S&A_Characteristics.pdf

Measurement & Instrumentation
MTC502: Sensors & Actuators
Presented by
Dr. Raghvendra Upadhyay
Associate professor
Department of Mechatronics
Terna Engineering College, Navi Mumbai
August 24, 2022
Dr. Raghvendra Upadhyay MTC502: Sensors & Actuators

Outline
1 Measurement & Instrumentation

Measuring Instrument
provides information about the physical value of some variable
being measured
Typical elements of a measuring instrument

Sensor
Primary sensor
is the first element in any measuring system.
It gives an output which is mostly a linear function of input.
Secondary sensor
Many times the output variable of a primary transducer is in
an inconvenient form and need to be converted to amore
convenient form
For instance, the displacement-measuring strain gauge has an
output in the form of a varying resistance.The resistance
change cannot be easily measured and so it is converted to a
change in voltage by a bridge circuit, which is a typical
example of a variable conversion element.
The primary sensor and variable conversion element are
combined, and known as a secondary sensor.

Signal processing elements
Signal processing elements exist to improve the quality of the
output of a measurement system in some way.
A very common type of signal processing element is the
electronic amplifier, which amplifies the output of the primary
transducer or variable conversion element, thus improving the
sensitivity and resolution of measurement.
This element of a measuring system is particularly important
where the primary transducer has a low output.
For example, thermocouples have a typical output of only a
few millivolts.

Functional classification of measuring instruments
On the basis of application of measurement, instruments can be
classified into three ways:
Simple Instruments
measure simple physical quantities such as length, volume and
mass in terms of standard units.
Alarming Instruments
perform monitoring functions. provide information that
enables human beings to take some prescribed action
for example The gardener uses a thermometer to determine
whether he should turn the heat on in his greenhouse or open
the windows if it is too hot.
Control purpose Instruments
Integral component of the automatic process control systems.

Error Analysis
Error
Difference between a measured (or calculated) value and its
true (or exact) value
Error is always present.
Eastmation: How much error is present?

Types of errors
Errors during experimentation (Measurement)
Systematic errors
Use of improperly caliberated instruments
Random errors
Because unpredictable things happen
Errors during simulation (Numerical errors)
Round off errors
Iteration error
Discretization error

Static chracteristics
Accuracy & Precision
The figure shows the results of tests on three industrial robots
that were programmed to place components at a particular
point on a table.
The target point was at the centre of the concentric circles.
The black dots represent the points where each robot actually
deposited components at each attempt.

Static chracteristics.....
Accuracy & Precision
Robot 1 places the component at the wrong position i.e. away
from the correct target position inconsistently.
Robot 2 puts the component down at approximately the same
place consistently but this is the alertwrong position.
Robot 3 places the component at the correct target position
consistently.

Accuracy
a measure of how close the output reading of the instrument
is to the correct value.
In practice, it is more usual to quote the inaccuracy figure
rather than the accuracy figure for an instrument.
Inaccuracy is the extent to which a reading might be wrong,
and is often quoted as a percentage of the full-scale (f.s.)
reading of an instrument.
Robot 3 is most accurate than others.

Precision
If a large number of readings are taken of the same quantity by
an instrument, then the spread of readings describes precision.
If the spread of readings will be very small, then Instrument is
of high precision and vice versa
High precision does not imply anything about measurement
accuracy. A high precision instrument may have a low
accuracy.
Precision is a term that estimate an instruments degree of
freedom from random errors.
Precision is often, though incorrectly, confused with accuracy.

Repeatability/reproducibility
Repeatability
The closeness of output readings when the same input is applied
repetitively over a short period of time, with the same
measurement conditions, same instrument and observer, same
location and same conditions of use maintained throughout
Reproducibility
The closeness of output readings for the same input when there are
changes in the method of measurement, observer, measuring
instrument, location, conditions of use and time of measurement.
both the terms mean approximately the same sense, describe
the spread of output readings for the same input.
This spread is referred to as repeatability if the measurement
conditions are constant and as reproducibility if the
measurement conditions vary.

Linearity
It is normally desirable that the output
reading of an instrument is linearly
proportional to the quantity being
measured.
Normal procedure is to draw a good fit
straight line through the Xs, as shown
in Figure.
The linearity is expressed as
percentage departure from linear value.
Typical output
The Xs marked on
Figure, a plot of the
typical output readings
of an instrument when
a sequence of input
quantities are applied
to it.

Sensitivity
The sensitivity of measurement is a
measure of the change in instrument
output that occurs when the quantity
being measured (input) changes by a
given amount.
Sensitivity =
Change in output
Change in input
The sensitivity of measurement is
therefore the slope of the straight line
If, for example, a pressure of 2 bar
produces a deflection of 10 degrees in
a pressure transducer (assuming that
the deflection is zero with zero
pressure applied).
Typical output
The sensitivity of the
instrument is 5
degrees/bar

Sensitivity......
The following resistance values of a
platinum resistance thermometer were
measured at a range of temperatures.
Table: Examples
Resistance 307 314 321 328
Temperature 200 230 260 290
Determine the measurement sensitivity of
the instrument
If above values are plotted on a graph, the
straight-line relationship between resistance
change and temperature change is obvious.
in ohms/C.
Typical output
For a change in
temperature of 30C,
the change in
resistance is 7 ohm.
the measurement
sensitivity =7/30 =
0.233 Ohm/C.

Sensitivity to disturbance
The specifications of an instrument are only valid under
controlled conditions of temperature, pressure etc.
These standard ambient conditions are usually defined in the
instrument specification. As variations occur in the ambient
conditions, certain static instrument characteristics change.
The sensitivity to disturbance is a measure of the magnitude
of this change.
Such environmental changes affect instruments in two main
ways:
zero drift
Sensitivity drift

Zero Drift
Zero drift or bias describes the effect
where the zero reading of an
instrument is modified by a change in
ambient conditions.
This causes a constant error that
exists over the full range of
measurement of the instrument.

Sensitivity Drift
Sensitivity drift (also known as scale
factor drift) defines the amount by which
an instruments sensitivity of measurement
varies as ambient conditions change.
It is quantified by sensitivity drift
coefficients that define how much drift
there is for a unit change in each
environmental parameter that the
instrument characteristics are sensitive to
such as temperature changes.
Zero and sensitivity drift may occur simultanously

A spring balance is calibrated in an environment at a temperature
of 20oC and has the following deflection/load characteristic.
Table: Case 1
load 0 1 2 3
deflection 0 20 40 60
It is then used in an environment at a temperature of 30oC and
the following deflection/ load characteristic is measured.
Table: Case 2
load 0 1 2 3
deflection 5 27 49 71
Determine the zero drift and sensitivity drift per C change in
ambient temperature.

Threshold
If the input to an instrument is gradually increased from zero,
the input will have to reach a certain minimum level before
the change in the instrument output reading is of a large
enough magnitude to be detectable. This minimum level of
input is known as the threshold of the instrument.
Manufacturers vary in the way that they specify threshold for
instruments. Some quote absolute values, whereas others
quote threshold as a percentage of full-scale readings.
As an illustration, a car speedometer typically has a threshold
of about 15 km/h. This means that, if the vehicle starts from
rest and accelerates, no output reading is observed on the
speedometer until the speed reaches 15 km/h.

Resolution
When an instrument is showing a particular output reading,
there is a lower limit on the magnitude of the change in the
input measured quantity that produces an observable change
in the instrument output.
Like threshold, resolution is sometimes specified as an absolute
value and sometimes as a percentage of f.s. deflection.
One of the major factors influencing the resolution of an
instrument is how finely its output scale is divided into
subdivisions.
Using a car speedometer as an example again, this has
subdivisions of typically 20 km/h. This means that when the
needle is between the scale markings, we cannot estimate
speed more accurately than to the nearest 5 km/h. This figure
of 5 km/h thus represents the resolution of the instrument.

Range
The range of an instrument defines interval between the minimum
and maximum values of a quantity that the instrument is designed
to measure.
Span
The span of an instrument defines the difference between the
maximum and minimum values of a quantity that the instrument is
designed to measure.
Oftenly range and span are used in same sense

Dynamic chracteristics
If a measurement system is subjected to time varying input,
the response of system for output is also different
The dynamic response of such systems can be modelled by
differential equations.
The basic dynamic characteristics depend upon the order of
differential equation.
First order system
Second order system

Differential Equation
Generalized Form of Differential Equation
anyn +an−1yn−1 +−−−−−−−−−+a2y2 +a1y1 +a0y +a = F(t)
First Order of a differential Equation
a1y1 + a0y + a = F(t)
Second Order of a differential Equation
a2y2 + a1y1 + a0y + a = F(t)

Response of First Order System
Natural response
dy
dt
=
a0
a1
y = λy
The rate of
change of a
variable, is directly
proportional to the
immediate value
of that variable.
when slope negative; varriable decays
when slope positive; varriable grows
Solution
The solution is y = Aeλt, whereλ =
a0
a1
A can be determined by initial condition.

Response of Second Order System
Mechanical system
Electrical system
Governing differential equation
m
d2x(t)
dt2
+ c
dx(t)
dt
+ Kx(t) = F(t)
L
d2Vc
dt2
+ R
dVc
dt
+
1
C
Vc = V (t)
Most of the second order system
may consist of an inertia, a
compliant and a damping terms.
The variation of output (x) with
time depends on amount of
damping present in the system.
Damping causes oscillations to die
away until steady displacement of
mass is obtained.

Time domain analysis of mass spring damper

Frequency domain analysis of RLC series circuit

Performance parameters
Delay time (td )
Rise time (tr )
Peak time (tp)
Settling time (ts)
Maximum overshoot (Mp)

Frequency Response
Sinusoidal input is an important input in design and analysis
of a mechatronics system.
Since sinusoidal function have property that when
differentiated the result is also sinusoid with the same
frequency.
F(t) = Aosin(ωt)
dF(t)
dt
= ωAocos(ωt) = ωAosin(ωt + φ)
Thus output is expected to be of same frequency but different
amplitude and phase than input.
Sinusoidal signals are better represented by a phasor.
Phasor can be described by complex number.
Frequency response can be analysed by use of Bode Plot.

Frequency Response
Phasor representation of a sinusoidal function
For a sinusoidal v = Vsin(ωt + φ), Where V is amplitude, ω is
angular frequency and φ is phase angle.
Phasor can be represented by a line of length |V |, making an
angle φ with the phase reference axis.

Frequency Response
Representation of a Phasor(sinusoidal function) in complex plane
Phasor can be described by complex number.
On a graph with imaginary component as the
y axis and real part as the x axis.
Join this point to the origin to represent the
phasor.
The phase angle of the phasor is represented by tanφ =
y
x
v = |V |(cosφ + j sinφ)
|V | =
p
x2 + y2
In complex notation differentiation means multiplication of
original phasor by jω.
Multiplication by ω will multiply the magnitude by ω.
multiplication by j will rotate phasor by 90O wrt previous
phasor.

Frequency Response
1st order system
2nd order system

Frequency Response
Peak resonance
the maximum value of magnitude
Bandwidth
Frequency band between which the
magnitude does not fall below -3dB

Mesurement Techniques
Bridge circuits
Resistance measurement
Inductance measurement
Capacitance measurement
Current measurement
Frequency measurement

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