2- Sensor Characteristics


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Sensors & Actuators
Aleppo – February 2012
Department of Mechatronics Engineering
EEM304 Mechatronics
2- Sensor Characteristics
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
2/28
Linearity and Accuracy.
Accuracy and precision.
Nonlinearities.
Hysteresis.
Saturation.
Dead band.
Sensorshavemanycharacteristicsthataffecttheirmeasurementcapabilitiesandtheirsuitabilityforeachapplication.
Sensor Characteristics:
some of the more
Transfer Function.
Span.
Resolution.
Sensitivity.
Error.
Repeatability.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
3/28
Transfer Function
Thetransferfunctionshowsthefunctionalrelationshipbetweenphysicalinputsignalandelectricaloutputsignal.
Usually,thisrelationshipisrepresentedasagraphshowingtherelationshipbetweentheinputandoutputsignal.
ES
N-ES
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
4/28
Span or Dynamic Range
Therange(orspan)ofasensoristhedifferencebetweentheminimum(ormostnegative)andmaximuminputsthatwillgiveavalidoutput.(i.e.therangeofinputphysicalsignalsthatmaybeconvertedtoelectricalsignalsbythesensor).
TypicalunitsareKelvinor°C,Pascal,Newton…etc.
Rangeistypicallyspecifiedbythemanufacturerofthesensor.
Ex.
-acommontypeKthermocouplehasarangeof800°C(from-50to750°C).
-LM35hasarangeof205°C(from-55°Cto+150°C)
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
5/28
Resolution
Theresolutionofasensoristhesmallestincrementofinputthatcanbereliablydetected.
Resolutionisalsofrequentlyknownastheleastcountofthesensor.
Resolutionofdigitalsensorsiseasilydetermined.
A1024ppr(pulseperrevolution)incrementalencoderwouldhavearesolutionof360/1024=0.3516degree/pulse
Theresolutionofanalogsensorsisusuallylimitedonlybylow-levelelectricalnoiseandisoftenmuchbetterthanequivalentdigitalsensors.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
6/28
Sensitivity
Sensorsensitivityisdefinedastheratiobetweenasmallchangeinelectricalsignal(output)toasmallchangeinphysicalsignal(input).
Typicalunitsarevolts/kelvin,millivolts/kilopascal…etc.
Ex:Athermometerwouldhave“highsensitivity”ifasmalltemperaturechangeresultedinalargevoltagechange.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
7/28
Thesensitivityofdigitalsensorsiscloselyrelatedtotheresolution.
Thesensitivityofananalogsensoristheslopeoftheoutputversusinputline.
P.s.
Asensorexhibitingtrulylinearbehaviorhasaconstantsensitivityovertheentireinputrange.
Othersensorsexhibitnonlinearbehaviorwherethesensitivityeitherincreasesordecreasesastheinputischanged.
Sensitivity
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
8/28
Error
Erroristhedifferencebetweenameasuredvalueandthetrueinputvalue.Twoclassificationsoferrorsarebias(orsystematic)errorsandprecision(orrandom)errors.
Biaserrorsarepresentinallmeasurementsmadewithagivensensor,andcannotbedetectedorremovedbystatisticalmeans.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
9/28
These bias errors can be further subdivided into
1.calibrationerrors(azeroornullpointerrorisacommontypeofbiaserrorcreatedbyanonzerooutputvaluewhentheinputiszero),
2.loadingerrors(addingthesensortothemeasuredsystemchangesthesystem),and
3.errors due to sensor sensitivity to variables other than the desired one (e.g., temperature effects on strain gages).
Error
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
10/28
Repeatability
Repeatability(orreproducibility)referstoasensor’sabilitytogiveidenticaloutputsforthesameinput.
Precision(orrandom)errorscausealackofrepeatability.
Fortunately,precisionerrorscanbeaccountedforbyaveragingseveralmeasurementsorotheroperationssuchaslow-passfiltering.
Electricalnoiseandhysteresis(describedlater)bothcontributetoalossofrepeatability.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
11/28
Linearity and Accuracy
Theaccuracyofasensorisinverselyproportionaltoerror,i.e.,ahighlyaccuratesensorproduceslowerrors.
Manymanufacturersspecifyaccuracyintermsofthesensor’slinearity.
ThereareseveralmeasuresofLinearity.
Themostcommoncomparestheactualtransferfunctionwiththe“beststraightline,”whichliesmidwaybetweentwolinesthatencompasstheentiretransferfunctionoverthespecifieddynamicrangeofthedevice.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
12/28
Linearity(oraccuracy)isspecifiedasapercentageoffullscale(maximumvalidinput).
Linearity and Accuracy
Linearity(oraccuracy)isspecifiedasapercentageofthesensorreading.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
13/28
Accuracy and precision
Accuracyandprecisionaretwotermsthatarefrequentlyconfused.
NextFiguresshowsfoursetsofhistogramsfortenmeasurementsofangularvelocityofanactuatorturningataconstant100rad/s.
Precise but not accurate
Thefirstsetofdatashowsahighdegreeofprecision(lowstandarddeviation)andrepeatability,buttheaverageaccuracyispoor
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
14/28
Accurate but not Precise
Thesecondsetofdatashowsalowdegreeofprecision(highstandarddeviation),buttheaverageaccuracyisgood.
Accuracy and precision
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
15/28
Neither precise nor accurate
Both accurate & precise
Thethirdsetofdatashowsbothlowprecisionandlowaccuracy
Thefourthsetofdatashowsbothhighprecision,highrepeatability,andhighaccuracy.
Accuracy and precision
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
16/28
Accuracy and precision
-Low accuracy.
-The repeatability is higher.
-The accuracy is higher.
-Low repeatability.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
17/28
Nonlinearities
Linearsystemshavethepropertyofsuperposition.IftheresponseofthesystemtoinputAisoutputA,andtheresponsetoinputBisoutputB,thentheresponsetoinputC(=inputA+inputB)willbeoutputC(=outputA+outputB).
Manyrealsystemswillexhibitlinearornearlylinearbehavioroversomerangeofoperation.
Therefore,linearsystemanalysisiscorrect,atleastovertheseportionsofasystemoperatingenvelope.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
18/28
Nonlinearities
Unfortunately,mostrealsystemshavenonlinearitiesthatcausethemtooperateoutsideofthislinearregion,andmanycommonassumptionsaboutsystembehavior,suchassuperposition,nolongerapply.
SeveralnonlinearitiescommonlyfoundinMechatronicsystemsincludestaticandcoulombfriction,eccentricity,hysteresis,saturation,anddeadband.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
19/28
Hysteresis
Somesensorsdonotreturntothesameoutputvaluewhentheinputstimulusiscycledupordown.Thewidthoftheexpectederrorintermsofthemeasuredquantityisdefinedasthehysteresis.
Transfer functionwithhysteresis
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
20/28
Forexample,adisplacementsensorwhentheobjectmovesfromlefttorightatacertainpointproducesavoltagewhichdiffersby20mVfromthatwhentheobjectmovesfromrighttoleft.Ifthesensitivityofthesensoris10mV/mm,thehysteresiserrorintermsofdisplacementunitsis2mm.
Typicalcausesforhysteresisarefrictionandstructuralchangesinthematerials.
Hysteresis
Dr. Hassan SHARABATY Sensors & Actuators – Sensor Characteristics 21/28
 This type of nonlinearity must be considered in Mechatronic control
system design, since maximum velocity and force or torque limitations
affect system performance.
Saturation
Saturation
 All real actuators have some maximum output capability, regardless of the
input. This violate the linearity assumption, since at some point the input
command can be increased without significantly changing the output;
 Control systems modeled with linear system
theory must be carefully tested or analyzed to
determine the impact of saturation on system
performance.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
22/28
Anothernonlinearcharacteristicofsomeactuatorsandsensorsisknownasdeadband.
Thedeadbandistypicallyaregionofinputclosetozeroatwhichtheoutputremainszero.
Deadband
Deadband
Oncetheinputtravelsoutsidethedeadband,thentheoutputvarieswithinput.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
23/28
Deadbandiscommonlyfoundinhouseholdthermostatsandotherprocesstypecontrollers.
DeadbandControl
Whenaroomwarmsandthetemperaturereachesthesetpoint(ordesiredvalue)onthethermostat,theoutputremainsoff.
Ex: Air condition system
Deadband
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
24/28
Onceroomtemperaturehasincreasedtothesetpointplushalfthedeadband,thenthecoolingsystemoutputgoestofullyon.
Astheroomcools,theoutputstaysfullyonuntilthetemperaturereachesthesetpointminushalfthedeadband.
Atthispointthecooling
systemoutputgoes
fullyoff.
Deadband
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
25/28
References:
For further reading students are referred to:
RobertBishop(2002):“TheMachatronicsHandBook,.“Copyright2002CRCPressLLC.
SensorTechnologyHandbook,copyright©2005,Elsevierinc.
Dr. Hassan SHARABATY
Sensors& Actuators -Sensor Characteristics
26/28
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