Table Of ContentChapter 1
The instrumentation system
1.1 Introduction
Whethermankindissimplyanotherpartoftheanimalworldorissomehow
uniqueisaquestionthathasoccupiedthemindsofphilosophersforgenera-
tions. The human attributes of self-awareness, empathy, morality and what
constitutes consciousness and creativity have become part of the current
debate surrounding the development of machine intelligence. What is
beyond question is the insatiable thirst mankind has to discover more
abouttheindividualselfandtheuniversearound.Observationsforscientific
purpose have been made since thebeginnings of history and instrumentsto
facilitate this have existed for millennia. However, during the latter half of
the 20th century the growth in instrumentation technology, and in con-
junction control theory, has been phenomenal.
For a nation’s instrumentation industry to remain at the fore in world
marketssensordevelopmentisessential.Inadditiontothegeneraltechnolo-
gical development of traditional sensors, during the past twenty years a
number of specific fields have emerged centred on novel sensing techniques
and materials. The global market for all sensor types is estimated at €15–
30 billion per annum. The current growth in sales of traditional sensors is
around 4% per annum compared with that of 10% per annum for novel
sensors. (Source: UK Foresight Programme.)
Initially, the Japanese were the leaders at commercially exploiting
academic innovations. However, the established industrial countries of the
west are now firmly committed, both at governmental as well as company
level, to strategic programmes for sensor development. Key fields are
regularly identified by funding agencies in order to stimulate research and
toassistincommercial exploitation.
The benefitsofimprovementsmadein sensors will enhancethe quality
andperformanceofindustryandotherfields.Forexample,ithasbeensaid
that advances in process automation are presently limited to the quality of
Copyright 2004 IOP Publishing Ltd
2 The instrumentation system
the instrumentation and in particular the plant–instrument interface. In
medicine, novel developments occurring in diagnostic instrumentation will
reduce response time and costs, and increase throughput. Non-invasive
sensors and invasive microsensors can reduce patient trauma. In the field
of transportation, modern vehicles contain large numbers of sensors for
safety,engineefficiencyandgloballocationsystems.Medical,environmental
and automotive applications have the largest potential market growth.
Inanynewdeviceitisimportantthatthespecificationortransferchar-
acteristic should be well defined and stable. This is often the most difficult
problem to resolve when going from laboratory prototype to commercial
product.Manynovelmicrosensor-prototypeshavebeenreportedmeasuring,
for example, position, flow, humidity, acceleration, liquid level, ionic
concentration, temperature, pressure and dissolved oxygen. However, the
percentage of devices that has become commercially available is relatively
small.Nevertheless,manyofthosethathaveenjoylargevolumeproduction
which isencouraging the general growth ofthe novel sensor industry.
It is important to realize that to be commercially successful a device
must be able to meet the cost constraints of the market for which it is
Table1.1. Acceptablesensorparametersinsomecommonfields.
Domestic Industrial Medical Automotive Environmental
Acceptable 1 500 Disposable10, 5 Disposable10,
cost(£) non-disposable non-disposable
250 250
Acceptable 10.0 0.1–5.0 0.1–2.0 1.0–5.0 1.0–10.0
error(%)
Meantime 103 during 105 during Disposable150 1:5(cid:1)104 Disposable150
between 10yearsof 10yearsof during1week during10 during1week
failures intermittent continuous ofcontinuous yearsof ofcontinuous
(hours) use. use. use,non- intermittent use,non-
disposable use. disposable104
5(cid:1)103during5 during10years
yearsof ofintermittent
intermittent use.
use.
Temperature (cid:2)20to400 (cid:2)200to Disposable10 (cid:2)30to400 (cid:2)30to100
range(8C) 1500 to50,non-
disposable0to
250
Response 1 0.1–10 1 10(cid:2)3–1 100
time(secs)
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The philosophy of measurement 3
intended.Also,somefieldsofapplicationrequireahigherspecificationthan
doothers.Table1.1indicatesacceptablecostsandotherdesiredparameters
insome common fields.
Summarizing, it is important that for any newly developed sensor to
becomecommerciallysuccessfulitmustnotonlybeeffectively‘ruggedized’,
whengoingfromthelaboratoryprototypetomarketedproduct,butalsofit
within the constraints of theapplication field.
1.2 The philosophy of measurement
Lord Kelvinisreputedto have said,
‘Whenyoucanmeasurewhatyouarespeakingaboutandexpressit
in numbers, you know something about it; but when you cannot
measureit,whenyoucannotexpressitinnumbers,yourknowledge
isof a meagre and unsatisfactorykind.’
Experimental observations are thebasis on which our understanding of the
universe around us develops. In science and engineering all hypotheses
and theories before they develop into rules and laws have to be rigorously
examined to discover their validity and its extent. Universal constants and
parameters relating to materials and structures and other artefacts all have
to be painstakingly examined to produce the most reliable data possible. A
good example is the measurement of the speed of light, which has taxed
someofthecleverestexperimentersforcenturiesandforonemaninparticu-
lar, A A Michelson (1852–1931), took up a large proportion of his life
earning him theNobelPrize in1907.
The philosophy of measurement is that of striving to reach some
notional real or true value. The more effort made the greater the precision
ofthe measurement and the smaller theuncertainty.
1.2.1 Randomerrors
Wheneverthemeasurementofaparameterorvariableismadeanerrorwill
occur.Themeasuredvalueormeasurandwillhaveanassociateduncertainty
due to the natural fluctuation of real physical quantities. Gauss postulated
that such variations are as equally likely to be above the mean as below
it. This random error may not be noticed if the measurement system is
insensitive, and may not be of any concern in some applications.
However, at the microscopic scale nature is never still and highly sensitive
instruments will reveal such fluctuations. The instrumentation system is
partofthephysicalworldandwillitselfintroduceanobservablerandomness
to any measurements taken. All such random errors have to be treated
statistically.
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4 The instrumentation system
ThebestestimateofthetruevalueXofsomevariableorparameterxis
the mean xx(cid:1).In the usual way,
PN x
xx(cid:1)¼ i¼1 i ð1:1Þ
N
from N observations. It is expected that for large N, xx(cid:1)!X. Incidentally,
when calculating the mean it is argued that the numerical value obtained
from alarge number ofobservationscanberoundedtoan extrasignificant
figuremore than that of theprecision of theequipment used.
Ameasureofthespreadordispersionoftheresultsaroundthemeanis
very useful as an indication of the repeatability of the measurement. The
deviation of a single result from the mean is x (cid:2)xx(cid:1). Because the deviations
i
can be positiveor negative the sum of the deviations is likely to be zero for
a large set of values. Consequently, the square of the deviations is used.
The mean of the squared deviations is called the variance. To obtain a
measure of the dispersion in the same units as the original measurements
thesquarerootofthevariancemustbetaken.Thisisthestandarddeviation.
It issimply determinedusing
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
PN ðx (cid:2)xx(cid:1)Þ2
s¼ i¼1 i : ð1:2Þ
N
Thestandarddeviationisalsoknownasthestandarderror.Itisameasureof
therandomnessorfluctuationsintheresultsobtained.ItisindependentofN,
the number of observations made. As can be seen in equation (1.2) making
many, repeated observations does not reduce the value of s but simply
gives agreater confidencein its estimate.
Intuitivelyitisfeltthattakingmoremeasurementsoughttoimprovethe
quality of the mean in some quantifiable way, ‘more must be better’. To
provide this extra quantifier imagine that instead of one set of N results
the measurement set was repeated p times under identical conditions, each
set having N results. Each of the p sets of results could produce its own
mean xx(cid:1)and standard deviation as before. But now these p means could be
averaged to give the mean ofthe means xxxx(cid:1)(cid:1)(cid:1):
xxxx(cid:1)(cid:1)(cid:1) ¼Ppk¼1xx(cid:1)k ¼1Xp (cid:2) 1 XN x(cid:3): ð1:3Þ
p p N i
k¼1 i¼1
Thisdoesnotlookanythingofsignificance.Afterall,itisthesameresultas
would have been obtained having made pNobservations initially:
PpN x
xxxx(cid:1)(cid:1)(cid:1) ¼xx(cid:1)¼ i¼1 i: ð1:4Þ
pN
The most significant and useful result is obtained from the standard devia-
tion of the p means. This standard deviation s is a measure of the spread
m
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The philosophy of measurement 5
of the means and indicates the precision of the value of the mean of the
means. In principlethis couldbe determined using
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pp ðxx(cid:1) (cid:2)xxxx(cid:1)(cid:1)(cid:1)Þ2
s ¼ k¼1 k : ð1:5Þ
m p
Inpracticeequation(1.5)isnotused.Itcanbeshown(seeSquires1968)that
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s PN ðx (cid:2)xx(cid:1)Þ2
s ffip ¼(cid:4) i¼1 i : ð1:6Þ
m ffiNffiffiffiffiffi(cid:2)ffiffiffiffi1ffiffiffi NðN(cid:2)1Þ
So forlarge N,
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
PN ðx (cid:2)xx(cid:1)Þ2
s !(cid:4) i¼1 i : ð1:7Þ
m N2
As equation (1.7) indicates, the estimate of s can be seen to improve by
m
increasing the number of observations made. ‘More is better’ is correct
here. However, this rule suffers from diminishing returns. Large values of
N may not be worth the effort. To appreciate the different meanings of s
and s the following examplesmay be helpful.
m
Standarderror ofthe measurements (s)
Consider the manufacture of 10k(cid:2) resistors on a production line. Each
day 100 samples could be taken from the production run and the value of
s determined. This denotes the spread of the results about the mean and
indicatestotheproductionmanagerwhetherthebatchiswithinthetolerance
limitsspecifiedonthepackets,e.g.(cid:4)10%.Theprobabilityofasingleresistor
being outside of the (cid:4)10% is related to s. In section 6.3.2 this is described
further within the topic on probability distributions. For a value to be
more than three standard errors from the mean is statistically unlikely
at about 2.7 in 103. So, if s is arranged to be about 3%, by using good
production technology, then most resistors produced will be within 10% of
themarketed value of10k(cid:2).
This‘3s’conceptcanalsobeappliedtoidentifyanerroneousresult.Ifa
reading from a set of identical measurements is more than three standard
errors from the mean of the set it can be considered dubious and be dis-
carded.
Standarderror inthe mean (s )
m
Inexperimentswheresomeparameteristobedetermined,suchasthespeed
oflight,thevalueofs isquoted.Thisprovidesanestimateoftheprecision
m
of the published value and incorporates the effort made in producing the
repeatedsetsofmeasurements.Therehavebeenoccasionswhenresearchers
Copyright 2004 IOP Publishing Ltd
6 The instrumentation system
Table1.2. Combinationofstandarderrors.
ThefunctionfðX;Y;ZÞ Combinationofstandarderrors
Q¼XþYþZorQ¼XþY(cid:2)Z s2 ¼s2 þs2 þs2
Q X Y Z
XZ (cid:2)s (cid:3)2 (cid:2)s (cid:3)2 (cid:2)s (cid:3)2 (cid:2)s (cid:3)2
Q¼XYZorQ¼ Q ¼ X þ Y þ Z
Y Q X Y Z
s s
Q¼Xn Q¼n X
Q X
s
Q¼lnðXÞ s ¼ X
Q X
s
Q¼expðXÞ Q¼s
Q X
haverepeatedexperimentsandobtainedresultsoutsideofthestandarderror
quoted originally.This has ledto the discoveryof systematicerrors.
Combining standard deviations
IfaparameterorvariableQistobedeterminedfrommeasurementsoftwo
or more parameters or variables X, Y, Z each having their own standard
deviationss ,s ,s ,itwillbenecessarytodeterminethestandarddeviation
X Y Z
of Q, s , by combining these contributing standard errors. It can be shown
Q
that if Qisa function fðX;Y;ZÞthen
(cid:2)@f (cid:3)2 (cid:2)@f (cid:3)2 (cid:2)@f (cid:3)2
s2 ¼ s2 þ s2 þ s2: ð1:8Þ
Q @x X @y Y @z Z
Table 1.2 shows how to combine the standard errors for some common
functions.
1.2.2 Systematic errors
Afurthererrormayoccurduetopoorcalibrationorpoorperformanceinthe
instrumentation system. Because such errors are inherent in the system and
are transmitted through to the measured value they are termed systematic
errors. They cannot be overcome by the statistical analysis of multiple
readings but areminimized by diligence incalibration andsystem design.
1.2.3 Environmental disturbances
The engineering environment within which the instrumentation system is
integrated can affect the input–output relationship of the sensor or of the
instrumentation system as a whole. The engineering environment includes
Copyright 2004 IOP Publishing Ltd
The philosophy of measurement 7
Figure1.1. Theinterferingeffect.
variablessuchastheambienttemperatureandhumidityandpowersupply
behaviour.Therearetwocommonwaysinwhichtheenvironmentcan
affecttheresponseandaredescribedbelowforanidealized,linearsensor
orsystem.
Zero-shiftortheinterferingeffect
Thisdisturbancehastheeffectofchangingtheinterceptvalueofthestraight-
linegraph,showninfigure1.1.Theinterferinginputisthechangeinor
deviationofsomeenvironmentalparameter.Thisinputcouplesintothe
systemviaasensitivityconstant.
Forexample,ifadriftintheambienttemperatureof5 8 Ccauseda
pressuremeasurementreadingtochangeby150Pathenthesystemwould
haveanenvironmentalsensitivityof30PaK (cid:2)1.
Variationinsensitivityorthemodifyingeffect
Thisenvironmentaldisturbancemodifiesthevalueofthesystemsensitivity,
thegradientofthegraph(figure1.2).Anexampleofthiseffectcouldbeofthe
float-typeliquidlevelgaugeascommonlyusedinautomobiles.Apotenti-
ometerfastenedtothefloatprovidesavariableresistancerelatedtothe
leveloftheliquid,whichinturnaltersthecurrentthroughthemilliammeter
petrolgauge.Ifthesupplyvoltagealtersthensodoesthereading.Typically,
whenthealternatorandregulatorareoperating,anautomobilepower
supplyisheldsteadyat14V.However,whentheengineisstoppedthe
powersupplysystemisreducedtothatofthe12Vbattery.Anenvironmental
sensitivityconstantcouldbedeterminedingallonsmA (cid:2)1/V.
Asimplewaytomonitorwhethertherehasbeensomeenvironmental
disturbanceistorepeatthefirstmeasurementtakenafterthecompletion
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8 The instrumentation system
Figure1.2. Themodifyingeffect.
ofasetofreadings.Moresophisticatedmethodscanbedevised.For
example,foralinearsystemdenotedby y¼mxþc theplottingof y(cid:2)mx
versus x shouldyieldafixedvalueif c isconstant(nointerferingeffect).
Similarly,plotting ðy(cid:2)cÞ=x versus x shouldgiveaconstantif m isfixed
(nomodifyingeffect).
1.2.4Systemdesignandthecontributionoferrors
Itwasshowninsection1.2.1howthestandarderrorsofanumberofrandom
variablescanbecombinedtogivethestandarderrorinsomederivedquan-
tity Q.Anappreciationofthewayerrorscombineisalsousefulwhenan
experimentorsystemisbeingdesigned.Itcanbeinstructivetoseehow
errorsinthecomponentmeasurandsofthequantitytobedeterminedand
anyadditionalsystemelementerrorscontributetothefinalresult.Inthis
waymorecarecanbetakenoverthosecomponentsthatcontributemost
totheglobalerror.
Aspreviously,supposeaquantity Qistobedeterminedfromobserva-
tionsofoneormorevariables.Inaddition,otherelementsintheinstrumen-
tationsystemsuchasafilteroranamplifiermayalsointroduceerrors.
Again, Q issomefunction fðX;Y;ZÞ where X and Y mightbethemeasur-
andsand Zthegainofanamplifier.Thevaluesof X,YandZhaveassociated
uncertainties(cid:1)X,(cid:1)Y,(cid:1)Zwhichcombinetoproduceanuncertainty (cid:1)QinQ.
Therelationshipbetween (cid:1)Qand(cid:1)X,(cid:1)Y,(cid:1)Z canbefoundusingthepartial
differentialequation
@f @f @f
(cid:1)Q¼ (cid:1)X þ (cid:1)Y þ (cid:1)Z: ð1:9Þ
@X @Y @Z
Table1.3givesexamplesofsomecommonfunctions.
Copyright 2004 IOP Publishing Ltd
The philosophy of measurement 9
Table1.3. Simplecombinationoferrors.
ThefunctionfðX;Y;ZÞ Combinationofstandarderrors
Q¼XþYþZorQ¼XþY(cid:2)Z (cid:1)Q¼(cid:1)Xþ(cid:1)Yþ(cid:1)Z
XZ (cid:1)Q (cid:1)X (cid:1)Y (cid:1)Z
Q¼XYZorQ¼ ¼ þ þ
Y Q X Y Z
(cid:1) (cid:1)
Q¼Xn Q¼n X
Q X
(cid:1)
Q¼lnðXÞ (cid:1) ¼ X
Q X
(cid:1)
Q¼expðXÞ Q¼(cid:1)
Q X
Addition/subtraction
Unless there is some a priori knowledge about the system behaviour, the
worst case is assumed and all the absolute errors are added. The error
estimates must all be in the same units and (cid:1)Q will also have these units.
Multiplication/division
Here, again assuming the worst case, all the relative errors are added. They
have no units and can be described as fractional errors or multiplied by
100%togivepercentageerrors.Therelativeerrorisalsousedwiththeloga-
rithmic function.
Simple determination ofthe global error
Therelationshipsintable1.3orothersderivedfromequation(1.9)canalso
beusedtomakeasimpleestimateoftheerrorinaderivedquantity,whether
determinedfromanumberofmeasurands,orastheoutputfromaninstru-
mentation system. These contributoryerrors might arise from
. aroughguessattherandomerrors,
. estimatedsystematicerrors,
. calibrationlimits,
. componenttolerances,
. estimatedlikelyenvironmentaldisturbance,
. theresolutionlimits,
. hysteresisor‘deadband’effects,
. estimatednonlinearities,
. digitizationerrors.
In the paragraph preceding equation (1.9) the word uncertainty was used
when describing (cid:1)X, (cid:1)Y, (cid:1)Z. When dealing with the quantities listed above
Copyright 2004 IOP Publishing Ltd
10 The instrumentation system
thisisapreferredexpressiontoerrorsinceitisallencompassing.Itemssuch
ascalibrationlimitsandtolerancesarethenincludedwhich,strictlyspeaking,
are not errors.
WORKED EXAMPLE
Thedensityofamaterialistobedeterminedfromthemassandvolumeofa
wire sample and a simple method used to estimate the uncertainty in the
answer obtained.The density isderived from
m
(cid:2)¼ :
(cid:3)ðd=2Þ2h
Fromequation (1.9)it can be seen that
(cid:1)(cid:2) (cid:1)m (cid:1)d (cid:1)h
¼ þ2 þ
(cid:2) m d h
revealingthatthefractionaluncertaintyinthediameterdisthemostsensitive
terminthedeterminationof(cid:2).Greatercaremustthereforebetakenwiththis
measurement.
Themassofthespecimenisfoundtobe1:25(cid:1)10(cid:2)3kgandthebalance
usediscalibratedto(cid:4)1mg.Thelengthismeasuredas0.1845musingarule
readable to the nearest 0.5mm. The thickness is measured ten times at
various points and orientations along the length using a micrometer
capable of measuring to (cid:4)10(cid:2)5m and is found to be 0.984mm with a
standard error inthe mean of(cid:4)0.024mm. The density isdetermined as
1:25(cid:1)10(cid:2)3
(cid:2)¼ ¼8:909(cid:1)103kgm(cid:2)3:
(cid:2)9:84(cid:1)10(cid:2)4(cid:3)2
(cid:3) (cid:1)0:1845
2
The fractional uncertainty isdetermined,
(cid:1)(cid:2) 10(cid:2)6 0:024 0:5
¼ þ2 þ
(cid:2) 1:25(cid:1)10(cid:2)3 0:984 184:5
¼8(cid:1)10(cid:2)4þ0:04878þ2:71(cid:1)10(cid:2)3
¼0:05229:
The uncertainty in (cid:2)is
(cid:1)(cid:2)¼(cid:2)(cid:1)0:05229¼465:9kgm(cid:2)3:
It isusual to express theresultin the form
(cid:2)¼8:909(cid:4)0:4659(cid:1)103kgm(cid:2)3:
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