the commutator along with its brushes is subjected to sparking
(b) the material used for the commutator softens at higher temperature
(c) the commutator is subjected to environmental features such as dirt and
moisture
(d) the commutator is mounted on the shaft by the side of the rotor
8. Any slight torque ripple at the shaft of the brushless dc motor can be suppressed
by
.
(a)
(b)
(c)
(d)
closed-loop operation by means of speed feedback
inserting an inductor in the stator circuit
using damper windings on the rotor
using special magnetic materials for the rotor
Exercises
755
9. The inverter supplying a brushless dc motor cannot have a multimotor output
because
.
(a) the leads from the position sensor may be subjected to interference from
external signals
(b) the motor load takes a larger starting current and this current may
demagnetize the permanent magnet
(c) the inverter cannot operate independently of the rotor
(d) the heat-generating windings are close to the stator surface
, and in a brushless
10. In a brushless dc motor the total torque is
.
synchronous motor the total torque is
(a) directly proportional to current, slightly fluctuating in nature
(b) inversely proportional to current, slightly fluctuating in nature
(c) slightly fluctuating in nature, highly fluctuating in nature
(d) slightly fluctuating in nature, directly proportional to current
11. In an earthed neutral unfaulted three-phase system, the current given by the
expression I = (2/3)(IR + aIY + a 2 IB ), where a = ej (2π /3) , is
, and
.
in an isolated neutral unfaulted three-phase system it is
(a) non-zero, non-zero
(c) zero, zero
(b) zero, non-zero
(d) non-zero, zero
True or False
Indicate whether the following statements are true or false. Briefly justify your choice.
1. The construction of a brushless dc motor is identical to that of a self-controlled
synchronous motor.
2. The self-controlled synchronous motor is supplied with quasi-square wave
current and the brushless dc motor is supplied with sinusoidal current.
3. For optimum performance, a four-segment electronic commutator has to be
used in a brushless dc motor.
4. The electromagnetic sensor is preferred for rotor position sensing in a brushless
dc motor.
5. In a three-phase, full-wave, brushless dc motor, the conduction period of the
transistors is 240◦ , whereas each motor phase winding conducts for 120◦ .
6. In ramp-comparison current control, the output goes high when the error
exceeds the instantaneous values of the triangular waveform, whereas it goes
low when the error is less than the instantaneous values.
7. The conventional brush dc machine has a limited current rating because the
commutator, along with its brushes, is subjected to sparking.
8. Any slight torque ripple occurring in the brushless dc motor can be suppressed
by closed-loop operation using speed feedback.
9. The inverter supplying a brushless dc motor cannot have a multimotor output
because the motor load takes a large starting current and this current may
demagnetize the permanent magnet.
10. In a brushless dc motor the total torque is directly proportional to current,
whereas in a brushless synchronous motor the total torque is slightly fluctuating
in nature.
756
Brushless Dc Motors
11. In an earthed neutral unfaulted three-phase system, the current given by the expression I = (2/3)(IR + aIY + a 2 IB ), where a = ej (2/3) , is non-zero, whereas
in an isolated neutral unfaulted three-phase system it is zero.
Short Answer Questions
1. Describe the constructional features of a brushless dc motor.
2. In what aspects does the sinusoidal brushless dc motor differ from the
trapezoidal motor.
3. Explain how the supply to the stator winding of a brushless dc motor is switched
with electronic components so as to develop a unidirectional torque.
4. Explain the principle of the Hall effect and describe a method for rotor position
sensing using Hall generators.
5. With the help of a schematic diagram and waveforms, explain the operation
of (i) a three-phase, half-wave, brushless dc motor and (ii) a three-phase, fullwave, brushless dc motor.
6. Describe the different modules of a typical closed-loop brushless dc drive
system.
7. Explain the operation of a hysteresis current controller.
8. Explain the principle of (a) a ramp comparison current controller, (b) a delta
current controller, and (c) a space vector current controller.
9. What are the three important aspects of the modern brushless dc drive which
have been improved by R & D effort?
10. Compare and contrast a brush dc motor with a brushless dc motor.
11. Compare and contrast a brushless dc motor with an induction motor.
12. Compare and contrast a brushless synchronous motor with a brushless dc motor.