Alciatore D.G., Histand M.B. Introduction to Mechatronics and Measurement Systems

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■ CLASS DISCUSSION ITEM 10.4

Dissection of Radio Shack Motor

Purchase an inexpensive 1.5–3-V DC motor (e.g., Radio Shack Catalog No.

273-223) and disassemble it. Identify the brushes, the commutator segments, the

armature windings, the laminated rotor poles, and the stator permanent magnets.

Sketch the magnetic field produced by the stator permanent magnets. For different

commutator positions, determine the direction of current flow (and the resulting

field direction) in the armature windings. Determine the direction of torque pro-

duced by the field-field and field-current interactions. Which effect do you think is

stronger in this motor?

Other problems not discussed with these simple models are a back electromo-

tive force (emf) and induction. As the rotor windings cut through the stator magnetic

field, a back emf is induced opposing the voltage applied to the rotor. Also, when

the commutator switches the direction of current, a voltage is induced to oppose the

change in current direction.

The principles of operation of AC motors are similar regarding interaction of

the magnetic fields, but commutation is not required. This is because the magnetic

field rotates around the stator as a result of the AC voltages and the arrangement of

the coils around the stator housing. The rotor windings of asynchronous AC motors

have no external voltage applied; rather, voltages are induced in the rotor windings

due to the rotating fields around the stator. The rotor rotates at slower speeds than

the rotating stator fields (this is called slip ), making the induction possible, hence

the term asynchronous. Because of this action, asynchronous motors are sometimes

referred to as induction machines. With synchronous AC motors, the rotor wind-

ings are energized but through slip rings instead of a commutator. Brushes provide

constant uninterrupted contact with the slip rings, causing fields to rotate around the

rotor windings at the same rate as the fields rotate around the stator. Due to the inter-

action of these fields, the rotor rotates at the same speed as the stator fields, hence

the term synchronous.

Internet Lin

10.2Electric

motor illustrations

and animations

Internet Link 10.2 provides excellent illustrations and animations showing the

fundamentals of how various motors, generators, and transformers function.

10.5 DC MOTORS

Direct current (DC) motors are used in a large number of mechatronic designs

because of the torque-speed characteristics achievable with different electrical con-

figurations. DC motor speeds can be smoothly controlled and in most cases are

reversible. Since DC motors have a high ratio of torque to rotor inertia, they can

respond quickly. Also, dynamic braking, where motor-generated energy is fed to a

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442 CHAPTER 10 Actuators

resistor dissipater, and regenerative braking, where motor-generated energy is fed

back to the DC power supply, can be implemented in applications where quick stops

and high efficiency are desired.

Figure 10.11 illustrates a typical torque-speed curve that displays the torques

a motor can provide at different speeds at rated voltage. For a given torque provided

by the motor, the current-torque curve can be used to determine the amount of

current required when rated voltage is applied. As a general rule of thumb, motors

deliver large torques at low speeds, and large torques imply large motor currents.

The starting torque or stall torque T

is the maximum torque the motor can pro-

duce, at zero speed, associated with starting or overloading the motor. The no-load

speed 

max

is the maximum sustained speed the motor can attain. This speed can be

reached only when no load or torque is applied to the motor (i.e., only when it is free

running).

Based on how the stator magnetic fields are created, DC motors are classified

into four categories: permanent magnet, shunt wound, series wound, and compound

wound. The electrical schematics, torque-speed curves, and current-torque curves

for each configuration are illustrated in Figures 10.12 through 10.15 . In the figures,

V is the DC voltage supply, I

is the current in the rotor (armature) windings, I

the current in the stator (field) windings, and I

is the total load current delivered by

the DC supply.

The stator fields in permanent magnet (PM) motors (see Figure 10.12 ) are

provided by permanent magnets, which require no external power source and there-

fore produce no I

R heating. A PM motor is lighter and smaller than other, equivalent

DC motors because the field strength of permanent magnets is high. PM motors are

easily reversed by switching the direction of the applied voltage, because the current

and field change direction only in the rotor. The PM motor is ideal in control applica-

tions because of the linearity of its torque-speed relation. The design of a controller

is always easier when the actuator is linear since the system analysis is greatly sim-

plified. When a motor is used in a position or speed control application with sensor

feedback to a controller, it is referred to as a servomotor. PM motors are used only

in low-power applications since their rated power is usually limited to 5 hp (3728 W)

or less, with fractional horsepower ratings being more common. PM DC motors can

be brushed, brushless, or stepper motors.

Shunt motors (see Figure 10.13 ) have armature and field windings connected

in parallel, which are powered by the same supply. The total load current is the sum

of the armature and field currents. Shunt motors exhibit nearly constant speed over

a large range of loading, have starting torques about 1.5 times the rated operating

torque, have the lowest starting torque of any of the DC motors, and can be economi-

cally converted to allow adjustable speed by placing a potentiometer in series with

the field windings.

Series motors (see Figure 10.14 ) have armature and field windings connected

in series so the armature and field currents are equal. Series motors exhibit very

high starting torques, highly variable speed depending on load, and very high speed

when the load is small. In fact, large series motors can fail catastrophically when

they are suddenly unloaded (e.g., in a belt drive application when the belt fails) due

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Figure 10.11 Motor torque-speed curve.

torque

current

speed

torque

starting

torque (T

)

no-load

speed (ω

max

)

Figure 10.12 DC permanent magnet motor schematic and torque-speed curve.

magnet

torque

speed

torque

current (I

)

Figure 10.13 DC shunt motor schematic and torque-speed curve.

torque

speed

variable

resistor

small (1–5%)

field current

nearly

constant

torque

current (I

)

Figure 10.14 DC series motor schematic and torque-speed curve.

heavy

coil

speed

run-away

torque

speed

torque

current (I

)

to dynamic forces at high speeds. This is called run-away. As long as the motor

remains loaded, this poses no problem. The torque-speed curve for a series motor is

hyperbolic in shape, implying an inverse relationship between torque and speed and

nearly constant power over a wide range.

Compound motors (see Figure 10.15 ) include both shunt and series field wind-

ings, resulting in combined characteristics of both shunt and series motors. Part

of the load current passes through both the armature and series windings, and the

remaining load current passes through the shunt windings only. The maximum speed

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Figure 10.15 DC compound motor schematic and torque-speed curve.

series

shunt

torque

speed

torque

current (I

)

444 CHAPTER 10 Actuators

of a compound motor is limited, unlike a series motor, but its speed regulation is not

as good as with a shunt motor. The torque produced by compound motors is some-

what lower than that of series motors of similar size.

Note that, unlike the permanent magnet motor, when voltage polarity for a

shunt, series, or compound DC motor is changed, the direction of rotation does not

change (i.e., these motors are not reversible). The reason for this is that the polar-

ity of both the stator and rotor changes because the field and armature windings are

excited by the same source.

10.5.1 DC Motor Electrical Equations

As illustrated in Figure 10.16 , the impedance of a DC motor’s armature can be mod-

eled as a resistance R in series with the parallel combination of an inductance L and

a second resistance R

. However, as the conducting armature begins to rotate in the

magnetic field produced by the stator, a voltage called the back emf V

emf

is induced

in the armature windings opposing the applied voltage. The back emf is proportional

to the speed of the motor  in rad/sec:

emf

ω=

(10.2)

where the proportionality constant k

is called the electrical constant of the motor.

, the equivalent resistive loss in the magnetic circuit, is usually an order of

magnitude larger than R, the resistance of the windings, and can be neglected. If the

voltage applied to the armature is V

, the current through the armature is I

, and if

we assume R

≈ 0, the electrical equation for the motor is

--------

ω++=

(10.3)

Figure 10.16 Motor armature equivalent circuit.

emf

−

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10.5.2 Permanent Magnet DC Motor Dynamic Equations

Since the permanent magnet DC motor is so important and is the easiest to under-

stand and analyze, we look at its governing equations in more detail. Due to the

interaction between the stator field and the armature current, the torque generated by

a PM DC motor is directly proportional to armature current:

(10.4)

where k

is defined as the torque constant of the motor. A PM motor’s electrical

constant k

and torque constant k

are very important parameters, and they are often

reported in manufacturer specifications. When the dynamics of a motor and its load

are considered, the generated motor torque T is given by

T (J

+ )

-------

++=

(10.5)

where J

and J

are the polar moments of inertia of the armature and the attached

load, T

is the frictional torque opposing armature rotation (including drag created by

air resistance), and T

is the torque dissipated by the load.

When voltage is applied to a PM DC motor, the rotor accelerates until a steady

state operating condition is attained. At steady state, Equation 10.3 becomes

ω+=

(10.6)

Note that, at steady state, from Equation 10.5 , the motor torque balances the friction

and load torques.

By solving for I

in Equation 10.4 and substituting into Equation 10.6 , we get

---

⎝⎠

⎛⎞

ω+=

(10.7)

and by solving for the motor torque in this equation, we get

---

⎝⎠

⎛⎞

--------

⎝⎠

⎛⎞

ω–=

(10.8)

This equation predicts the linear torque-speed relation for a PM DC motor with a

fixed applied voltage.

Figure 10.17 shows the linear torque-speed curve and the power-speed curve for

a permanent magnet DC motor with a fixed supply voltage V

. The linear relation in

Equation 10.8 can also be expressed in terms of the starting torque T

and the no-load

speed 

max

T(ω) T

max

---------- -–

⎝⎠

⎛⎞

(10.9)

The no-load speed is the steady-state speed at which the motor will run if there is no load

torque ( T

 0). At this speed, the motor torque balances the friction torque (i.e., T  T

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Figure 10.17 Permanent magnet DC motor characteristics.

max

power-speed

curve

speed

max

power

torque

torque-speed

curve

446 CHAPTER 10 Actuators

By comparing Equations 10.8 and 10.9 , you can see that the stall torque and no-load

speed are related to the motor parameters according to

---

⎝⎠

⎛⎞

(10.10)

and

max

---------

( 10.11)

Using Equation 10.9 , the power delivered by the motor at different speeds can

be expressed as

P ω() TωωT

max

-----------

–

⎝⎠

⎛⎞

(10.12)

The maximum power output of the motor occurs at the speed where

dω

-------

2ω

max

-----------

–

⎝⎠

⎛⎞

0==

(10.13)

Solving for the speed gives

-- -

max

(10.14)

Therefore, the best speed to run a permanent magnet motor to achieve maximum

power output is half the no-load speed.

In addition to the electrical and torque constants, manufacturers often specify

the armature resistance R. Using Equations 10.4 and 10.10 , the stall current I

can

be found in terms of the armature resistance and supply voltage:

-------

(10.15)

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This equation for current is valid only when the motor rotor is not turning; otherwise,

the rotor current is affected by the back emf induced in the rotor windings. The stall

current is the maximum current through the motor for a given supply voltage.

10.5.3 Electronic Control of a Permanent Magnet DC

Motor

The simplest form of motor control is open loop control, where one simply sets the

drive voltage value, and the motor characteristics and load determine the operat-

ing speed and torque. But most interesting problems require some sort of automatic

control, where the voltage is automatically varied to produce a desired motion. This

is called closed-loop or feedback control, and it requires an output speed and/or

torque sensor to feed back output values to continuously compare the actual output to

a desired value, called the set point. The controller then actively changes the motor

output to move closer to the set point. Electronic speed controllers are of two types:

linear amplifiers and pulse width modulators. Pulse width modulation controllers

have the advantage that they either drive bipolar power transistors rapidly between

cutoff and saturation or they turn FETs on and off. In either case, power dissipation

is small. Servo amplifiers using linear power amplification are satisfactory but pro-

duce a lot of heat, because they function in the transistor linear region. You will find

commercial servo controllers using linear amplifiers, but because of lower power

requirements, ease of design, smaller size, and lower cost, we focus on the switched

amplifier designs, which are generally called pulse-width modulation (PWM)

amplifiers.

The principle of a PWM amplifier is shown in Figure 10.18 . A DC power supply

voltage is rapidly switched at a fixed frequency f between two values (e.g., ON and

OFF). This frequency is often in excess of 1 kHz. The high value is held during a

variable pulse width t within the fixed period T where

-- -

(10.16)

The resulting asymmetric waveform has a duty cycle defined as the ratio between

the ON time and the period of the waveform, usually specified as a percentage:

duty cycle

---

100%=

(10.17)

As the duty cycle is changed (by the controller), the average current through

the motor changes, causing changes in speed and torque at the output. It is primar-

ily the duty cycle, and not the value of the power supply voltage, that is used to

control the speed of the motor. Video Demo 10.15 explains how PWM signals

are used to control standard radio-controlled (RC) servomotors. Lab Exercise 11

explores how to use a microcontroller to generate a PWM signal to vary the speed

of a DC motor. The end result of the exercise is demonstrated in Video Demo 7.5.

The block diagram of a PWM speed feedback control system for a DC motor

is shown in Figure 10.19 . A voltage tachometer produces an output linearly related

Video Demo

10.15RC servo

with pulse-width-

modulation input

7.5Pulse-width-

modulation speed

control of a DC

motor, with keypad

input

Lab Exercise

Lab 11Pulse-

width-modulation

motor speed

control with a PIC

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448 CHAPTER 10 Actuators

Figure 10.18 Pulse width modulation of a DC motor.

DC power

supply

)

PWM

electronics

motor

example drive circuit

faster

(large t)

slower

(small t)

pulses

pulses:

Figure 10.19 PWM velocity feedback control.

motor

power

amp

tachometer

measured speed

set point

(desired)

speed

−

error signal =

set point –

measured speed

PWM

regulator

electronics

Figure 10.20 PWM voltage and motor current.

PWM

voltage

motor

current

high duty cycle

low duty cycle

to the motor speed. This is compared to the desired speed set point (another voltage

that can be manually set or computer controlled). The error and the motor current

are sensed by a pulse-width-modulation regulator that produces a width-modulated

square wave as an output. This signal is amplified to a level appropriate to drive the

motor.

In a PWM motor controller, the armature voltage switches rapidly, and the cur-

rent through the motor is affected by the motor inductance and resistance. Since the

switching speed is high, the resulting current through the motor has a small fluctua-

tion around an average value, as illustrated in Figure 10.20 . As the duty cycle grows

larger, the average current grows larger and the motor speed increases.

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Although it is possible to design and build a drive circuit for a servomotor with discrete con-

trol and power components, several integrated circuit designs are available that save enor-

mously on time and money in mechatronic design. Consider the very ordinary problem of

controlling a DC motor. Your ultimate intent may be to control speed, direction of rotation,

angle, and/or torque.

To control the speed of a DC motor, we must be able to change the current supplied to

the motor. To control the direction of rotation, the direction of current supplied to the motor

must be reversible. This requires a current amplifier and some means to switch the current

direction. The concept of an H-bridge meets these requirements. It uses four switches

(relays or transistors) arranged in an H configuration around the DC motor (see the fol-

lowing figure). The switches are turned on one pair at a time for the desired direction of

motion.

If switches Q

and Q

are on and Q

and Q

are off, current flows through the motor in

the direction shown and the motor rotates in one direction. Alternatively, if switches Q

and

are on and Q

and Q

are off, the motor rotates in the other direction.

An H-bridge can be constructed easily with relays (four SPSTs or two DPDTs); how-

ever, relays cannot be switched very fast, so this limits our PWM options. Also, because

relays are mechanical devices, they can wear out and fail after many switching cycles.

However, for applications where you need only reversibility and not PWM speed control,

relays can be a good option. For applications where we want PWM speed control, tran-

sistors or solid-state relays are better choices. An excellent resource for information and

advice on how to build H-bridges using a variety of components can be found at Internet

Link 10.3.

One can also build a discrete H-bridge with power BJTs or MOSFETs, but it may be

difficult to properly choose and bias the transistors. Therefore, we utilize a monolithic solu-

tion using National Semiconductor’s line of motion control ICs, which can be conveniently

adapted for driving DC motors. Consider the LMD15200, a 3 A, 55 V H-bridge specifically

designed to drive DC and stepper motors. It allows for current direction control, and also

offers features for overcurrent and overtemperature detection, pulse width modulation, and

dynamic braking. The functional diagram follows.

H-Bridge Drive for a DC Motor

(continued )

DESIGN

EXAMPLE 10.1

Internet Lin

10.3H-bridge

resource

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450 CHAPTER 10 Actuators

This design uses power MOSFETs with flyback protection diodes that suppress large

reverse transients across the transistors. The motor poles are connected between Output 1

and Output 2. The voltage supply can be up to 55 V. External digital signals control direc-

tion, braking, and pulse width modulation. A thermal sensor shuts down the outputs when

the device temperature exceeds 170C.

The complete block diagram for our speed controller design is shown in the next figure.

The speed set point is controlled with a potentiometer or input voltage value. A tachometer

is added to the motor as the sensor to provide a measure of the motor speed. The National

Semiconductor pulse width modulation IC LM3524D is conveniently used here to drive the

H-bridge motor controller input.

(continued )

THERMAL FLAG OUTPUT

Functional Diagram

Function Diagram and Ordering Information

9 1 2 6 10 11

GROUND

CURRENT

SENSE

OUTPUT

BOOTSTRAP 1

(Courtesy of National Semiconductor Inc., Santa Clara, CA)

BOOTSTRAP 2

TL/H/10564-1

OUTPUT 1 OUTPUT 2V

THERMAL

SENSING

UNDERVOLTAGE

LOCKOUT

OVERCURRENT

DETECTION

SHUTDOWN

DIRECTION 3

CHARGE

PUMP

DRIVE

CHARGE

PUMP

DRIVE

CURRENT

SENSING

INPUT

LOGIC

BRAKE 4

PWM 5

•

MOUNTING TAB CONNECTED TO GROUND (PIN 7)

Top View

TL/H/10568-2

Order Number LMD 15200T

See NS Package TA11B

THERMAL FLAG OUTPUT

GROUND

CURRENT SENSE OUTPUT

BOOTSTRAP 1

BOOTSTRAP 2

OUTPUT 1

OUTPUT 2

POWER SUPPLY

DIRECTION INPUT

BRAKE INPUT

PWM INPUT

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