Jeff Shelton – 24 February 2015

1

Jeff Shelton – 24 February 2015

2

Jeff Shelton – 24 February 2015 3

Jeff Shelton – 24 February 2015

4

Jeff Shelton – 24 February 2015

vs.

5

Jeff Shelton – 24 February 2015

6

Jeff Shelton – 24 February 2015

7

Jeff Shelton – 24 February 2015

H W G

VS VW

8

Jeff Shelton – 24 February 2015

𝑅𝑃 = 𝑅1 + 𝑅2 𝑅2 = 𝑥𝑅𝑃 𝑅1 = 1 − 𝑥 𝑅𝑃 𝑅𝑃

𝑅1 𝑅2

VS Vout +

–

9

Jeff Shelton – 24 February 2015

OUT

𝑉𝑂𝑈𝑇 =1

1 +𝑅𝑃𝑅𝐿

𝑥 1 − 𝑥 𝑥𝑉𝑠

Maximum nonlinearity occurs at: 𝑥 ≈2

3

Max nonlinearity: =400

27

𝑅𝑃

𝑅𝐿% f.s.d.

10

Jeff Shelton – 24 February 2015

•

•

•

•

•

•

•

•

•

11

Jeff Shelton – 24 February 2015

•

•

•

•

•

•

12

Jeff Shelton – 24 February 2015

Absolute Encoding

Incremental Encoding

13

Jeff Shelton – 24 February 2015

Ch. 0

Ch. 1

Ch. 2

14

Jeff Shelton – 24 February 2015

90∘

Channel A

Channel B

Index

15

Jeff Shelton – 24 February 2015

•

•

•

Light Source

Moving Grate

Light Receiver

Collimated Beam

16

Jeff Shelton – 24 February 2015

Channel A

Channel B

4X

2X

1X

17

Jeff Shelton – 24 February 2015 18

Jeff Shelton – 24 February 2015

19

Jeff Shelton – 24 February 2015

20

Jeff Shelton – 24 February 2015

21

Jeff Shelton – 24 February 2015

Channel A

Channel B

22

Jeff Shelton – 24 February 2015

23

Rotary Encoder Linear Encoder

Jeff Shelton – 24 February 2015 24

Jeff Shelton – 24 February 2015

Target

Retro-reflector

Beam Splitter

Interferometer Receiver &

Signal Processing

Collimated

Laser Beam

Electrical Signal

Quadrature Output

25

Jeff Shelton – 24 February 2015

𝑉𝑇 = 𝐾𝐸𝑀𝐹 ⋅ 𝜔 = 𝐾𝑉 ⋅ 𝜔

26

Jeff Shelton – 24 February 2015

27

Jeff Shelton – 24 February 2015

Time (sec)

Vel

oci

ty (

m/s

)

28

Jeff Shelton – 24 February 2015

29

Jeff Shelton – 24 February 2015

30

Jeff Shelton – 24 February 2015

31

Jeff Shelton – 24 February 2015

•

•

•

32

Jeff Shelton – 24 February 2015

33

Jeff Shelton – 24 February 2015 34

Jeff Shelton – 24 February 2015

Clear Output Latch

Reset Counter Set Timer

Start Timer Running

Read Counter (Load Output Latch)

Timer not done

Timer done

START

35

Jeff Shelton – 24 February 2015

Timer not done and

no overflow

Timer done and no

overflow

Clear Output Latch

Reset Counter Set Timer

Start Timer

Read Counter (Load Output Latch)

Running

START

Set Output Latch to

Max Counter overflow

36

Jeff Shelton – 24 February 2015

37

Jeff Shelton – 24 February 2015

•

•

•

•

38

Jeff Shelton – 24 February 2015

•

•

•

•

•

•

39

Jeff Shelton – 24 February 2015

•

40

Jeff Shelton – 24 February 2015

𝐸𝑖 = sin 𝜔𝑡

𝑉𝐴= 𝐸𝑖 ⋅ sin 𝜃

𝑉𝐶= 𝐸𝑖 ⋅ cos 𝜃

41

Jeff Shelton – 24 February 2015

42

Jeff Shelton – 24 February 2015

•

•

𝑉𝐴 = sin 𝜃 ⋅ sin 𝜔𝑡

𝑉𝐵 = cos 𝜃 ⋅ sin 𝜔𝑡

Resolver

𝑉𝑋 = sin 𝜃 ⋅ sin 𝜔𝑡

𝑉𝑌 = cos 𝜃 + 120° ⋅ sin 𝜔𝑡

𝑉𝑍 = cos 𝜃 − 120° ⋅ sin 𝜔𝑡

Synchro

43

Jeff Shelton – 24 February 2015

𝑉𝐴 = cos 𝜙 ⋅ sin 𝜃 ⋅ sin 𝜔𝑡 𝑉𝐵 = sin 𝜙 ⋅ cos 𝜃 ⋅ sin 𝜔𝑡

sin 𝜃 − 𝜙 ⋅ sin 𝜔𝑡

44

sin 𝜃 − 𝜙

sin 𝜔𝑡

Jeff Shelton – 24 February 2015 45

Resolver Encoder

Cost Higher Lower

Implementation Complex Simple

Shock Resistance Rugged Limited

Inertia High Low

Weight Heavy Lighter

Output Analog Analog or Digital

Noise Immunity Sensitive Robust

Accuracy 4—40 arc minutes 0.25—6 arc minutes

Angle Measurement Absolute Absolute or Incremental

Jeff Shelton – 24 February 2015

46