MEASUREMENT AND INSTRUMENTATION
BMCC 4743
LECTURE 2: PERFORMANCE OF STATIC
CHARACTERISTICS IN MEASUREMENT
AND INSTRUMENTATION
Mochamad Safarudin
Faculty of Mechanical Engineering, UTeM
2008
Contents
 Definition of static
 Requirement of static characteristics
preservation
 Static calibration
 Passive & active sensors
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Definition of Static

The steady state relationship between input
and output of an instrument
 Measurement of quantities that are constant
or vary quite slowly with respect to time.
 It does not involve differential equations.
 All the static performance characteristics are
obtained by one form or another via a
process called static calibration.
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Contents

Definition of static
 Requirement
of static
characteristics preservation
Static calibration
 Passive & active sensors

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Requirement of static characteristics
preservation

Precise & Accurate
– Measurements that are close to each other
are precise
– Measurements that are close to the correct
value are accurate
– Measurements can be:
• Precise but inaccurate
• Neither precise nor accurate
• Precise and accurate
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Examples
Three industrial robots were programmed to place components
at a particular point on a table. The target point was the center
of a circle shown below. The results are:
(a) Low precision,
low accuracy
(b) Precise not
accurate
(c) Precise and accurate
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Output of device
Accuracy
Ideal device
40
20
0
Accuracy at % of FS
20 40
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Value of measurand
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Requirement of static characteristics
preservation

Repeatability
– The ability of an instrument to register readings accurately
repeatedly

Linearity
– The input and output relationship of a linear transducer can
be represented by the following equation:
y = mx + c
– where y is the output of transducer, x is the input of
transducer, m is the slope of curve (transfer function), c is
the offset.
– Often, the straight line approach is used for certain range of
operation for a non-linear system.
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Requirement of static characteristics
preservation

Hysteresis
– Hysteresis results in predictable error. May be due
to internal friction, freeplay or looseness in the
mechanism of an instrument.
– Also in electrical phenomena (relation between the
output voltage and the input field current in a d.c.
generator) - the effect is due to magnetic
hysteresis of the iron in the field coils.
– The transfer functions differ with the increase and
decrease of inputs as shown in the following
figure.
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Generalized graph of output/input relationship
where hysteresis is present. (From P. H. Sydenham,
Handbook of Measurement Science, Vol. 2,
Chichester, U.K., John Wiley & Sons, 1983)
Linearity
It is highly desirable that the measurement system has a
linier relationship between input and output means that
the change in output is proportional to the change in the
value of the measurand
Deviation from true linearity is called linearity error
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Sensitivity

Sensitivity is the ratio of change in
magnitude of the output to the change
in magnitude of the measurand
– Sensitivity=D(output)/D(input)
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Sensitivity and Non Linearity
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Contents
Definition of static
 Requirement of static characteristics
preservation

 Static calibration
 Passive & active sensors
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Static Calibration





Imagine a situation in which all inputs (desired,
interfering or modifying) except one are kept at some
constant values.
The one input under study is varied over some range
of constant values which causes the output(s) to vary
over some range of constant values.
The input/output relationships developed in this way
comprise a static calibration valid under the stated
constant conditions of all other inputs.
The procedure may be repeated for other inputs for
overall instrument static behaviour
Ultimate objective is to define measurement accuracy
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Contents
Definition of static
 Requirement of static characteristics
preservation
 Static calibration

 Passive
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& active sensors
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Passive & Active Sensors


Sensors are often transducer in that they are devices
that convert input energy of one form into output
energy of another form.
Categorisation of sensors: depends on how they
interact with the environment they are measuring
– Passive sensors: they do not add energy as part of the
measurement process but may remove energy in their
operation. E.g. thermocouple converts a physical
temperature into a voltage signal
– Active sensors: they add energy to the measurement
environment as part of the measurement process. E.g. in a
radar or sonar system, the distance to some object is
measured by actively sending out a radio (radar) or acoustic
(sonar) wave to reflect off some object and measure its
range from the sensor
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EXERCISE

What is the meaning of the following
words:
– Measurand
– Physical quantity
– Data
– Parameter
– Transducer
– Actuator
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ANSWER TO EXERCISE
– Measurand: Physical quantity being measured
– Physical quantity: Variable such as pressure,
temperature, mass, length, etc
– Data: Information obtained from the
instrumentation/measurement system as a result of the
measurements made of the physical quantities
– Parameter: Physical quantity within defined (numeric)
limits.
– Transducer: A device that converts one form of energy to
another
– Actuator: Electronic transducer that converts electrical energy
into mechanical energy
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Next Lecture
Analysis on Experimental Data
End of Lecture 2
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