Transcript Static characteristics of sensors

Lecture 8
Properties of Sensor
Contents of this Lecture:

Outlines: Static & dynamic properties of sensor

Learn from example: System accuracy analysis.
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Static Characteristics of Sensors
The ways in which a
sensor affects the
measurement
performance due to the
feature of the sensor
are termed its static
characteristics.
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Input and Out Range
 Input Range
Output
the interval between the
maximum and minimum
admissible input range:
Imax, Imin
 Output Range
Output
Range
Input Range
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Input
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the interval between the
maximum and minimum
reachable output range:
Omax, Omin
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Span and Zero

Output
Span: the interval of
output range of a
measurement device:
Span Omax  Omin
Span
 Zero: the system output
corresponding to a zero
input.
Zero
Input
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Accuracy & Error Bands
O
 Error Bands ±h
manufacturer defined
performance values
Oideal
h
h
Error bands is an
indication of accuracy
in terms of a statistical
density function.
I
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Resolution
Di
Resolution is the smallest
detectable incremental
change of input that can be
detected in output signal.
For any devices, their
resolution is fixed.
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Sensitivity & Gain
dO
dI
Sensitivity (Gain) is
the rate of change in
output corresponding
to the rate of change in
input dO/dI.
At different range, the
sensitivity may be
different a device
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Repeatability
Inability of a sensor to
represent the same valve
under identical conditions.
o
Run 2
s1
Run 1
r 
D
D
 100%
Omax  Omin
i
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Bias and Drift
 Bias (offset)
22.0
the residual error
between the output and
the true value after all
possible compensations.
21.5
21.0
Bias
 Drift
20.5
Drift
20.0
output with time NOT
caused by input.
True value
19.5
0
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10
rate of change of the
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Deadband
 Deadband
(Dead Band)
o
range of input in which
the output remains at 0:
d
o(i )  0; "x £ xd
Xd
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i
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Saturation
 Saturation
o
range of input in which
the output gives constant
value:
o(i )  const; "x ³ xs
Xd
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Xs
i
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Hysteresis
 Hysteresis
o
the delay phenomenon
in output due to energy
dissipation.
i
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The actual output is either
smaller or greater than the
theoretical output depends
on increasing or decreasing
in input.
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Non-Linearity
Linearity is an ideal
o
relationship between
input and output:
o  ki  a
Linearity is often specified
k
in terms of percentage of
non-linearity:
a
i
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NL(%) 
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max(N ( i )  ( ki  a ))
 100%
Omax  Omin
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Dynamic Characteristics of Sensors
Thermocouple
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The ways in which a
sensor responds to
sudden input changes
are termed its dynamic
characteristics, and
these are summarized
using transfer functions.
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Dynamic Characteristics
o
A measure of sensor’s
capability of following
rapid changes in input.
Overshoot
Input




Output
Delay
Rise Time
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Settling Time
Delay (response time)
Rise time
Overshoot
Settling time
i
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Transfer Function of 1st Order
One of the most commonly
used standard signal is step
input. The response (that is
described using a transfer
function) of a 1st order
element can be represented as
follows:
fO(t)
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
T/t
f O s   G s  f I s  
Response of a 1st order
element to a step input
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1  ts s
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First-Order Elements (Thermal Sensing)
Output,
O
TF °C
T °C
W
Temperature Sensor in Fluid
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The T sensor with an initial
temperature of TC suddenly
put in fluid of TFC at time t =
0, its temperature will start
increasing immediately.
It loses its steady state, and
its dynamic behavior can be
described by a heat balance
equation:
W  UATF  T 
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First-Order Differential Equation
Output,
O
The increase of the sensor’s
heat content:
TF °C
T °C
W
Temperature Sensor in Fluid
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Where:
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Analogous 1st Order Elements
Volume flowrate:
Density, r
Cross-sectional
area AF
where:
hIN
Fluid
resistance RF
h
Governing equation:
Q
Fluidic Element
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Analogous 1st Order Elements
Force balance:
Damper, l
FIN
where:
F
x
Governing equation:
Spring, k
Mechanical Element
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Analogous 1st Order Elements
Voltage drop:
i
VIN  V  iR
R
where:
VIN
C
V
i
dq
CdV

dt
dt
Governing equation:
dV
RC
 V  VIN
dt
t
Electrical Element
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dV
 V  VIN
dt
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2nd Order Element (Mechanical)
Force balance:
Damper, l
FIN
FIN
l
m
dx
dt
F
x
Spring, k
d 2 Dx 
d Dx 
m

l
 kDx  DF
dt 2
dt
Define F and x to be the
deviations in F and x from
initial steady-state conditions:
Dx 
Mechanical Element
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dx
d 2x
 kx  l
m
dt
dt 2
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DF
k
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2nd Order Element (Mechanical)
Undamped natural frequency:
Damper, l
FIN
Damping ratio:
m
F
x
Spring, k
Transfer function:
Mechanical Element
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TF Identification, Sinusoidal-Response
We often use sinusoidal
response test to obtain the
frequency response.
G j 
1.00
0.80
0.60
0.40
0.20
0.00
0.1
0.2 0.3
-20.00
0.5
1.0
2.0 3.0
5.0
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t
Frequency response test will
provide information about:
amplitude ratio, &
phase difference
G  j  
-40.00
-60.00
-80.00
  j 
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1
2


2

22
1  
2   4
2
n 
 n 




2  n 


  j    t an1 
2


2 
1 
n 

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Dynamic Errors
DI(s)
DO(s)
K1G1 (s)
K2G2 (s)
KiGi (s)
True
signal
KnGn (s)
Measured
signal
Transfer Function:
Dynamic Error:
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Compensation of Dynamic Errors
GUC(s)
GC(s)
Open-loop
dynamic compensation
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Sensors should have enough
bandwidth for signals.
Otherwise, large dynamic
errors might be resulted.
Common compensation method
 identify element dominating
the dynamic behavior

improve it dynamic response
open-loop compensation

high gain negative feedback

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Frequency, Amplitude, and Phase
Frequency response is
common in engineering
measurements.
Amplitude
T
Amp. Change
Phase Delay
Time
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Response to different
input frequencies in terms
of:
 Phase delay
 Change in amplitude
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Other Effects
Other than the
static and dynamic
characteristics,
there are many
other effects will
affect the
performance of
measurement
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Human Element
Human is inherently
involved in the process of
the measurement, even
though the computers and
automated equipment are
tending to reduce the
human errors. However,
human still plays the key
role in getting accurate
measurements
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Environment Element
Environment is always a
big player in
measurement process:
not only on the
measurement system,
but also on the
measured system!
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Uncertainty
No matter how accurate
the measurement is, it’s
only an approximation or
estimation of the true
value of the specific
quantity subject to the
measurement. There is
uncertainty involved in
measurements
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There are two classes of
uncertainty:
those which can be
evaluated by statistical
methods
those which need to be
evaluates by other
means.
More discussions will be
in data analysis session.
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Learn from Example: Accuracy Analysis
Problem:
A digital voltmeter with an input range of 0 to 30 V and
displays three significant figures (xx.x). The specifications
published by the manufacturer indicate that its accuracy is
±2% of full scale. With a voltage reading of 5 V, what are
the percentage uncertainties of the reading due to accuracy
and resolution?
If the voltmeter reads 2 V when the leads are shorted
together, estimate the maximum error when reading a voltage
of 20 V in both volts and as percentage of reading. What will
be the maximum error when reads 20 V if we tuned the
voltage so it reads 0 V when the leads are shorted?
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