Motors for Mechatronics
An Introduction
Dr. Kevin Craig
Professor of Mechanical Engineering
Rensselaer Polytechnic Institute
Motors for Mechatronics – An Introduction
K. Craig
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Introduction to Motors
• The actuator in a motion control system is the component that
delivers the motion. It is the component that delivers the
mechanical power which may be converted from an electric,
hydraulic, or pneumatic power source.
• Here we study the two power-conversion components: the
electric motor and the drive. The drive is the poweramplification and power-supply components that work with
the motor; it controls current to produce torque.
• We focus on motor-drive technologies that can be used in
high-performance motion control applications, i.e., involving
closed-loop position and velocity control with high accuracy
and high bandwidth.
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• The focus will be on:
– Brushed DC Motors
– Brushless DC Motors
– Stepper Motors (permanent magnet, hybrid, and variable
reluctance)
• Shown are the typical motor control functions to be implemented
in a motor – drive – sensor system
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• What is a Servo System?
– A servo system is the drive, motor, and feedback device that
allows precise control of position, velocity, or torque using
feedback loops.
– Stepper motors allow precise control of motion, but they are
not servos because they most often run open-loop.
– The most easily recognized characteristic of servo motion is
the ability to control position at high bandwidths.
– However, there are servo applications that do not require fast
acceleration, e.g., web-handling applications process rolled
material and usually attempt to hold velocity constant in the
presence of torque disturbances.
– Servos must have feedback signals to close control loops,
either independent (e.g., encoder and resolver) or intrinsic
(e.g., motor current), often called sensorless (a misnomer).
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• The operating principle of any electric motor involves one
or more of the following three physical phenomena:
– Opposite magnetic poles attract and like magnetic poles
repel.
– Magnets attract iron and seek to move to a position to
minimize the magnetic reluctance (analogous to electrical
resistance) to the magnetic flux (analogous to electrical
current).
– Current-carrying conductors create an electromagnet and
act like a current-controlled magnet.
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• Consider the electromagnet shown below.
– The magneto-motive force (analogous to electrical voltage)
is mmf = ℑ = Ni
– N is the number of turns of coil and i is the current
– The flux path is through the iron core and back through the
air to complete the magnetic circuit
– Note the right-hand rule for flux
ℜ total = ℜcore + ℜair
Electrical / Magnetic Circuit Analogy
ℑ = Ni magnetomotive force
V⇔ℑ
V = iR
Ac
reluctance
ℜ=
i⇔Φ
ℑ = Φℜ
μA
R⇔ℜ
1
= permeance
ℜ
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• Below steel has been substituted for air in the return path; this
material is called back iron.
– The reluctance of the magnetic circuit may be reduced
thousands of times compared to the previous case where
the flux return path was air.
• In all magnetic circuits, some flux escapes the core and this is
called fringing. Also the permeability of steel and other
magnetic materials declines as the applied field increases.
This is called saturation.
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• Servomotors
– The key characteristic of a servomotor is the ability to
provide precise torque control.
– Ideally, the output torque of a servo system should be
highly responsive and independent of motor position and of
speed across the system’s entire operating speed range.
Most servomotors are close enough to this ideal that simple
models for servo systems can be based on this assumption.
– More accurate models of servomotors show torque
declining as speed increases due to increased loses due to
windage and bearing friction, brush commutator
limitations, and current controller limitations.
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• Servomotor Torque Ratings
– A motor’s peak torque is the maximum torque it can
generate for a short period of time (usually one to two
minutes).
– The continuous torque indicates how much torque the
motor can generate over an indefinite period of time.
– These represent thermal limits in the motor. When a motor
outputs power, it does so with less than 100% efficiency.
Most power that is lost in the motor is lost to heat and that
drives up motor temperature. Excessive temperature in the
motor will degrade lubricants and winding insulation.
Limiting torque output (both peak and continuous) protects
the motor by limiting its internal temperature. In addition,
exceeding a motor’s peak torque can permanently
demagnetize the magnets.
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– The torque-speed curve given by a motor manufacturer is
static; it does not specify the length of time a motor-drive
system requires to produce that torque. In most servo
systems, the limit to torque responsiveness is the
responsiveness of the current loop, which is bandwidth
limited by stability requirements, as are all control loops.
The bandwidth of current loops varies from 300 Hz to 2500
Hz in servo systems.
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• Each motor has the following components:
– Rotor on a shaft (moving component)
– Stator (stationary component)
– Housing (with end plates for rotary motors)
– Bearings to support the rotor in the housing with allowance
for some axial play between the shaft and the housing
• Commutation means the distribution of current into
appropriate coils of a motor as a function of rotor position.
– Brush-type motors have a commutator and brush assembly
to direct current into the proper coil segment as a function
of rotor position.
– Brushless motors have some type of rotor position sensor
for electronic commutation of the current (e.g., Hall effect
sensor or incremental encoder).
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• Traditionally AC induction motors have been used in constantspeed applications, whereas DC motors have been used in
variable-speed applications. With the advances in solid-state
power electronics and digital signal processors, an AC motor can
be controlled in such a way that it behaves like a DC motor (e.g.,
using field-oriented vector control in the drive for current
commutation).
• An electric motor converts electrical power to mechanical power.
The input to the motor is in the form of voltage and current, and
the output is mechanical torque and speed. The key physical
phenomenon in this process is different for various motors.
– DC Motors:
• DC motors have two magnetic fields. In brush-type
motors, one of the magnetic fields is due to the current
through the armature winding on the rotor.
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• The other magnetic field is due to the permanent magnets
in the stator (or due to field excitation of the stator
winding if electromagnets are used instead of permanent
magnets).
• In the case of brushless DC motors, the roles of the rotor
and stator are swapped.
• When two magnetic field vectors are perpendicular,
maximum torque is generated per unit current.
– AC Induction Motors
• In AC induction motors, the first magnetic field is set up
by the excitation current on the stator. This magnetic field
in turn induces a voltage in the rotor conductors by
Faraday’s induction principle. The induced voltage at the
rotor conductors results in current which in turn sets up its
own magnetic field, the second magnetic field.
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• The torque again is produced by the interaction of the two
magnetic fields. In the case of a DC Motor and an AC
induction motor (with field-oriented vector control), the
two magnetic fields are always maintained at a 90 degree
angle in order to maximize the torque generation
capability per unit current. This is accomplished by
commutating the stator current (mechanically or
electronically) as a function of the rotor position.
– Stepper Motors
• Stepper motors (permanent magnet type) work on
basically the same principle as brushless DC motors,
except that the stator winding distribution is different. A
given stator excitation state defines a stable rotor position
as a result of the attraction between electromagnetic poles
of the stator and permanent magnets of the rotor.
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• The rotor moves to minimize the magnetic reluctance.
At a stable rotor position of a step motor, two magnetic
fields are parallel.
• In the case of a variable (switched) reluctance stepper
motor, the rotor is not a permanent magnet, but a soft,
ferromagnetic material such as iron. As the
electromagnetic pole state of the stator changes by
changing the current in stator winding phases, the rotor
moves to minimize the magnetic reluctance while it is
being temporarily magnetized by the stator’s field.
• The torque generation (electrical energy to mechanical energy
conversion process) in any electric motor can be viewed as a
result of the interaction of two magnetic flux density vectors:
one generated by the stator and one generated by the rotor.
These vectors are generated differently in different motors.
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– In a permanent magnet brushless motor, the magnetic flux
of the rotor is generated by permanent magnets and the
magnetic flux of the stator is generated by current in the
windings.
– In the case of an AC induction motor, the stator magnetic
flux vector is generated by the current in the stator winding,
and the rotor magnetic flux vector is generated by induced
voltages on the rotor conductors by the stator field and the
resulting current in the rotor conductors.
• It can be shown that the torque production in an electric motor
is proportional to the strength of the two magnetic flux vectors
(stator’s and rotor’s) and the sine of the angle between these
two vectors. The proportionality constant depends on the
motor size and design parameters.
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• Every motor requires some sort of current commutation by
either mechanical means, as in the case of a brush-type DC
motor, or by electrical means, as in the case of a brushless DC
motor. Current commutation means modifying the direction
and magnitude of current in the windings as a function of the
rotor position. The goal of the commutation is to give the
motor the ability to produce torque efficiently, i.e., maintain he
angle between the two magnetic flux density vectors at 90º.
• Electric motors can act either as a motor (convert electrical
power to mechanical power to drive loads) or as a generator
(convert mechanical power to electrical power when driven
externally by the load).
– When the mechanical power output (product of torque and
speed) is positive (torque and speed in the same direction),
the motor is the in the motoring mode.
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– When the motor takes mechanical energy from the load
instead of delivering mechanical energy to the load, the
mechanical power output is negative and the motor is in the
generator mode or regenerative breaking mode. This energy
can either be dissipated in the motor-drive combination,
stored in a battery or capacitor set, or returned to the supply
line by the drive.
– There are two different motion conditions where regenerative
energy exists and the product of torque and speed is negative:
• During deceleration of a load when the applied torque is in
opposite direction to the speed
• In load-driven applications, i.e., in tension-controlled webhandling applications where a motor is used to apply a
torque opposite to the direction of motion of the motor and
web in order to maintain a desired tension
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• Another load-driven application is the case where the
gravitational force provides more than needed force to
move an inertia and the actuator needs to apply force in
the direction opposite to the motion in order to provide a
desired speed.
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• Coil Winding
– Col winding (either on the stator as in the case of a
brushless DC motor and stepper motor, or on the rotor as in
the case of a brush-type DC motor) determines one of the
magnetic fields essential to the operation of a motor.
– There are two types of windings in terms of the spatial
distribution of a wire on the stator:
• Distributed winding (brushless DC motor) where each
phase winding is distributed over multiple slots and one
phase winding has overlaps with the other windings.
• Concentrated winding where a particular winding is
wound around a single pole (stepper motor).
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Winding Types on the Stator
Distributed Winding
Motors for Mechatronics – An Introduction
Concentrated Winding
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– In a concentrated winding, one coil is placed around a
single tooth. By controlling the current direction in that
particular coil, magnetic polarity (N or S) of that tooth is
controlled. Hence, a desired N and S pole pattern can be
generated by controlling each coil current direction and
magnitude.
– In distributed winding, there are many variations on how to
distribute the coils. The most common type is a threephase winding, and each slot has two coil segments. The
coil can be distributed to generate two pole, four pole, eight
pole, etc. on the stator at any given current commutation
condition. By controlling the current in each phase, both
magnitude and direction of the magnetic field pattern are
controlled.
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Permanent Magnet
DC Motor
Types
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Components of a Brush-Type DC Motor
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DC Motor
Operating Principles
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Commutation
and
Torque Variation
as a function of
Angular Position
of the
Rotor
Torque ripple magnitude
and frequency are a
function of the number of
commutation segments.
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DC Motor Types
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• Permanent-Magnet (PM) Brush Motors
– Motors create torque with flux from two different sources:
the armature and the field.
– In permanent-magnet motors, the field flux ΦF is created by
magnets, as shown for a four-pole brush motor. Rotor
armature windings are not shown.
The magnetic circuit
reluctance for each of
the 4 circuits is the
sum of the
reluctances of the
magnets, the back
iron (steel on the
outside of the stator),
the rotor steel, and
the air gap.
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– The second flux that must be created for torque is that from
the armature windings. Shown is the flux ΦT created from
the armature windings in a four-pole brush motor.
– The flux travels from the rotor between the magnets,
through the back iron, and then again between the magnets
to return to the rotor.
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– The armature of a brush motor has many windings, and only
some portion of those windings is excited with current when
the motor is in any one position.
– Commutation is the process of selecting the proper windings
in a given rotor position and brush motors use mechanical
commutation so that the drive needs no knowledge of motor
position to regulate torque.
Brush Motor
showing
Commutator
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– Electromagnetic torque is created by the interaction of the
field flux and the armature flux and is proportional to both:
TE ∝ ( Φ T )( Φ F ) sin Θ E
– ΘE is the electrical angle between the field and armature
flux. The diagram below shows both fluxes (only air-gap
fluxes shown).
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– The relationship between the mechanical angle and the
electrical angle is given by:
# Poles
ΘE =
ΘM
2
– In the situation presented, the angle between the two flux
vectors is 90º electrical, which is equivalent to 45º mechanical
for this 4-pole motor.
– In any given position, torque is created by producing current
in one or more of the windings. The winding must be
selected so that ΘE remains at or near 90º electrical.
– For brush PM motors, the commutation angle (difference
between ΦF and ΦT) is fixed by the placement of the brushes
on the commutator. As the rotor rotates, the commutator,
which is fixed to the rotor, rotates and switches in the winding
set that maintains the commutation angle at about 90º.
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– For a brush PM motor, the torque output is approximately
proportional to the armature current. This can be shown as
follows:
TE ∝ ( Φ T )( Φ F ) sin Θ E
TE ∝ ( Φ T )( Φ F )
Θ E = 90D
TE ∝ ( Φ T )
Φ F ≈ constant
ℑ
ℜ
TE ∝ ℑ
ℑ
ℜ
ℜ ≈ constant
TE ∝
ΦT =
TE ∝ Ni
ℑ = Ni
TE ∝ i
N = constant
TE = K T i
K T = motor torque constant
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– The constant KT is an approximation. It usually falls as the
current increases because of saturation of the steel in the
path of the armature flux. This effect causes the average
reluctance of the armature-flux path to increase, reducing
the flux created by the magneto-motive force.
– The effective torque constant at peak current will be lower
than that at low current, often by a factor of 20% or more.
– Since magnets usually weaken at high temperature, the
torque constant may fall another 10% or so at peak
operating temperature.
– Back EMF is the phenomenon in which a PM motor
generates a voltage proportional to rotor speed (generator
action). The constant of proportionality is KB. KB is
proportional to KT. When using SI units, KB = KT.
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– Back EMF is an undesirable although unavoidable effect in
servomotors; it subtracts from the current-generating
voltage applied from the controller. It limits the top speed
of the motor for a given applied voltage because when the
speed produces enough back emf, the power stage no
longer has sufficient voltage to force current into the
armature.
– Other factors within the motor reduce the voltage that can
be applied to generate current; resistive losses, especially
when large currents are applied to the motor; inductive
losses occur when the current is changing, especially
changing rapidly.
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– Brush motors are relatively easy to control because the
commutation is mechanical.
– As shown below, servo controllers generate a torque
command which is scaled by the estimated torque constant to
create an armature-current command. A current controller
processes the difference of the commanded and sensed
current to generate a command voltage, which is converted to
an actual voltage through pulse-width modulation. The
modulated voltage is applied to the motor to generate actual
current, which, when scaled by KT, generates torque.
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– The diagram below is an expanded view of the PM Brush
Motor Control. KM is the approximate linear constant of
the modulation process.
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• Note on Pulse Modulation
– Pulse modulation uses time averaging to convert digital
signals to analog signals.
– The two most common forms of pulse modulation are
shown below: Pulse Width Modulation (PWM) and Pulse
Period Modulation (PPM).
– Both output pulses are smoothed by the output element so
that a digital signal is converted to an analog signal.
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– The smoothing is often the implicit integration of the plant. If
an inductor is the output element, a pulsed voltage waveform
is smoothed by the inductor to produce an analog current.
– Pulse modulation is used because it greatly reduces the power
losses in the transistor. Since the transistor is digital – either
on or off – power losses in the transistor are minimized.
That’s because when the transistor is off, the current is low,
and when it’s on, the voltage is low; in either case, the
conduction loses (product of voltage and current) remain low.
– The primary disadvantage of pulse modulation techniques is
the creation of undesirable harmonics in the output. For
inductor-based current control, harmonics in the output
voltage create harmonics in the current called ripple.
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– These harmonics create problems such as audible noise. In
addition, the fast voltage transients generated by the switching
transistors cause electromagnetic interference (EMI). The
amplitude of output harmonics is reduced by increasing the
modulation frequency; however, this usually increases EMI.
– It is important to note that the time to turn off a power
transistor is longer by a few microseconds than to turn one on.
Because turn-off time is longer, if a transistor is commanded
to turn on simultaneously with its opposite being commanded
to turn off, both transistors will be on for a short time. Even
though the time is brief, a large amount of current can be
produced because two transistors being on simultaneously
will connect the positive and negative voltage supplies.
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– The normal means of assuring that the transistors will not
be on simultaneously is to have a short time period in
which it is guaranteed that both transistors will be off. This
time results in a small deadband.
– For the control system, modeling modulation usually
requires only knowing the relationship between the
command to the modulator and the average output of the
modulator; harmonics can be ignored in most cases as they
have little impact on traditional measures of control
systems. Most pulse-width modulators are approximately
linear with some deadband; if the deadband is small enough
to ignore, only a constant of linearity need be derived. In
the simplest case, the constant is the output span divided by
the input span.
– End of Note on Pulse Modulation
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– Voltage modulation is the process of converting a voltage
command to a series of on-off, high-voltage pulses.
Modulation is used because power transistors are most
efficient when they are fully on or fully off. When a
transistor is fully off, there is no current flow (no power
lost). When a transistor is fully on, there is a small voltage
drop, typically < 2 volts (small power lost even with high
current).
Four-Transistor
H-Bridge
allows both
+ and –
voltages to be
applied to the
winding
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– The pulsed inputs to the power transistors connect the Aphase to either UBUS (when A+ is on) or ground (when Ais on). This switching of A-phase drives current in and out
of the winding, as shown below. This assumes that the Bphase is held at zero. The current ripple results because the
current is pulsed. Modulation methods rely on motor
inductance to smooth the current produced by pulsed
voltages.
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– The most common modulation technique used is pulsewidth modulation (PWM). This method outputs voltage
pulses at a fixed frequency and then varies the width of the
pulse to increase or decrease the average applied voltage.
– The ripple in the current waveform is small if the
modulation frequency is high relative to the inductance of
the motor. A PWM frequency of 8 to 16 kHz will usually
work well for an iron-core motor with inductance in the 550 mH range. For an air-core motor, with inductance just a
few µH, a PWM frequency as high as 100kHz may be
required. If the PWM frequency is too low for a motor
inductance, the magnitude of ripple current will be
excessive. This ripple generates heat without generating
torque. It also can vibrate the windings, causing audible
noise.
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Brush-Type DC Motor Drive:
PWM Amplifier with Current Feedback Control
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– Note that the H-bridge amplifier uses four power transistors.
When controlled in pairs (Q1 and Q4, Q2 and Q3), it changes
the direction of the current, hence the direction of generated
torque.
– Note that the pair Q1 and Q3 or the pair Q2 and Q4 should
never be turned ON at the same time because it would form a
short-circuit path between supply and ground.
– The diodes across each transistor serve the purpose of
suppressing voltage spikes and provide a freewheeling path
for the current to follow. Large voltage spikes occur across
the transistor in the reverse direction due to the inductance of
the coils. If a current flow path is not provided, the transistors
may be damaged. The diodes provide the alternative current
path for inductive loads and lets current pass through the coil.
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Carrier signal is a highfrequency triangular signal.
The input signal is an analog
signal value. The output pulse
has fixed frequency, which is
the carrier frequency. The ON /
OFF pulse width is varied as a
function of the value of the
input signal relative to the
carrier signal. By modulating
the ON-OFF time of the pulse
width at a high switching
frequency, a desired average
voltage can be controlled.
Here, when the analog input
signal is larger than the carrier
signal, the pulse output is ON,
when it is smaller, the pulse
output is OFF.
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PWM Circuit Function
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– Brush motors have many strengths:
• Commutation is mechanical so that control is simple.
• Only a single current sensor is required where other
servomotor types usually require two.
• Fewer power transistors are required, usually four instead of
six required by brushless motors.
• Smooth torque is generated in large measure because offsets
in current sensors (very common) do not result in torque
ripple; they do cause ripple in brushless motors.
– Brush motors also have weaknesses:
• Brushes wear, especially when exposed to contaminants.
• When the commutator disconnects windings carrying heavy
current, arcing results, which can generate substantial
electrical noise.
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• Brush motors are usually larger than equivalent
brushless motors because of the space taken by the
commutator assembly.
• The armature, where most of the loses are generated, is
on the rotor, which is usually inside the stator and thus
more difficult to cool.
• The commutator is complex to manufacture.
• Bushes riding on the commutator generate audible noise
at higher speeds and also lose efficiency because of
brush friction and because the voltage drops across the
brush-commutator interface, both of which dissipate
power.
• Because of mechanical commutation, the top speed of
brush motors is limited.
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• The rotor of a brush motor is heavier than its brushless
equivalent because the windings are wound around a
steel core; so the steel and copper wire add considerable
inertia. In brushless motors, the magnets rotate; the
brushless magnet assembly is light compared to a brush
motor armature. Light inertia is often an advantage in
servo applications where high acceleration is required.
Reducing the motor inertia while providing the same
torque often allows a smaller motor to do the same job.
– Brushless motors can provide as much as ten times the
torque of a brush motor with the same rotor inertia.
– Brush motor control systems are low cost and are attractive
for cost-sensitive applications, especially in low-power
applications where cost of control is a large factor.
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– It should be noted that disk-style brush motors offer the
simplicity and smooth torque of brush motors while
enjoying comparatively light rotors and long brush life.
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• Brushless DC Motor
– The brushless DC motor is sometimes refereed as a
synchronous AC permanent magnet motor.
– It has a wound stator, a permanent magnet rotor assembly,
and rotor-position sensing devices.
– The sensors provide signals for electronically switching
(commutating) the stator windings in a proper sequence so
as to maintain rotation of the magnet assembly.
– It substitutes electronic commutation for the conventional
mechanical brush commutation.
– Electronic commutation in a brushless DC motor exactly
duplicates the brush commutation in conventional DC
motors.
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– The brushless DC motor is an inside-out version of the
brush-type DC motor, i.e., the rotor has the permanent
magnets and the stator has the winding.
– In order to achieve the same functionality of the brush-type
motor, magnetic fields of the rotor and stator must be
perpendicular to each other at all rotor positions.
– As the rotor rotates, the magnetic field rotates with it. In
order to maintain perpendicular relationship between the
rotor and stator magnetic fields, the current in the stator
must be controlled as a vector quantity (both magnitude
and direction) relative to rotor position.
– Control of current to maintain this vector relationship is
called commutation.
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– Commutation is done by solid-state power transistors based
on a rotor position sensor. Note that a rotor position sensor
is necessary to operate a brushless DC motor, whereas a
brush-type DC motor can be operated as a torque source
without any position or velocity sensor.
– The brushless DC motor has the same motor constants and
obeys the same performance equations as the brushed DC
motor.
– Brushless DC motors have been around since the 1960s,
but inexpensive electronics and the advent of
microprocessors, for which it is ideally suited, have made
these motors a very competitive design alternative.
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• Advantages of Brushless DC Motors
– High Reliability
• The life of brushless DC motors is almost indefinite.
Bearing failure is the most likely weak point.
– Quiet
• A lack of mechanical noise from brushes makes it ideal
for a people environment. An added advantage is that
there is no mechanical friction.
– High Speed
• Brush bounce limits DC motors to 10,000 RPM.
Brushless DC motors have been developed for speeds
up to 100,000 RPM, limited by the mechanical strength
of the permanent magnet rotors.
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– High Peak Torque
• Brushless DC motors have windings on the stator
housing. This gives efficient cooling and allows for
high currents (torque) during low-duty-cycle, stop-start
operation. Peak torques are more than 20 times their
steady ratings compared to 10 times or less for
conventional DC motors. Maximum power per unit
volume can be 5 times conventional DC motors.
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• Disadvantages of Brushless DC Motors
– Cost
• The relatively high cost of brushless DC motors is
usually acceptable when considering complex
machinery where normal downtime and maintenance
are not only costly in itself, but often unacceptable.
– Choice
• Choice is restricted because there are few
manufacturers.
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• Types of Brushless DC Motors
– Inside Rotor
• Windings on the stator with the rotor on the inside.
• Inside rotors have less inertia and are better suited for
start-stop operation.
– Outside Rotor
• Windings on the stator with the rotor on the outside.
• Outside rotors are better for constant load, high-speed
applications.
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• Windings of brushless PM motors are distributed about the
stator in multiple phases, usually three. Each phase must be
individually controlled from the drive, implying a separate
motor lead and set of power transistors for each phase. Shown
is a simple winding set for a three-phase, four-pole motor.
Each phase is
separated from
the others by
120 degrees
electrical.
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59
• Brushless motors rely on electronic commutation. The drive
monitors the rotor position and excites the appropriate winding
to maintain a 90º commutation angle. The figure below shows
a brushless rotor in a sequence of three positions as it rotates
clockwise. The large arrows show the winding fluxes which
are maintained in quadrature; the field flux is not shown.
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• Sinusoidal Commutation
– Unlike a brush motor, a brushless motor can control current in
multiple phases independently. This allows the controller to
move the winding flux angle in small increments.
– Quadrature can be maintained precisely by independently
regulating the phase currents according to the following
equations:
I A = IS sin ( θE )
I B = IS sin ( θE − 120D )
IC = IS sin ( θE − 240D )
– IS is the magnitude of current in the motor. This is called
sinusoidal commutation. It provides smooth efficient
operation of the brushless motor. Torque is approximately
proportional to IS, i.e., T ≈ KT IS.
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61
– Assume that the brushless motor has three-phase winding
and each phase has a sinusoidal back emf as a function of
rotor position. As a result, the current-to-torque gain for
each individual phase has the same sinusoidal function.
For each phase, they are displaced from each other by a
120º angle as a result of the physical distribution of the
windings around the periphery of the stator.
– Consider that the rotor is at angular position θ and each
phase has current values IA, IB, and IC. The torque
generated by each winding is TA, TB, and TC.
TA = I A K T sin ( θE )
TB = I B K T sin ( θE − 120D )
TC = IC K T sin ( θE − 240D )
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– The total torque developed as a result of the contribution
from each phase is:
I A = IS sin ( θE )
I B = IS sin ( θE − 120D )
IC = IS sin ( θE − 240D )
TA = I A K T sin ( θE )
TB = I B K T sin ( θE − 120D )
TC = IC K T sin ( θE − 240D )
Motors for Mechatronics – An Introduction
TM = TA + TB + TC
After
trigonometric
manipulation
TM = K T IS
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63
• Phase control for brushless PM motors is show below. The
concept is to command each of the phase currents according
to:
TC
TC
I AC =
sin ( θE )
I BC =
sin ( θE − 120D )
KT
KT
ICC
TC
=
sin ( θE − 240D )
KT
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• Phase control regulates each of the phase currents with
independent current loops. Two current sensors are required;
the third phase current is calculated from the other two
because all three currents must sum to zero in a wye-connected
three-phase motor, such as shown.
• In phase control, the modulation is equivalent to that of a
brush motor, the biggest difference being that there are three
phases to modulate rather than the two phases of a brush
motor. The H-bridge is also nearly the same, except that the
brushless motor requires a third leg of the power stage.
• The electrical model of the brushless motor is similar to that of
the brush motor. Three copies of the electrical model of the
brush motor are required, one for each phase.
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• The main difference is that the back-emfs are sinusoidal when
the motor is moving a a constant speed, whereas in a brush
motor the back-emf is constant during constant speed. The
commanded currents are sinusoidal at constant speed as well.
• Inductive losses do affect steady-state torque in a brushless
motor because phase currents are changing even at constant
speed and constant load. This is one factor hat makes
brushless motors more difficult than brush motors to control;
the quality of the current loop affects the torque-speed curve.
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• Shown is a block diagram of a phase-controlled brushless PM
drive.
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• Phase-controlled brushless motors produce smooth torque.
However, there are torque perturbations, including those
caused by current sensors. Current sensors commonly have
1% or 2% current DC offset. In the brush motor, such an
offset does not contribute to torque ripple; the brush motor will
rotate smoothly, but the actual torque is offset from the
commanded torque by a small amount. In the brushless motor,
problems caused by current-sensor offset are more serious.
DC offset in the current sensors causes ripple at the electrical
frequency of the motor. To determine this frequency, multiply
the motor speed (rev/sec) by # poles / 2. For example, if a sixpole motor were rotating at 300 rpm, offset in the current
sensor would generate torque ripple at (300/60)(6/2) = 15 Hz.
A 2% offset in a current sensor indicates that the current
sensor may cause offset as much as 2% of the drive peak
current.
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• For a 10 A drive with a peak rating of 20 A, 2% would be 400
mA. Were the motor rotating with a small load drawing just 1
A, the ripple caused by 400 mA of offset would be a serious
problem for many applications. This is one reason it is
important to not to specify larger brushless drives than
necessary; the offset increases with the drive rating, so
oversized drives can cause unnecessary torque ripple.
• The performance of brushless motors at higher speeds can be
enhanced by advancing the commutation angle beyond the
ideal 90º. There are three reasons to advance the commutation
angle:
– Angle advance allows the commanded phase currents to be
greater than 90º so that after he phase lag caused by the
current loop, the actual current will be at 90º.
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– The angle can be advanced to weaken the flux field.
– Some brushless motors can generate reluctance torque; here
the ideal angle will usually be above 90º.
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Brushless
Servo
Motor
Drive
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• Brushless Servo Motor Drive
– Here there are three bridge legs instead of two legs as is the
case for an H-bridge drive for brush-type DC motors.
– Each leg of the H-bridge has two power transistors and so
the brushless motor has six power transistors.
– The so-called Y-connection shown is the most common
type of phase winding connection. At any given time, three
of the transistors are ON and three of them are OFF.
– Furthermore, two of the windings are connected between
the DC bus voltage potential and have current passing
through them in positive or negative direction, whereas the
third winding terminals are both connected to the same
voltage potential (either VDC or 0 V) and act as the balance
circuit.
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72
– The combination of the ON / OFF transistors determines
the current pattern on the stator, hence the flux field vector
generated by the stator. In order to generate the maximum
torque per unit current, the objective is to keep the stator’s
magnetic field perpendicular to that of the rotor.
– By controlling the phase currents in the stator phase
windings, we control the stator’s magnetic field (magnitude
and direction, a vector quantity).
– Therefore, the torque direction and magnitude can be
controlled by controlling the stator’s magnetic field relative
to that of the rotor.
– There are two types of brushless drives based on the
commutation algorithm: sinusoidal commutation and
trapezoidal commutation.
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– If the winding distribution and the effective magnetic circuit
of the motor are such that the back emf function is a
sinusoidal function of rotor angle, such a motor should be
controlled using a drive that uses a sinusoidal commutation
algorithm.
– Similarly, if the motor back emf is a trapezoidal type, the
drive should be the type which uses trapezoidal current
commutation.
– The sinusoidal commutation drive provides the best rotational
uniformity at any speed or torque.
– The primary difference between the two types of drives is a
more complex control algorithm. For best performance, the
commutation method of the drive is matched to the back emf
type of the motor, which is determined by its winding
distribution, lamination profile, and magnets.
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• Operation of a Brushless DC Motor
– Similar to the operation of a step motor.
– A permanent magnet rotor with pairs of N-S poles aligns
itself with the N-S field of a wound stator.
– Several separate windings (phases) surround the stator.
– Electronic switching of power to the phases advances the
field around the stator (electronic commutation) with the
rotor following.
– Brushless DC motor design stresses continuous rotation as
opposed to step motion.
– To determine the instant when to switch the field, Halleffect sensors are strategically located around the stator and
near the rotor.
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• These sensors are small semiconductor slabs of
indium/antimony. A voltage is generated across its
output terminals proportional to the magnetic flux from
the rotor poles. A high signal is generated as long as the
N-pole is across from a sensor.
• The sensors are usually mounted in the stator structure
where they sense the polarity and magnitude of the
permanent magnet field in the air gap. These signals are
amplified and processed to form logic-compatible signal
levels (high/low). These signals activate the transistors,
acting as switches, such that current is provided to the
proper coil in the stator, in the appropriate direction.
• The sensors may be located 120º/60º/30º… apart. This
location governs the control logic for the transistors.
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– Most brushless DC motors have three phases and two or
four poles.
Two-Pole, Three-Phase
Brushless DC Motor
The transistors behave like switches:
if the base is at a high, the emitter gets
shorted to the collector; otherwise, the
emitter and collector remain
disconnected.
Two transistors per phase allow a current
to flow in either direction in that phase of
winding, leading to a smooth torque
function. With only one transistor per
phase, current flow is possible only in one
direction.
Motors for Mechatronics – An Introduction
θ = 0°
CCW+
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77
– Two power transistors are required for each of three
terminals, six transistors in total.
– Wye-connected stator windings are alternately shared when
the field commutates, and the current through the various
phases changes direction as in conventional brushcommutated armatures.
– Three Hall sensors are located near each phase 120
mechanical degrees apart.
– ON Transistors are governed by a unique sensor logic
combination:
A + = bc B+ = ac C + = ab
A − = bc
B− = ac
C − = ab
– Rotor direction can be reversed by simply reversing the
logic (negate signals a, b, c).
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Commutation Logic and Phase Switching
For a Two-Pole Brushless DC Motor
(sensor logic – 120 mechanical degrees)
Rotor
Position
Hall Sensors
a b c
ON Transistors
0º - 60º
1
0
1
C+ A-
60º - 120º
1
0
0
C+ B-
120º - 180º
1
1
0
A+ B-
180º - 240º
0
1
0
A+ C-
240º - 300º
0
1
1
B+ C-
300º - 360º
0
0
1
B+ A-
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• Brushless DC Motor: Position and Velocity Control
– DC brushless motors are used in the same types of
applications as brushed DC motors, e.g., servo (position
control), constant speed, variable speed, controlled torque,
etc.
– The methods of control are similar to those for a brush-type
motor.
• Linear control using position/velocity feedback and
employing PD, PID, lead, lag, lead-lag controllers.
Voltage or current to the motor is regulated.
• Pulse-width modulation (PWM) or pulse-frequency
modulation (PFM) can be used for control. This is wellsuited for the brushless DC motor since logic circuitry is
already in place. PWM is most popular.
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