Chapter 2: Performance Characteristics of Instruments
Chapter 2: Performance Characteristics of Instruments
Chapter 2: Performance Characteristics of Instruments
Instruments
Goals for this Chapter
Define classification of sensors and some terminologies
Introduce various types of sensors for measurement
purpose and their applications
Example: Displacement, motion, level, pressure, temperature, …
2
Introduction
• Sensors
• Elements which generate variation of electrical quantities (EQ)
in response to variation of non-electrical quantities (NEQ)
Examples of EQ
• Temperature, displacement, humidity, fluid flow, speed, pressure,…
3
Cont’d…
4
Introduction - Use of Sensors
1. Information gathering: Provide data for display purpose
This gives an understanding of the current status of the system
parameters
Example: Car speed sensor and speedometer, which records the
speed of a car against time
2. System control: Signal from the sensor is an input to a
controller.
5
Range and Span
Range: Is the limits between which the input can vary
Range of an instrument defines the minimum and
maximum values of a quantity that the instrument is
designed to measure, i.e.,
Input range – Imin , Imax
Output range – Omin , Omax
7
Sensitivity
Ratio of the change in output to
the corresponding change in
input under steady-state
conditions
Is the slope of the input-output
curve
Indicates by how much the
output of an instrument changes
when the quantity being
measured changes by a given
amount
The sensitivity can be linear or
non-linear
8
Threshold and Resolution
Threshold
If the instrument’s input is increased very gradually from zero,
there will be some minimum value below which no output change
can be detected
This minimum value defines the threshold of the instrument
Resolution
Smallest possible increment discernible between measured values
Or the minimum input change that can be detected by the system
As the term is used, higher resolution means smaller increments
An instrument with a five-digit display (say, 0.0000 to 9.9999) is
said to have higher resolution than an identical instrument with a
three-digit display (say, 0.00 to 9.99)
9
Hysteresis
This is an effect of producing different readings when the
measured quantity is approached from above or below
Instrument will not have the same output for the same input in
repeated trials
It may be the result of mechanical friction, or thermal
effects Curve B
Variable decreasing
Output
variable
Maximum
output hysteresis
Measured variable
Maximum input
hysteresis
Dead Space
10
Accuracy
Is defined as the closeness of indicated value to the true
value of the quantity being measured.
Accuracy of an instrument is a measure of how close the output
reading of the instrument is to the true/correct value
Equivalently, accuracy is the extent to which the value indicated
by a measurement system or element might be wrong
11
Precision
Indicates the ability of an instrument to reproduce a certain
reading of a constant input with a given accuracy
12
Accuracy vs. Precision
13
System Disturbances (or Environmental Effects)
Zero drift or bias or interfering input
Describes the effect where the zero reading (or intercept) of an
instrument is modified by a change in the ambient conditions
14
Sensitivity to Disturbance
Instrument’s specifications are
valid only under controlled
conditions of temperature,
pressure etc…
15
Error
Two types of errors, namely systematic and random errors
Systematic error: Cause repeated readings to be in error
by the same amount, i.e., consistent error signs
Due to instrument short coming and environmental effects
Related to calibration errors and can be eliminated by correct
calibration
Accuracy is related to such type of errors
Random errors: Caused by random electronic fluctuations
in instruments, unpredictable behavior of the instrument,
influences of friction, etc…
Such errors are related to precision
Characterized by positive and negative errors
Random fluctuations usually follow certain statistical distribution
16
Error
Difference between result of measurement and true value
of the quantity being measured
Error xm xtrue
xm x true
Percentage error 100%
xfull
E.g., If the measured value is 10.1 when the true value is
10.0, the error is +0.1. If the measured value is 9.9 when
the true value is 10.0, the error is-0.1.
17
Tolerance
A term that is closely related to accuracy and defines the
maximum error that is to be expected in some value
When used correctly, tolerance describes the maximum deviation
of a manufactured component from some specified value
Electric circuit components such as resistors have tolerances of
perhaps 5%
One resistor chosen at random from a batch having a nominal value
1000 ohm and tolerance 5% might have an actual value anywhere
between 950 ohm and 1050 ohm
18
Overview
Static characteristics
Dynamic characteristics
19
Dynamic Characteristics of Instruments
Describe behaviors between the time an input quantity
changes its value and the time when the instrument output
attains a steady value
Are useful when the input signal is rapidly varying
Used to study performance under transient conditions
20
Dynamic Characteristics …
In an LTI system, input and output, for time t > 0, are
related as:
d n qo d n 1qo dqo
an n
a n 1 n 1
... a1 ao qo
dt dt dt
d m qi d m1qi dq (2.1)
bm m bm1 m1 ... b1 i bo qi
dt dt dt
where qi is the measured (input) quantity, q0 is the output reading
and a0 . . . an, b0 . . . bm are constants
bo
So that H (S )
an S n an1 S n1 ... a1 S ao
22
Zero-order Instrument
When all the coefficients a1 . . . an other than a0 and bo are
assumed to be zero, Equation (2.3) then degenerates into
a0 qo b0 qi (2.4)
Any instrument that closely obeys Equation (2.4) is defined to be a
zero-order instrument
24
First-order Instrument
If all the coefficients a2 . . . an except for a0, a1, and b0 are
assumed zero in equation (2.3) then:
dqo
a1 ao qo bo qi (2.6)
dt
Using the Laplace transform and rearranging, we get
b0 / a0 (2.7)
Qo Qi
1 (a1 / a0 ) S
25
First-order Instrument …
Examples of first-order instruments
Temperature measurement system
Amplifiers
Electromechanical and electronic meters
Graphical recorders
26
First-order Instrument …
If equation (2.8) is solved analytically, the output q0 in
response to a step change in qi at time t is shown in the
figure below
Time constant is the time taken for the output quantity q0 to
reach 63% of its final value
27
Performance Parameters
Dynamic characteristics that are useful in characterizing
the speed of response of any instrument include
Rise Time: Time required for a response to reach 90% of
the step input (final value)
Settling time: Time to reach and stay within a stated
tolerance value around its final value
Knowing fast response requires a small value of
Need to know which parameters to vary to reduced settling time
28
Second-order Instrument
If all coefficients a3 . . . an other than a0, a1 and a2 in
equation (2.2) are assumed zero, then we get:
d 2 qo dqo
a2 2
a1 ao qo bo qi
dt dt
Applying Laplace transform and rearranging:
bo
H (S ) (2.9)
a2 S 2 a1S ao
29
Second-order Instrument …
If equation (2.10) is solved analytically, the shape of the step
response depends on the value of
A. = 0 is no damping case and
constant amplitude oscillations
B. = 0.2, we is still oscillatory
response, but the oscillations
gradually die down
C. When is increased further,
oscillations reduces and overshoot
(see curves (C) and (D))
D. Over damped response as shown
by curve (E)
• Output reading creeps up
slowly towards the correct
reading
30
Dynamic characteristics of Measurement System
Measurement Systems especially in industrial, aerospace
and Biological applications are subject to inputs which are
not static but dynamic in nature i.e. the inputs vary with
time and also the output vary with time.
The Dynamic characteristics of any measurement system
described by
1. Speed of Response
2. Measuring Lag
3. Fidelity
4. Dynamic Error
31
Terms used for dynamic characteristics
1. Response time: Time elapsed between an input is applied and
the time in which the system gives an output corresponding to
some specified percentage, e.g. 95%, of its final value
Rise time: Time taken for the output
to rise to some specified percentage
of the steady-state output. Often the
rise time refers to the time taken for
the output to rise from 10% of the
steady-state value to 90% of the
steady-state value.
Settling time: This is the time taken
for the output to settle to within some
percentage, e.g. 2%, of the steady-
state value
32
Contd.
2. Measuring Lag:-An instrument does not immediately react
a change in output.
Measuring Lag is defined as the delay in the response of
an instrument to a change in a Measuring quantity.
Two types of Measuring Lag
1. Retardation type:-In this case the response of the instrument
begins immediately after a change in the measured has occurred.
2. Time Delay type:-In this case the response of the system begins
after a “Dead Time” that means after the application of the input.
3. Fidelity of a measurement system is defined as the ability
of the system to reproduce the output in the same
variation of the input.
In Fidelity measurement system , there is no time lag
or Phase shift between the input and output
33
Contd.
4. Dynamic Error is the difference between the measured
value of the instrument changing with time and the value
indicated by the instrument if no static error is assumed.
34
Example
A Step input of 5A is applied to the Analogue current meter.
the Analogue current meter pointer swings to 5.18A and
finally comes to rest at 5.02A.
a) Determine the Overshoot of the reading in Ampere and in
percentage of final reading
b) Determine the percentage error of the instrument.
Given
ISTEP= 5 A
I1A= 5.18 A
I2A= 5.02 A
35
Solution
A) The overshoot of the reading
Overshoot Reading= I1A - I2A =5.18 A – 5.02 A =0.16 A
36
37