Motors for Mechatronics an Introduction

8/12/2019 Motors for Mechatronics an Introduction

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Motors for Mechatronics An Introduction K. Craig 1

Motors for Mechatronics

An Introduction

Dr. Kevin Craig

Professor of Mechanical Engineering

Rensselaer Polytechnic Institute


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Introduction to Motors

The actuatorin 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 thepower-amplification andpower-supply components that work with

the motor; it controls current to produce torque.

We focus on motor-drive technologies that can be used inhigh-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 usingfeedback 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 fastacceleration, 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 oneor 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 electricalcurrent).

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

N is the number of turns of coil and i is the current

The flux path is through the iron core and back through theair to complete the magnetic circuit

Note the right-hand rule for flux

mmf Ni= =

Vi

R

V iR=

= c

Ni magnetomotive force

reluctanceA

1permeance

=

=

=

Electrical / Magnetic Circuit Analogy

total core air = +


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Below steel has been substituted for air in the return path; this

material is calledback 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 iscalled 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 toprovide precise torque control.

Ideally, the output torque of a servo system should be

highly responsive and independent of motor position and ofspeed across the systems 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 commutatorlimitations, and current controller limitations.


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Servomotor Torque Ratings

A motorspeak 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) protectsthe motor by limiting its internal temperature. In addition,

exceeding a motors 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-drivesystem requires to produce that torque. In most servo

systems, the limit to torque responsiveness is the

responsiveness of the current loop, which is bandwidthlimited 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 allowancefor 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 constant-

speed applications, whereas DC motors have been used in

variable-speed applications. With the advances in solid-statepower 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 currentcommutation).

An electric motor converts electrical power to mechanical power.

The input to the motor is in the form of voltage and current, andthe 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 permanentmagnets).

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 byFaradays 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 bycommutating 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. Agiven 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 isbeing temporarily magnetized by the stators field.

The torque generation (electrical energy to mechanical energy

conversion process) in any electric motor can be viewed as aresult 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 themagnetic 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

(stators and rotors) and the sine of the angle between thesetwo 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 DCmotor. 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 themotor the ability to produce torque efficiently, i.e., maintain he

angle between the two magnetic flux density vectors at 90.

Electric motors can act either as a motor(convert electricalpower 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 thegenerator 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 supplyline 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 web-handling 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 tomove 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 abrushless 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 eachphase 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 Concentrated Winding


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In a concentrated winding, one coil is placed around a

single tooth. By controlling the current direction in thatparticular 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 three-

phase 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, bothmagnitude 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 MotorOperating 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 F 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 T

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 motorposition 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:

E is the electrical angle between the field and armature

flux. The diagram below shows both fluxes (only air-gap

fluxes shown).

( )( )E T F ET sin


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The relationship between the mechanical angle and the

electrical angle is given by:

In the situation presented, the angle between the two flux

vectors is 90 electrical, which is equivalent to 45 mechanicalfor this 4-pole motor.

In any given position, torque is created by producing current

in one or more of the windings. The winding must beselected so that E remains at or near 90 electrical.

For brush PM motors, the commutation angle (difference

between

F and

T) is fixed by the placement of the brusheson 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 90.

E M#Poles

2 =


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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:

( )( )

( )( )

( )

E T F E

E T F E

E T F

E T

E

E

E

E T T

T sin

T 90

T constant

T

T constant

T Ni NiT i N constant

T K i K 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 (generatoraction). 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-generatingvoltage 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 nolonger has sufficient voltage to force current into the

armature.

Other factors within the motor reduce the voltage that canbe 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 sensedcurrent 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 actualcurrent, 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 ofthe 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 waveformis 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 eitheron or off power losses in the transistor are minimized.

Thats because when the transistor is off, the current is low,

and when its 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 commandedto 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 beproduced 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 controlsystems. 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. Inthe 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 voltagedrop, typically < 2 volts (small power lost even with high

current).

Four-TransistorH-Bridge

allows both

+ and

voltages to be

applied to the

winding


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The pulsed inputs to the power transistors connect the A-

phase to either UBUS (when A+ is on) or ground (when A-

is on). This switching of A-phase drives current in and outof the winding, as shown below. This assumes that the B-

phase is held at zero. The current ripple results because the

current is pulsed. Modulation methods rely on motorinductance to smooth the current produced by pulsed

voltages.


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The most common modulation technique used ispulse-

width modulation (PWM). This method outputs voltage

pulses at a fixed frequency and then varies the width of thepulse 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 ofthe motor. A PWM frequency of 8 to 16 kHz will usually

work well for an iron-core motor with inductance in the 5-

50 mH range. For an air-core motor, with inductance just afew H, 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 beexcessive. 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 changesthe direction of the current, hence the direction of generated

torque.

Note that the pair Q1 and Q3 or the pair Q2 and Q4 shouldnever 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 transistorsmay be damaged. The diodes provide the alternative current

path for inductive loads and lets current pass through the coil.


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PWM Circuit FunctionCarrier signal is a high-

frequency 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 afunction of the value of the

input signal relative to the

carrier signal. By modulating

the ON-OFF time of the pulsewidth at a high switching

frequency, a desired average

voltage can be controlled.

Here, when the analog input

signal is larger than the carriersignal, the pulse output is ON,

when it is smaller, the pulse

output is OFF.

B h t h t th


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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 otherservomotor 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 ofbrush 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 inservo 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 attractivefor 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 whileenjoying comparatively light rotors and long brush life.


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Brushless DC Motor

The brushless DC motor is sometimes refereed as asynchronous 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 exactlyduplicates 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 permanentmagnets 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 beperpendicular to each other at all rotor positions.

As the rotor rotates, the magnetic field rotates with it. In

order to maintain perpendicular relationship between therotor 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 sensoris 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 statorhousing. This gives efficient cooling and allows for

high currents (torque) during low-duty-cycle, stop-start

operation. Peak torques are more than 20 times theirsteady 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 complexmachinery 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 separatemotor lead and set of power transistors for each phase. Shown

is a simple winding set for a three-phase, four-pole motor.

Each phase isseparated from

the others by

120 degrees

electrical.


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Brushless motors rely on electronic commutation. The drive

monitors the rotor position and excites the appropriate windingto maintain a 90 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.

Si id l C t ti


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Sinusoidal Commutation

Unlike a brush motor, a brushless motor can control current in

multiple phases independently. This allows the controller tomove the winding flux angle in small increments.

Quadrature can be maintained precisely by independently

regulating the phase currents according to the followingequations:

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.

( )

( )( )

A S E

B S E

C S E

I I sin

I I sin 120

I I sin 240

=

=

=


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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

120 angle as a result of the physical distribution of thewindings around the periphery of the stator.

Consider that the rotor is at angular position and each

phase has current values IA, IB, and IC. The torquegenerated by each winding is TA, TB, and TC.

( )

( )

( )

A A T E

B B T E

C C T E

T I K sin

T I K sin 120

T I K sin 240

=

=

=


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The total torque developed as a result of the contribution

from each phase is:

M A B CT T T T= + +

( )

( )( )

A S E

B S E

C S E

I I sin

I I sin 120

I I sin 240

=

=

=

( )

( )

( )

A A T E

B B T E

C C T E

T I K sin

T I K sin 120

T I K sin 240

=

=

=

M T ST K I=

After

trigonometric

manipulation

Phase control for brushless PM motors is show below The


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Phase control for brushless PM motors is show below. The

concept is to command each of the phase currents according

to: ( ) ( )

( )

C CAC E BC E

T T

C

CC ET

T TI sin I sin 120K K

T

I sin 240K

= =

=


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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 brushmotor. 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 whenthe 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.

Phase-controlled brushless motors produce smooth torque.


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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 have1% 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, multiplythe motor speed (rev/sec) by # poles / 2. For example, if a six-

pole 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, sooversized drives can cause unnecessary torque ripple.

The performance of brushless motors at higher speeds can be

enhanced by advancing the commutation angle beyond theideal 90. There are three reasons to advance the commutation

angle:

Angle advance allows the commanded phase currents to begreater than 90 so that after he phase lag caused by the

current loop, the actual current will be at 90.


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The angle can be advanced to weaken the flux field.

Some brushless motors can generate reluctance torque; herethe ideal angle will usually be above 90.


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BrushlessServo

Motor

Drive

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 samevoltage potential (either VDC or 0 V) and act as the balance

circuit.


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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 stators

magnetic field perpendicular to that of the rotor.

By controlling the phase currents in the stator phase

windings, we control the stators magnetic field (magnitude

and direction, a vector quantity).

Therefore, the torque direction and magnitude can be

controlled by controlling the stators 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.

If the winding distribution and the effective magnetic circuit


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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 becontrolled using a drive that uses a sinusoidal commutation

algorithm.

Similarly, if the motor back emf is a trapezoidal type, thedrive should be the type which uses trapezoidal current

commutation.

The sinusoidal commutation drive provides the best rotationaluniformity at any speed or torque.

The primary difference between the two types of drives is a

more complex control algorithm. For best performance, thecommutation 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.

Operation of a Brushless DC Motor


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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, Hall-

effect sensors are strategically located around the stator and

near the rotor.

Th ll i d t l b f


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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 structurewhere 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 signallevels (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 120/60/30 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 remaindisconnected.

0 = CCW+

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.

T t i t i d f h f th


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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 brush-

commutated armatures.

Three Hall sensors are located near each phase 120

mechanical degrees apart.

ON Transistors are governed by a unique sensor logic

combination:

Rotor direction can be reversed by simply reversing the

logic (negate signals a, b, c).

A bc B ac C ab

A bc B ac C ab

+ + +

= = =

= = =

Comm tation Logic and Phase S itching


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Rotor

Position

Hall Sensors

a b c

ON Transistors

0 - 60 1 0 1 C+ A-

60 - 120 1 0 0 C+ B-

120 - 180 1 1 0 A+ B-

180 - 240 0 1 0 A+ C-

240 - 300 0 1 1 B+ C-

300 - 360 0 0 1 B+ A-

Commutation Logic and Phase Switching

For a Two-Pole Brushless DC Motor

(sensor logic 120 mechanical degrees)

Brushless DC Motor: Position and Velocity Control


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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-typemotor.

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 well-suited for the brushless DC motor since logic circuitry is

already in place. PWM is most popular.

Motors for Mechatronics an Introduction

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