BITS Pilani
Instructor Information
INSTRUCTOR IN-CHARGE: Dr. Puneet Mishra
Email ID: puneet.mishra@pilani.bits-pilani.ac.in
INSTRUCTOR: Dr. Puneet Mishra, Dr. Sujan Yenuganti
Email ID: yenuganti.sujan@pilani.bits-pilani.ac.in
BITS Pilani, Deemed to be University under Section 3, UGC Act
COURSE DESCRIPTION
Course covers
Generalized measurement systems
Functional elements
Static and Dynamic characteristics
Primary sensing elements
Transducers and associated topics
Measurement techniques for different variables
MEMS based transducers
BITS Pilani, Deemed to be University under Section 3, UGC Act
Text Book / Reference Book
Measurement Systems, by Ernest O. Doebelin, Tata McGraw Hill
Theory and applications of Measurement Science, By Surekha
Bhanot, EDD Notes
Principles of Measurement Systems, By John P. Bentley, Pearson
Education
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Evaluation scheme
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Note to students
These slides should only be considered as supporting material. To have a
thorough understanding of the course, these must be accompanied by
textbook, reference materials and lecture notes.
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Introduction
The purpose of a Measurement System is to present an observer with a
numerical value corresponding to the variable being measured.
Typical variable which are needed to be measured,
BITS Pilani, Deemed to be University under Section 3, UGC Act
BITS Pilani, Deemed to be University under Section 3, UGC Act
Structure of a measurement system
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Examples
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Another representation of Measurement
system
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Example
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Transducer
It is a usually a manufactured package which normally gives an electrical signal
(typically voltage) corresponding to an input variable being measured.
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Null type v/s Deflection type
Measurement
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Application of measurement system
Monitoring of processes and operations
Control of processes and operations
Experimental Engineering analysis
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Characteristics of a measurement
system
Static characteristics
Systematic characteristics
Statistical characteristics
Dynamic characteristics
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Static characteristics: Systematic
characteristics
Consider a system with output O and input I, which is either steady or varying
very slowly.
Say, the maximum and minimum value of O is OMAX and OMIN, respectively.
Similarly, IMAX and IMIN are maximum and minimum values of I, respectively.
Range
The input range of an element is specified by the minimum and maximum values of
I, i.e. IMIN to IMAX. The output range is specified by the minimum and maximum
values of O, i.e. OMIN to OMAX.
Span
Span is the maximum variation in input or output, i.e. input span is IMAX IMIN, and
output span is OMAX OMIN.
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Static characteristics: Systematic
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Static characteristics: Linearity
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Non-linearity
Nonlinearity can be defined as,
Also, in terms of maximum nonlinearity, ,
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Non-
In many cases, O(I) can also be expressed as polynomial, as,
A typical example can be the expression of output voltage of a copper
constantan thermocouple for the range of 0-4000C,
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Sensitivity
It is the ratio of change in output of the system to the change in input to the
system,
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Hysteresis
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Resolution
The largest amount of change in I, corresponding to which no change in O is
detected.
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Example
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Effects of modifying and interfering input
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Generalized model of a system element
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Strain gauge
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Thermocouple
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Methods for compensating the nonlinear
effects and environmental effects
1. Compensating nonlinear element in the system
Example:
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Methods for compensating the nonlinear
2. Providing Isolation from environmental changes.
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Methods for compensating the nonlinear
3. Method of opposing (differential) environmental inputs,
4. Method of inherent insensitivity
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Methods for compensating the nonlinear
5. Method of high gain feedback in the system,
If,
Then,
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Statistical characteristics: Repeatability
Repeatability is the ability of an element to give the same output for the same
input when repeatedly applied to it.
Lack of repeatability is mostly due to random effects in its environment i.e.
randomness in IM and II.
By making reasonable assumptions for probability density functions of the
inputs IM and II , the probability density function of output O can be found.
The most likely probability density function for I, IM and II is the Gaussian
distribution function.
BITS Pilani, Deemed to be University under Section 3, UGC Act
BITS Pilani, Deemed to be University under Section 3, UGC Act
BITS Pilani, Deemed to be University under Section 3, UGC Act
Repeatability v/s Reproducibility
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Tolerance
Statistical variation amongst a batch of similar
elements...
Example:
Say, a batch of 100 Resistors is made. Then the
value of these resistances will also follow
Gaussian distribution curve around a mean value
of 100 ohm.
This effect is due to small random variations in
manufacture.
but Tolerance limits = .
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Accuracy and precision
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Uncertainty analysis: Error probability
density function of a system
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Uncertainty analysis: Error probability
density function of a
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Example 1
Consider a temperature measurement system, shown in above figure. The model equation of Platinum
RTD is,
,
Also, the standard deviation and mean values of different components and variables are given as,
Calculate, standard deviation (uncertainty) in RT and i at a mean temperature value of 117 0C.
BITS Pilani, Deemed to be University under Section 3, UGC Act
