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

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Figure 9.7 Linear variable differential transformer.

out

core centered

(null position)

secondary

primary

movable

iron core

out

excitation voltage

output voltage with

core left of null

output voltage with

core right of null

−

+−

++− −

magnetic field

Figure 9.8 LVDT linear range.

out

amplitude

core displacement

rightleft

linear

range

Figure 9.9 LVDT demodulation.

primary

secondary

out

secondary

core

out

excitation voltage

output voltage with

core left of null

output voltage with

core right of null

−

magnetic fields

and associated

voltage polarities

−

9.2 Position and Speed Measurement 381

■ CLASS DISCUSSION ITEM 9.2

LVDT Demodulation

Trace the currents through the diodes in the demodulation circuit shown in

Figure 9.9 for different core positions (null, left of null, and right of null) and explain

why the output voltage behaves as shown. Assume ideal diodes. Also, explain why

the output is 0 when the core is in the null or center position.

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Figure 9.10 LVDT output filter.

−

out

low-pass filter

output voltage with

core left of null

output voltage with

core right of null

out

Figure 9.11 Commercial LVDT. (Courtesy of Sensotec,

Columbus, OH)

382 CHAPTER 9 Sensors

As illustrated in Figure 9.10 , a low-pass filter may also be used to convert the

rectified output into a smoothed signal that tracks the core position. The cutoff fre-

quency of this low-pass filter must be chosen carefully to filter out the high fre-

quencies in the rectified wave but not the frequency components associated with the

core motion. The excitation frequency is usually chosen to be at least 10 times the

maximum expected frequency of the core motion to yield a good representation of

the time-varying displacement.

Commercial LVDTs, such as the one shown in Figure 9.11 , are available in

cylindrical forms with different diameters, lengths, and strokes. Often, they include

internal circuitry that provides a DC voltage proportional to displacement.

The advantages of the LVDT are accuracy over the linear range and an analog

output that may not require amplification. Also, it is less sensitive to wide ranges

in temperature than other position transducers (e.g., potentiometers, encoders, and

semiconductor devices). The LVDT’s disadvantages include limited range of motion

and limited frequency response. The overall frequency response is limited by inertial

effects associated with the core’s mass and the choice of the primary excitation fre-

quency and the filter cutoff frequency.

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9.2 Position and Speed Measurement 383

A resolver is an analog rotary position sensor that operates very much like the

LVDT. It consists of a rotating shaft (rotor) with a primary winding and a stationary

housing (stator) with two secondary windings offset by 90 ⬚ . When the primary is

excited with an AC signal, AC voltages are induced in the secondary coils, which are

proportional to the sine and cosine of the shaft angle. Because of this, the resolver is

useful in applications where trigonometric functions of position are required.

Two other types of linear position sensors that measure linear displacement

directly, based on magnetic principles, are the voice coil and magnetostrictive posi-

tion transducers. Video Demos 9.5 and 9.6 show two example devices and describe

how they work.

9.2.4 Digital Optical Encoder

A digital optical encoder is a device that converts motion into a sequence of dig-

ital pulses. By counting a single bit or decoding a set of bits, the pulses can be

converted to relative or absolute position measurements. Encoders have both linear

and rotary configurations, but the most common type is rotary. Rotary encoders are

manufactured in two basic forms: the absolute encoder where a unique digital word

corresponds to each rotational position of the shaft, and the incremental encoder,

which produces digital pulses as the shaft rotates, allowing measurement of relative

displacement of the shaft. As illustrated in Figure 9.12 , most rotary encoders are

composed of a glass or plastic code disk with a photographically deposited radial

pattern organized in tracks. As radial lines in each track interrupt the beam between

a photoemitter-detector pair, digital pulses are produced.

Video Demo 9.7 shows and describes all of the internal components of a small

digital encoder. In this case the code disk is made of stamped sheet metal. Video

Demos 9.8 and 9.9 describe two interesting applications of encoders: a computer

mouse and an industrial robot. View Video Demos 1.1 and 1.2 to see a demonstra-

tion of how the robot works and how the encoders are incorporated into the internal

design. Video Demo 1.5 shows another application of encoders where cost is a major

concern and a custom design is necessary.

The optical disk of the absolute encoder is designed to produce a digital word

that distinguishes N distinct positions of the shaft. For example, if there are eight

tracks, the encoder is capable of measuring 256 (2

) distinct positions corresponding

to an angular resolution of 1.406 ⬚ (360 ⬚ /256). The most common types of numerical

encoding used in the absolute encoder are gray and natural binary codes. To illus-

trate the action of an absolute encoder, the gray code and natural binary code disk

Video Demo

9.5Voice coil

9.6Magneto-

strictive position

sensor

■ CLASS DISCUSSION ITEM 9.3

LVDT Signal Filtering

Given the spectrum of a time-varying core displacement, what effect does the

choice of the primary excitation frequency have, and how should the low-pass filter

be designed to produce an output most representative of the displacement?

Video Demo

9.7Encoder

components

9.8Computer

mouse relative

encoder

9.9Adept robot

digital encoder

components

1.1Adept One

robot demon-

stration (8.0 MB)

1.2Adept One

robot internal

design and con-

struction (4.6 MB)

1.5Inkjet printer

components with

DC motors and

piezoelectric

inkjet head

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Figure 9.12 Components of an optical encoder.

1 or more LED

photoemitters

phototransistor

photodetectors

code disk

shaft

tracks

digital output

signals

(a) schematic

(b) typical construction (Courtesy of

Lucas Ledex Inc., Vandalia, OH)

Electronics board

(Signal conditioning)

Rotating

encoder disk

LED light source

Stationary mask

Photodetector

384 CHAPTER 9 Sensors

track patterns for a simple four-track (4-bit) encoder are illustrated in Figures 9.13

and 9.14 . The linear patterns and associated timing diagrams are what the photo-

detectors sense as the code disk circular tracks rotate with the shaft. The output bit

codes for both coding schemes are listed in Table 9.1.

The gray code is designed so that only one track (one bit) changes state for each

count transition, unlike the binary code where multiple tracks (bits) can change during

count transitions. This effect can be seen clearly in Figures 9.13 and 9.14 and in the last

two columns of Table 9.1. For the gray code, the uncertainty during a transition is only

one count, unlike with the binary code, where the uncertainty could be multiple counts.

■ CLASS DISCUSSION ITEM 9.4

Encoder Binary Code Problems

What is the maximum count uncertainty for a 4-bit gray code absolute encoder and

a 4-bit natural binary absolute encoder? At what decimal code transitions does the

maximum count uncertainty occur in a 4-bit natural binary absolute encoder?

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Figure 9.13 4-bit gray code absolute encoder disk track patterns.

direction of positive track motion

fixed

sensors

bit 3 (MSB)

bit 2

bit 1

bit 0 (LSB)

0° 360°

bit 3

bit 2

bit 1

bit 0

Figure 9.14 4-bit natural binary absolute encoder disk track patterns.

(b) actual disk (Courtesy of Parker

Compumotor Division, Rohnert Park, CA)

(a) schematic and signals

direction of positive track motion

fixed

sensors

bit 3 (MSB)

bit 2

bit 1

bit 0 (LSB)

0° 360°

bit 3

bit 2

bit 1

bit 0

9.2 Position and Speed Measurement 385

Because the gray code provides data with the least uncertainty but the natural

binary code is the preferred choice for direct interface to computers and other digi-

tal devices, a circuit to convert from gray to binary code is desirable. Figure 9.15

shows a simple circuit that utilizes Exclusive OR (XOR) gates to perform this

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Table 9.1 4-bit gray and natural binary codes

Decimal Code Rotation Range (⬚)

Natural binary

code (B

)

Gray code

)

0 0–22.5 0000 0000

1 22.5–45 0001 0001

2 45–67.5 0010 0011

3 67.5–90 0011 0010

4 90–112.5 0100 0110

5 112.5–135 0101 0111

6 135–157.5 0110 0101

7 157.5–180 0111 0100

8 180–202.5 1000 1100

9 202.5–225 1001 1101

10 225–247.5 1010 1111

11 24 7.5–270 1011 1110

12 270–292.5 1100 1010

13 292.5–315 1101 1011

14 315–337.5 1110 1001

15 337.5–360 1111 1000

Figure 9.15

Gray-code-to-binary-code conversion.

MSB

LSB

386 CHAPTER 9 Sensors

function. The Boolean expressions that relate the binary bits ( B

) to the gray code

bits ( G

) are

⊕=

(9.1)

For a gray-code-to-binary-code conversion of any number of bits N (e.g., N ⫽ 4 as

previously), the most significant bits of the binary and gray codes are always identi-

cal ( B

N ⫺ 1

⫽ G

N ⫺ 1

), and for each other bit, the binary bit is the XOR combination:

⫽ B

i 1 1

丣 G

for i ⫽ 0 to N ⫺ 2. This pattern can be easily seen in the 4-bit

example above ( Equations 9.1 ).

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Figure 9.16 Incremental encoder disk track patterns.

direction of positive track motion

fixed

sensors

INDEX

0° 360°

INDEX

(a) schematic and signals

(b) actual disk (Courtesy of Parker

Compumotor Division, Rohnert Park, CA)

9.2 Position and Speed Measurement 387

■ CLASS DISCUSSION ITEM 9.5

Gray-to-Binary-Code Conversion

Examine the validity of Equations 9.1 by applying them to the last two columns in

Table 9.1.

The incremental encoder, sometimes called a relative encoder, is simpler in

design than the absolute encoder. It consists of two tracks and two sensors whose

outputs are designated A and B. As the shaft rotates, pulse trains occur on A and B

at a frequency proportional to the shaft speed, and the lead-lag phase relationship

between the signals yields the direction of rotation as described in detail below. The

code disk pattern and output signals A and B are illustrated in Figure 9.16 . By count-

ing the number of pulses and knowing the resolution of the disk, the angular motion

can be measured. A and B are 1/4 cycle out of phase with each other and are known

as quadrature signals. Often a third output, called INDEX, yields one pulse per

revolution, which is useful in counting full revolutions. It is also useful to define a

reference or zero position.

Figure 9.16a illustrates a configuration using two separate tracks for A and B,

but a more common configuration uses a single track (see Figure 9.16b and

Video Demo 9.7) with the A and B sensors offset a quarter cycle on the track to

Video Demo

9.7Encoder

components

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Figure 9.17 Quadrature direction sensing and resolution enhancement.

forward (CW) reverse (CCW)

CCW

388 CHAPTER 9 Sensors

yield the same signal pattern. A single-track code disk is simpler and cheaper to

manufacture.

The quadrature signals A and B can be decoded to yield angular displacement

and the direction of rotation as shown in Figure 9.17 . Pulses appear on one of two

output lines (CW and CCW) corresponding either to clockwise (CW) rotation or

counterclockwise (CCW) rotation. Decoding transitions of A and B using sequential

logic circuits can provide three different resolutions: 1X, 2X, and 4X. The 1X reso-

lution provides an output transition at each negative edge of signal A or B, resulting

in a single pulse for each quadrature cycle. The 2X resolution provides an output

transition at every negative or positive edge of signal A or B, resulting in two times

the number of output pulses. The 4X resolution provides an output pulse at every

positive and negative edge of signal A or B, resulting in four times the number of

output pulses. The direction of rotation is determined by the level of one quadrature

signal during an edge transition of the second quadrature signal. For example, in the

1X mode, A ⫽ ↓ with B ⫽ 1 implies clockwise rotation, and B ⫽ ↓ with A ⫽ 1

implies counterclockwise rotation. If we only had one signal instead of both A and B,

it would be impossible to determine the direction of rotation. Furthermore, shaft

jitter around an edge transition in the single signal would result in erroneous pulses

(see Class Discussion Item 9.6).

■ CLASS DISCUSSION ITEM 9.6

Encoder 1X Circuit with Jitter

An incremental encoder connected to a 1X quadrature decoder circuit is experi-

encing a small rotational vibration with an amplitude roughly equivalent to one

quadrature pulse width. During this vibration, you observe many pulses on both the

CW and CCW lines but no net change in the output of the up-down counter. Explain

why this happens.

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Figure 9.18 1X quadrature decoder circuit.

up-down

counter

down

binary

count

output

CCW

CLR

CLR Q

9.2 Position and Speed Measurement 389

Figure 9.18 shows a circuit that will yield the 1X resolution by creating and

counting pulses at specific negative edges of the quadrature signals. The D flip-

flops decode whether the shaft is rotating clockwise or counterclockwise, and this

information is used to drive an up-down counter to keep the current pulse count for

the encoder rotation. In addition to the edges detected for the 1X resolution, circuits

can be designed to detect other edges in the quadrature signals resulting in two times

(2X) and four times (4X) the base resolution (1X). These quadrature decoder cir-

cuits can be constructed with discrete components, but they are also available on ICs

(e.g., Hewlett Packard’s HCTL-2016). Quadrature decoding can also be done with

software running on a microcontroller (Question 9.11).

Incremental encoders provide more resolution at lower cost than absolute

encoders, but they measure only relative motion and do not provide absolute posi-

tion directly. However, an incremental encoder can be used in conjunction with a

limit switch to define absolute position relative to a reference position defined by the

switch. Absolute encoders are chosen in applications where establishing a reference

position is impractical or undesirable.

■ CLASS DISCUSSION ITEM 9.7

Robotic Arm with Encoders

When a robotic arm with absolute encoders on its joints is powered up, the robot

knows exactly where its links are relative to its base. If the absolute encoders were

replaced with incremental encoders, would this remain true? If not, how would the

robot establish a home or zero reference position for the arm?

THREADED DESIGN EXAMPLE

DC motor position and speed controller—Digital encoder interface C.4

The figure below shows the functional diagram for Threaded Design Example C (see Section

1.3 and Video Demo 1.8), with the portion described here highlighted.

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390 CHAPTER 9 Sensors

microcontrollers

SLAVE

PIC

MASTER

PIC

H-bridge

driver

liquid crystal display

DC motor with

digital position encoder

1 2 3

4 5 6

7 8 9

0 #

keypad

decoder

button

buzzer

quadrature

decoder

and counter

The following figure shows all components and interconnections required to read the

digital encoder’s position from the slave PIC. A commercially available quadrature decoder/

counter interface IC, the HCTL-2016, is the main component in the design. Detailed informa-

tion about this component can be found in the data sheet at Internet Link 9.3. The HCTL-2016

requires a clock signal to operate. In this design, it is provided by a clock output on the master

PIC. The master PIC also resets the encoder counter at the appropriate time (via the RST line)

to define a zero position. The digital encoder quadrature signals (channels A and B) are also

connected to the HTCL-2016. Because the HTCL-2016 contains a 16-bit counter, and the

interface to the slave PIC is via the 8-bit PORTB, the data must be retrieved one byte at a time.

The thick line connecting PORTB on the PIC to D0-7 on the HCTL-2016 in the wiring dia-

gram indicates multiple wires (in this case, an 8-wire cable). The SEL pin is used to indicate

which byte is being read. Finally, the OE pin is used to latch the encoder values before they

are read by the PIC.

DC motor

with

encoder

HCTL-2016

CLK

CHA

CHB

D0-7

PIC16F84

SEL

PORTB

RA2

RA3

RA0

RA1

RST

6–13

1, 15–9

controlled

by the master PIC

for communication

with the master PIC

Shown below is the slave PIC code, which monitors the digital encoder position and

transmits the data back to the master PIC upon request. The full code for both PICs is

Video Demo

1.8DC motor

position and

speed controller

Internet Lin

9.3HTCL-2016

quadrature

decoder/counter

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