Chapter 1 Briefing Introduction

INSTRUMENTATION & MEASUREMENTS

Briefing

EE009-3-1-INM Instrumentation & Measurements Title of Slides

Module Description

.‹#›

Module Objectives • Contribute to the achievement of the Learning Outcomes specified

for the student’s award at Level 1• Enable students to develop their knowledge and skills in relation

to Instrumentation and Measurement• Develop the ability of students to apply the knowledge they gain in

relation to the study of Instrumentation and Measurement• Introduce students to the knowledge, skills and techniques

relevant to the study of Instrumentation and measurement • Enable students to develop their ability to:

– Critically Analyse– Solve complex problems– Innovate– Use ICT relevant to given situations

EE009-3-1-INM Instrumentation & Measurements Title of Slides ‹#›

Module Description

Learning Outcomes

On successful completion of this module, you should be able to:

• Appraise various types of instruments for engineering measurements and applications – PO1, PO3

• Describe measurement processes for accurate and precise measurement. - PO2

• Describe the characteristics, operation and limitations of various measurement sensors/transducers - PO2

• Construct suitable signal conditioning circuits for appropriate measurement performance. - PO1, PO2, PO3, PO5, PO10


Module Description

Programme Outcomes• PO1- Ability to gain and apply basic principles of

Mathematics, Science and Engineering. • PO2-Ability to identify engineering problems and

apply basic engineering principles to solve them. • PO3-Ability to recognize and apply suitable tools

and techniques for engineering practical applications.

• PO5-Ability to design solutions for complex engineering problems.

• PO10-Ability to function effectively as an individual or in a team.

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Module Description• Duration

– 16 weeks– Lectures (2.5 hours)– Tutorials/Labs (1 hour)

• Assessment– Class test+ Lab report(20% + 20%)

• Mode – Assignment: Written individual assessment– Lab : Group work with individual report

» Evidence - Report

– Exam (60%)• Problem solving• Discussion & Analysis

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EE009-3-1-INM Instrumentation & Measurements Title of Slides 6


What is expected of you

• You should abide by all the rules & regulation of UCTI• Proper attire• No speaking of dialects• Attendance is compulsory and valid medical

certificates or letters from parents /guardians must support any absence from class.

• Three lateness will be equal to one absence• Lateness = 20mins after class commencement• All mobile phones should be turned off or in silent

mode during lectures.

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What is expected of you

• Students doing things not related to the current lecture will be asked to leave the room and disciplinary action will be taken in accordance with the University’s rules and regulations.

• Students should not leave the room during a lecture except with the agreement of the lecturer

• Assignments should be submitted before 7.00p.m. on due date to the receptionist.

• Students have to submit the EC (Extenuating Circumstances) form for late assignments

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Essential Reading

1. A.S. Morris (2001) Measurement and Instrumentation Principles, Oxford: Butterworth-Heinemann ISBN 0750650818

2. Barney, G.C., Intelligent Instrumentation: Micro-processor Applications in Measurement and Control, Prentice Hall, 2nd Ed.

3. Bentley, J.P., Principles of Measurement Systems, Longman Scientific and Technical, third edition, 1995.

4. Doebelin, E.O., Measurement Systems: Application and Design, McGraw-Hill, fourth edition, 1992.Sheingold,

5. D.H. (editor), Analog-Digital Conversion Handbook, Prentice-Hall, third edition, 1986. 2nd edition 1988.

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CHAPTER 1INTRODUCTION

INSTRUMENTATION & MEASUREMENTS

EE009-3-1

CHAPTER 1 – OBJECTIVES

At the end of this chapter, you will be able to:

determine and explain units and quantities common in engineering measurement

discuss measurement processes and practices

Identify and calculate various types of error in measurement

explain the meaning of some terms in used in the instrumentation

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CHAPTER 1 – OUTLINE

1.1 Principles of instrumentation and measurements• Static and dynamic characteristics

1.2 The error identification and calculation in measurement• Statistical analysis

1.3 Measurement standard

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1.1 PRINCIPLES OF INTRUMENTATION AND MEASUREMENTS

“If something exists, it exists in some amount. If it exists in someamount, then it is capable of being measured.” -Rene Descartes, Principles of Philosophy

“Measurement is the first step that leads to control and eventually to improvement. If you can’t measure something, you can’t understand it. If you can’t understand it, you can’t control it. If you can’t control it, you can’t improve it.” -Dr. H. James Harrington

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• MEASUREMENT– To monitor processes and operations– To control processes and operations– To analyze processes and operations

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MeasurementInstrument

Input Output

Variable being measured

Measured valueof variable



• Monitoring– Measure and indicate– Thermometer, speedometer, voltmeter,

bellows• Controlling

– Bimetal thermostat in an A/C unit• Analysis

– Testing for validity

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• INSTRUMENTS – A transducer– A signal conditioning circuit– A device to display/record

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Analog signal

processing

Analog to digital

converter

Digital signal

processing

Display/recording unit

Measured physical variable

Signal conditioning circuitry

Transducer

INSTRUMENTATION

- to indicate a measurement

- to record a measurement

- to control based on measurement

measure a quantity using electrical and electronic instrument and display the value

the measured quantity is recorded for various purposes

Recorded quantity is processed and for control function


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• Instrument selection• Before any attempt for measurement is to be made,

please make sure that you have sound knowledge on the:

i. type of instrument to be used; its characteristics such as accuracy, limitation etc.

ii. methods and procedures of measurementiii. characteristics of the quantity measured (input)iv. characteristics of the measured quantity (output)v. quality of measurement in terms of time and cost factorvi. safety measure


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During the measurement activity ensure that:

• you can interpret and analyze the result• measured value is error-free or if there is an error you

take action accordingly• you have the best quality of the result• measured data is well indicated and recorded (if

necessary)• you have proper procedure and enough sampling

When measurement is complete, perform:

• the analysis of the data mathematically/statistically

• preparation of result and provide a complete documentation


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UNIT

What is a unit?A quantity used as a standard of measurement.

Why measurement needs the unit?So you can define and explain the meaning of the quantity measured.

Why standard unit is necessary? To achieve uniformity and universality of the measurement. So people around the would will have common description and explanation of a measured quantity.

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1.3 MEASUREMENT STANDARD

QUANTITY

What is quantity?Description of an amount in numerical form.

Some units below

Quantity Symbol Unit Unit Abbreviation

Time t Second s

Mass m kilogram kg

Electric Current I Ampere Amp

Temperature T Kelvin K

Length L meter m

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1.3 MEASUREMENT STANDARD


• SI BASE UNIT - modern metric system

There are seven SI units from which derived units are obtained

i. Unit of length (meter)

ii. Unit of mass (kilogram)

iii. Unit of thermodynamic temperature (kelvin)

iv. Unit of amount of substance (mole)

v. Unit of luminous intensity (candela)

vi. Unit of electric current (ampere)

vii. Unit of time (second)

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• 1.3 MEASUREMENT STANDARD

The characteristics of an instrument which are constant or change very slowly with time. Example, the resistance of a resistor at constant temperature is a static measurement.

1.1.1 STATIC CHARACTERISTICS OF INSTRUMENTS

Static Characteristics

Desirable Undesirable

Accuracy Sensitivity Precision Resolution Repeatability Reproducibility

DriftDead Zone

Static Error

Threshold Hysteresis Creep


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AccuracyAccuracy is the correctness of a single measurement. It is the closeness of the measured value to the true value. The closeness of an average to a true value is referred to as "trueness".

Example 1: Suppose a known voltage of 200 V is being measure by voltmeter and the successive readings are 204, 205, 203, 203, 205. Find the accuracy of each reading.

Error (%) = xt – xm x 100 xt

Accuracy = 100% - Error

STATIC CHARACTERISTICS OF INSTRUMENTS


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Where t = true valuem = measured valuex = measurand


• Accuracy

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PrecisionPrecision is reproducibility. Saying "These measurements are precise" is the same as saying, "The same measurement was repeated several times, and the measurements were all very close to one another". It is a measure of the stability and reliability of the instrument and its capability of resulting in the same measurement over and over again for the same input signal.

Poor accuracy results from systematic errors, poor precision results from random errors




• Precision

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• Accuracy vs Precision

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Resolution– It is the smallest increment of input signal change that

would produce a detectable change in the output, often expressed as a percentage of the measured range.

Measured range = xmax – xmin

For a detectable output y, if the minimum change in x is x,

Resolution (%) = xmin x 100

Measured range

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Example 1

Example 2


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Sensitivity

Absolute ratio of the change of the output signal (response) to that of the input signal (measurand).

S = y / x or in normalized form, Sn = y / x y / x

where y = change of output signal x = change of input signal

Example 2: The mercury in a thermometer moves by 1cm when temperature changes by 10oC. The sensitivity of the device is 1cm/10oC.



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Problem 1A force sensor device is known to produce 10 V if the force is 100N. However a successive reading provide the following data: 10.2V, 10.3V, 10.2 V, 10.4 V, and 10.2 V

Determine the following:a) Absolute error considering mean of datab) Accuracy in percentage considering mean of data

Problem 2It is known that a flowrate sensor produces an output change of 10mV when the flowrate increases by 20m3/s. What is the sensitivity of the sensor?



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Calibration errors– Inaccuracy permitted by the manufacturer during factory

calibration, systematic in nature– Span error, zero error, linearization error

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Linearity and Non-linearity

Most cases measurement is assumed to be linear but in reality it is not. This deviation could be any of the following:

a) Oscillation from fixed amplitudeb) Oscillation with varying amplitudec) Combined oscillation around the best –fit straight line


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a) Oscillation with fixed amplitude

The actual output of the instrument may oscillate with the same amplitude around the best-fit straight line. The nonlinearity therefore can be calculated using the maximum deviation (±) from the full scale deflection (FSD)



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b) Oscillation from varying amplitude

The actual output of the instrument may oscillate around the best-fit straight line, but its amplitude varies with input value.

The slopes of the lines connecting positive and negative are determined and the highest deviation from the best-fit line is used to express the percent nonlinearity with respect to the input value.


c) Combined oscillation around the best –fit straight line

The actual output may oscillate with a fixed amplitude around the best-fit straight line over a certain range and then the amplitude may become a function of the input over the rest.

The nonlinearity can be determined by parts:

fixed amplitude and expressed as ±% of the FSD, varying amplitude and expressed as ±% of the input

value.

Nonlinearity is expressed in terms of the higher value.


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46


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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

The degree of repeatability is an alternate way of expressing precision


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Reproducibility

Consistent measurement output from the same physical quantity when the measurement condition is changed. Example, dismantled and re-assembled instruments or measurements taken with long periods of rest in between.


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Zero Drift

Defined as the drift from the null reading of the instrument when the measurand is maintained at steady for a long period of time.



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Hysteresis – If the input measured quantity to the instrument is steadily increased from a negative value, the output variation is shown as curve A. Thenif the input is steadily decreased, the output curve is as depicted as in curve B



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Threshold If an input to a 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 defined as the threshold



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Creep – change of output with time following a step increase in the input from one value to another. It’s the maximum change of output over a specified time after increasing the input from zero to the rated maximum input. When the input is step changed from maximum to zero, then there’s a curve that represents the creep recovery.


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•Static characteristicsthe performance criteria for the measurement of

quantities that remain constant, or vary only quite slowly.

• Dynamic characteristics the relationship between the system input and output

when the measured quantity (measurand) is varying rapidly.

1.1.2 DYNAMIC CHARACTERISTICS OF INSTRUMENTS


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System = Static x dynamic

•One expresses the static behavior of the block, that is, the value it has after all transient (time varying) effects have settled to their final state.

•The other part tells us how that value responds when the block is in its dynamic state.



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Dynamic characteristics

•First order system•Second order system



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First order system• System response


First order system

• Performance specifications:– Time constant, t

• 1/a, time taken for response to rise to 63% of its final value

– Rise time, Tr• time taken for response to go from 10% to 90% of

its final value– Settling time, Ts

• time for response to reach and stay within 5% of final value


First order system


Second order system

• Performance specifications– damping ratio

– % Overshoot = cmax – cfinal x 100

cfinal

100/%ln

100/%ln22 OS

OS


Second order system

• 2nd order underdamped response

1.2 ERROR IDENTIFICATION IN MEASUREMENT

Error - the difference between the measured value and the expected value (true value) of the measurand.

What is static error?

It is numerical difference between the true value of a quantity and its value as obtained by measurement (i.e. repeated measurement of the same quantity gives different indications).

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Static Errors

Types of Static Errors

i) Absolute error ii) Gross error iii) Systematic error iv) Random error v) Limiting error


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Static Errors



The difference between the expected value of the variable and the measured value of the variable, ore = |Yn – Xn |

where: e = absolute error Yn = expected value Xn = measured value


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Static Errors



In percentage:

% error = (100)

Relative accuracy A:

Percentage accuracy a:a = A*100

n

nn

Y

XYA

1


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Static Errors



The expected value of the voltage across a resistor is 5.0 V. However, measurement yields a value of 4.9 V. Calculate:

a) absolute error

b) % error

c) relative accuracy

d) % accuracy


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Static Errors



Due to human mistakes: Example: incorrect reading, incorrect recording, improper use of instruments, etc

To minimize:

- take at least 3 separate reading

- take proper care in reading & recording


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Static Errors




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Observational Error

Errors that introduced by the observer. The two most common observational errors are probably the parallax error introduced in reading a meter scale and the error of estimation when obtaining a reading from a meter scale

Static Errors



Error due to instrument’s problem or environmental effects

Examples: defective or worn parts Ageing drift


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Static Errors



Instrumental Error

Error due to friction in the bearings of the meter movement, incorrect spring tension, improper calibration, or faulty instruments.


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Static Errors



Environmental Error

Due to external condition of the measurement. Examples, effects of change in temperature, humidity, barometric pressure, electrostatic fields etc.


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Static Errors



Errors that remain after gross and systematic errors have been substantially reduced

Are generally the accumulation of a large number of small effects

May be of real concern only in measurements requiring a high degree of accuracy such errors can only be analyzed statistically

Due to unknown causes


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Static Errors



Most manufacturers of instruments state that an instrument is accurate within a certain percentage of a full-scale reading Example, a voltmeter is accurate within ±3% at full-scale.


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Static Errors



A 300-V voltmeter is specified to be accurate within ±2% at full scale. Calculate the limiting error when the instrument is used to measure a 120-V source?

Solution

The magnitude of the limiting error is:

2/100 x 300 = 6V

Therefore, the limiting error at 120 V is:

6/120 x 100 = 5%


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Importance:• Data has be checked for its validity and integrity• Data has to be error-free before it should be used• Instruments reliability must be checked before it should be used

Thus analysis of data allows an analytical determination of the uncertainty of the final result especially in large number of measurements it is usually required.

Methods:• Arithmetic mean / average• Deviation• average deviation• standard deviation

STATISTICAL ANALYSIS OF MEASUREMENT DATA


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Importance:

• Data has to be checked for its validity and integrity• Data has to be error-free before it should be used• Instruments reliability must be checked before it should be used

Thus analysis of data allows an analytical determination of the uncertainty of the final result especially in large number of measurements it is usually required.

Methods:• Arithmetic mean / average• Deviation• average deviation• standard deviation

STATISTICAL ANALYSIS OF MEASUREMENT DATA


STATISTICS

• Collection of methods for planning experiments, obtaining data, organizing, summarizing, presenting, analysis, interpreting and drawing conclusion.

• Statistical steps:– Gather data– Organize data – Analyze data


Population & sample

• Population : collection of all elements of interest• Sample : subset of the population

population sample


NUMERICAL MEASURES

• Measurement of central tendency– Mean – Median– Mode

• Measurement of variations– Range– Variance– Standard deviation


• The MeanTo find the mean, you need to add up all the data, and then dividethis total by the number of values in the data.

• The MedianTo find the median, you need to put the values in order, then find themiddle value. If there are two values in the middle then you find the mean of these two values.

• The ModeThe mode is the value which appears the most often in the data. It ispossible to have more than one mode if there is more than one valuewhich appears the most.

• The RangeTo find the range, you first need to find the lowest and highest valuesin the data. The range is found by subtracting the lowest value from the highest value.


MEASUREMENT OF CENTRAL TENDENCY

MEAN

• The mean is the average value.

– Sample mean

– Population mean

n

xx i

N

xi


MEDIAN

• The middle value when the numbers are arranged in ascending or descending order

1 2

Ex: 3 median 4

5


MODE

• The data value that occurs with greatest frequency

1

1 mode

Ex: 1

3

5


Central Tendency Example

• Calculate the mean, median and mode for the list test scores below; 86,83, 98,96,88, 72,64,86,83,83,80,94,93,75,44,87

SOLUTION: Mean,μ

Median 98,96, 94,93,88,87,86,86,83,83,83,80,75,72,64,44

Mode = 83 ( repeating 3 times)

8216

44759394808383866472889698 8386

N

xi

5.84

2

8386


Exercise

• Find the mode, median and mean for

2, 3, 1, 2, 6, 8, 9, 3, 2, 3.


MEASUREMENT OF VARIATIONS

RANGE

• Difference between the largest and smallest value in the dataset

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Ex: 3 Range = 5 – 1= 4

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Calculating the Mean, Median, Mode and Range for a table of data

ExampleA dice was rolled 20 times. On each roll the dice shows a value from 1 to 6.The results have been recorded in the table below:


Finding the mean from a table of data

68/20 = ?


Finding the median from a table of data

1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6

Should be on 10th and 11th

(3 + 4) / 2 = ?


Finding the mode and range from a table of data

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Mode

In this case we can see that the value with the highest frequency is "2".

The mode of this set of data is therefore 2

Range

Look for the highest and lowest values in the values column.

In this case the lowest value is "1" and the highest value is "6", and 6 - 1 = 5.

The range of this set of data is therefore 5


Exercise

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Value Frequency

0 3

1 7

2 10

3 8

4 1

5 1

Value

Find mean, mode, median and range.


VARIANCE

• Measurement of the dispersion of values from the mean.

– Sample variance

– Population variance

N

xi

2

2

1

2

2

n

xxs i


STANDARD DEVIATION

• The positive square root of the variance

– Sample standard deviation

– Population standard deviation

2ss

2


variance

• variance is basically a measure of the general dispersion of data in a sample, it gives you a sense of how far away data points are from one another.

• the larger the variance, the more variability you have in your sample.


Standard deviation

• The Standard Deviation is a measure of how spread out numbers are.

• Its symbol is σ (the greek letter sigma)• Standard Deviation is the average distance of each point in the

sample from the sample mean in terms of the original units of measurement.

• for instance, say you want to estimate the average height of a high school male basketball player. you take a sample of 10 varsity basketball players from your school and calculate their height and standard deviation. say you find that the mean of the sample is 70 in with a standard deviation of 2, you can say that the average difference between any given high school varsity basketball player is 2 inches from the mean of 70

Chapter 1 Briefing Introduction

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