5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
1/20
GENERALIZED PERFORMANCECHARACTERISTICS OF
INSTRUMENTS
Lecture 6Instructor : Dr Alivelu M Parimi
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
2/20
Previously discussed
Concept of understanding function of any instrument in terms
of functional elements has been discussed.
Classification of instruments as Null/deflection, contact/non-
contact, manual/automated, intelligent/dumb, analog/digitalhas also been discussed with help of many examples.
Identification of various inputs affecting output and methods
to remove effect of spurious inputs has also been discussed.
2
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
3/20
Outline in this chapter
Static calibration
Static characteristics
Dynamic characteristics
3
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
4/20
Introduction
Detailed specifications of the functional characteristics of an
instrument are termed as performance.
Instrument performance has been divided into two sub areas:
Static Characteristics and Dynamic characteristics.
Both these types of performance is based on the response ofan instrument to a particular input.
For Static characteristics it is assumed that instrument is not
subjected to time varying inputs like acceleration, vibration,
shock and the measurand is changing slowly. The dynamic performance parameters specify how the output
changes with time in response to time-varying inputs.
4
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
5/20
Static CALIBRATIONS
Static calibration refers to a situation in which all inputs(desired, interfering and modifying) except one are kept atsome constant values.
Then the input under study is varied over some range ofconstant values, which causes the output to vary over somerange of constant values.
The input-output relations developed in this way comprise a
static calibration valid under the stated constant conditions ofall the other inputs.
If overall rather than individual effects were desired, thecalibration procedure would specify the variation of several
inputs simultaneously.
5
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
6/20
Static Characteristics
Accuracy,
Precision,
Range and Span,
Resolution and Threshold,
Sensitivity,
Linearity,
Drift and Hysteresis.
6
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
7/20
Static Characteristics:
Accuracy, The accuracy is defined as the closeness of the agreement
between the result of a measurement and the true value of
the measurand
Accuracy is measured by the absolute and relative errors.
Absolute error is the difference between a measurement and itstrue value.
Relative error is the ratio of an absolute error to the
true/specified /theoretically correct value of the quantity.
7
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
8/20
Accuracy Accuracy is expressed in the following ways:
Point accuracy: This is the accuracy of the instrument only at onepoint on its scale. The specification of this does not give anyinformation about the accuracy at other points on the scale and itdoes not give any information about the general accuracy of thesystem.
Accuracy as a percentage of Full Scale range: when an instrument
has uniform scale, its accuracy may be expressed in terms of scalerange. The accuracy of thermometer having a range of 500oC may beexpressed as 0.5% of scale range meaning reading may be in errorby + 2.5oC.
% of Full Scale deflection =
Accuracy as a percentage of the True value: Accuracy is specified interms of the true value of the quantity being measured.
% of true value =
8
100)(x
ValueScaleMaximum
TrueValueValueMeasured
100)(x
ValueTrue
TrueValueValueMeasured
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
9/20
Accuracy: Example
Example
A Voltmeter having a range 0 - 2V, 0 - 50V and 0 - 100V makes
measurement with an accuracy of 1% FSD (full scale
division). What will be the range of the readings when
voltmeter is used to determine voltage of i) 1V on 2V scale ii)5V on 50V scale iii)5V on 100V scale
Solution:
= 0.02 So well read 1V 0.02V
= 0.5 So well read 5V 0.5V
= 1.0 So well read 5V 1V
Note: Using a scale whose maximum value is close to
measurand gives better accuracy. 9
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
10/20
Static Characteristics :
Precision It is the measure of the reproducibility of the instruments i.e., given a
fixed value of a quantity, precision is a measure of how close thereadings are to each other. Two terms closely related to precision are:Repeatability and Reproducibility.
Repeatabilitydescribes closeness of output readings when the same
input is applied repeatedly over a short period of time, with the samemeasurement conditions, same instrument and observation, samelocation and same conditions of use maintained throughout. This is alsoknown as the inherent precision of the measurement equipment.
Reproducibility describescloseness of output readings for the same
input when there are changes in the method of measurement, observer,measuring instrument, location, condition of use and time ofmeasurement. It is the degree of closeness with which a given valuemay be repeatedly measured. Perfect reproducibility means that theinstrument has no drift. No drift means that with a given input themeasured values do not vary with time. 10
Precision does not guarantee accuracy but
accuracy guarantees precision.
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
11/20
Comparison Between
Accuracy and Precision
11
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
12/20
Example
Example 3.3
50 V is measured with certain voltmeter. Four readings taken
are 53, 52, 51 and 52 V. Find the accuracy and precision.
Solution
Maximum deviation from true value of 50 V is 3 V, so accuracy
is not better than 6%.
Mean reading is 52 and maximum deviation from mean value
is 1V, so precision is =
12
%2
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
13/20
Static Characteristics :Range
and Span, The region between the limits within which the instrument is
designed to operate is called range of instrument, expressedby stating lower and upper values.
Span represents algebraic differences between the upper andlower range values.
Example
The instrument span is given by x (max) - x(min)
For a pyrometer calibrated between 0 and 10000C ,
the range is 0 to 10000C and span is 10000C.
For a thermometer calibrated between 200C and 500C
the range is 200C to 500C and span is 300C.
13
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
14/20
Static Characteristics:
Resolution and Threshold, Threshold is the minimum value of input necessary to cause a
detectable change from zero output.
The range of values for which the instrument does not respond iscalled dead-zone.
In digital systems it is the input signal which is necessary to cause LSD
of output readings to change.
Resolution of an instrument is defined as the minimum resolvablevalue of the measurand.
It is the least count of instrument which is the smallest change in
input for which there will be a change in output. Both are not zero because of friction, backlash, and inertia of moving
parts and spacing of graduations.
Example: potentiometer14
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
15/20
LSD
Resolution is effectively the smallest change a meter can display. Forinstance a 4 digit voltmeter displaying the 12 volt system battery voltagecould display, as it's smallest change, 0.01 volts. It isn't possible for it todisplay anything smaller than this because there simply aren't enoughdigits available.
All measurements contain some error. The accuracy (or error) is usuallydefined as the percentage error. So a meter with a specified accuracy of1% displaying 12.50 volts, would mean that the actual voltage is within1% of this 12.5 volts, i.e. within the range 12.375 to 12.625 volts.
On top of this is the fact that, in the case of digital instruments, there is
another error. That of the last digit. A typical specification would statesomething like 1% +/-1 LSD. This means the meter will read accuratelyto within 1% of the actual voltage (giving the range in the aboveexample of 12.375 to 12.635 volts) plus or minus 1 Least SignificantDigit. As a 4 digit meter would not have the last digit (the 5) in theabove example, it would display somewhere in the range of 12.37 to12.64 plus or minus 1 LSD giving a final range of 12.36 to 12.65 volts.
15
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
16/20
Example
The scale of temperature measurement has 100 uniform
divisions, full scale reading is 200 C and one tenth of a scale
division can be estimated with fair degree of accuracy.
Determine the resolution.
Solution Full Scale Reading = 2000C
There are 100 divisions; therefore each division reads 2C. One
tenth of scale division corresponds to resolution so Resolution
= 0.2 C.
16
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
17/20
Static Characteristics:
Sensitivity Static sensitivity or scale factor or gain is the ratio of change in
instrument output to change in magnitude of measurand.
The reciprocal of sensitivity is called deflection factor or inversesensitivity.
Higher sensitivity implies better resolution/threshold.
Example
A Wheatstone bridge requires a change of 7 in the unknown armof the bridge to produce a change in deflection of 3mm of thegalvanometer. Determine the sensitivity. Also determine thedeflection factor.
Solution
Sensitivity =
= = 0.429 mm /
Inverse sensitivity or Scale factor = = 7 / 3mm = 2.33 /mm. 17
inputofmagnitude
responseoutputofmagnitude
7
mm3
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
18/20
Static Characteristics :
Linearity, The linearity is defined as the departure of the calibration
point from a straight line.
18
This is the closeness to a straight line ofthe relationship between the true
process variable and the measurement.
Lack of linearity does not necessarilydegrade sensor performance.
If the nonlinearity can be modeled andan appropriate correction applied to themeasurement before it is used formonitoring and control, the effect of thenon-linearity can be eliminated.
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
19/20
Static Characteristics: Drift
and Hysteresis.
19
5/19/2018 Lecture 6Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lec...
20/20
Static Characteristics: Drift
20
Top Related