Lecture 8 Properties of Sensor

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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
• the interval between the maximum and minimum
  admissible input range Imax, Imin
• Output Range
• the interval between the maximum and minimum
  reachable output range
• Omax, Omin

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Span and Zero

• Zero the system output corresponding to a zero
  input.

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Accuracy Error Bands

• Error Bands h
• manufacturer defined performance values
• Error bands is an indication of accuracy in
  terms of a statistical density function.

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Resolution

• 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

• 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

dO
dI
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Repeatability

• Inability of a sensor to represent the same valve
  under identical conditions.

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Bias and Drift

• Bias (offset)
• the residual error between the output and the
  true value after all possible compensations.
• Drift
• rate of change of the output with time NOT caused
  by input.

Bias
Drift
True value
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Deadband

• Deadband (Dead Band)
• range of input in which the output remains at 0

o
d
Xd
i
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Saturation

• Saturation
• range of input in which the output gives constant
  value

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Hysteresis

• Hysteresisthe delay phenomenon in output due to
  energy dissipation.
• 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
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Dynamic Characteristics of Sensors
The ways in which a sensor responds to sudden
input changes are termed its dynamic
characteristics, and these are summarized using
transfer functions.
Thermocouple
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Dynamic Characteristics

• A measure of sensors capability of following
  rapid changes in input.
• Delay (response time)
• Rise time
• Overshoot
• Settling time

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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
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First-Order Elements (Thermal Sensing)
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.
Output, O
Temperature Sensor in Fluid
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First-Order Differential Equation
The increase of the sensors heat content
Where
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Analogous 1st Order Elements
Volume flowrate
where
Governing equation
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Analogous 1st Order Elements
Force balance
Damper, l
FIN
where
F
Governing equation
Spring, k
x
Mechanical Element
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Analogous 1st Order Elements
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2nd Order Element (Mechanical)
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2nd Order Element (Mechanical)
Undamped natural frequency
Damping ratio
Transfer function
Mechanical Element
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TF Identification, Sinusoidal-Response
We often use sinusoidal response test to obtain
the frequency response.
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Dynamic Errors
Transfer Function
Dynamic Error
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Compensation of Dynamic Errors

• 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.
• 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, its
  only an approximation or estimation of the true
  value of the specific quantity subject to the
  measurement. There is uncertainty involved in
  measurements

There are two classes of uncertaintythose which
can be evaluated by statistical methodsthose
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?