The length of time from the application of an input

The length of time from the application of an input until the output to
respond and change

Example:
–
EV3 Touch sensor
23
time(sec)
x(mm)
time(sec)
touchsensor
x*
0
1
t*
(deadtime)
 
*
*
1,
0, 0
x x
f x
x x




 

T02 - Sensors © Mo-Yuen Chow, NC State University, All Rights Reserved

Static and dynamics
characteristics
A&H 4th: Chapter 4.7 – 4.9
Bolton 6th: Chapter 2, 19.3
24 T02 - Sensors © Mo-Yuen Chow, NC State University, All Rights Reserved

Static and Dynamic Characteristics

Response time of different thermometers

Infrared thermometer
–
Fluke 561 Infrared Thermometer
–
Response time: <500 milliseconds
–
Resolution: 0.1 °C
–
Cost: $199.00

Analog thermometer
–
Fridge / Freezer Thermometer
–
Response time: ~ 60 seconds
–
Resolution: 1 °C
–
Cost: $4.00
25
-
model/3563941?PubID=UX&persist=true&ip=no&gclid=Cj0KCQjwv_fKBRCGARIsAL6R6e
igQ9nzpWPPFuCwITG9FzwhNY73mLAn06d8K3b3si-78pWAl47CRGwaArSuEALw_wcB
-
fridge-freezer-thermometer-with-hook.html
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26
Time response of a sensor

The first order differential equation is:
Where u ( t ) is the input, y ( t ) is the output of the system.
T02 - Sensors © Mo-Yuen Chow, NC State University, All Rights Reserved
( ) u t
t
1
0
t
Input
ܽ
ଵ
݀ݕሺݐሻ
݀ݐ
൅ ܽ
଴
ݕ ݐ ൌ ܾ
ଵ
ݑሺݐሻ
ݕ ݐ ൌ
ܾ
ଵ
ܽ
଴
1 െ ݁
ି
௧
ఛ
, ݐ ൒ ݐ
଴
ݑ ݐ ൌ ቊ
0, ݐ ൒ ݐ
଴
1, 0 ൑ ݐ ൏ ݐ
଴
SteadyStateGainܩ
௦௦
ൌ
ܾ
ଵ
ܽ
଴
,
Time Constant ߬ ൌ
௔
భ
௔
బ
( ) y t
t
SS
G
0
t
Output

27
Time measures

Time Constant

Response Time

Rise Time

Settling Time
T02_Time_Measure_eg.slx
T02 - Sensors © Mo-Yuen Chow, NC State University, All Rights Reserved

28
Example: Time measure

Consider the following data which indicates how a thermometer
reading changed with time by plunging into a liquid at time t = 0.
–
What is the 95% response time?

Answer:
20
25
30
35
40
45
50
55
60
0 100 200 300 400
t (sec)
T (C)
The steady-state value is
55°C and so, since 95%
of 55 is 53.25°C:
 
0.95
20 0.95 55 20 53.25 T     
Time (s) 0 30 60 90 120 150 180 210 240 270 300 330 360
Temp (
O
C) 20 28 34 39 43 46 49 51 53 54 55 55 55
the 95% estimated
response time is about
247.5 s.
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Sensor selection
29 T02 - Sensors © Mo-Yuen Chow, NC State University, All Rights Reserved

30
Sensor Selection Considerations

The size of the displacement
–
Example: 1mm or 10 m

Whether the displacement is linear or angular
–
Example: Distance readings from Ultrasonic Sensor (linear) or Angular Velocity
readings from EV3 Motors (angular)

The resolution required
–
Example: EV3 Color (light) Sensor: Raw (0-1023) or Normalized (0-100)

The accuracy required
–
Example: 1cm (Ultrasonic Sensor for the course Project), 1 nm (nanotechnology)
or 10 m (astronomy)

What material the measured object is made of
–
Example: reflective surface (use Color Sensor to detect the Black Tape, use
Ultrasonic Sensor to detect obstacles) or magnetic (use Hall effect)
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31
Example: of Sensor Types

Non-contact sensor
–
Example: Proximity sensors

Contact sensor
–
Example: potentiometer sensor
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