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Lecture Notes Part 5aET 438B Sequential Control and Data Acquisition1et438b-5a.pptxPosition Sensorset438b-5a.pptx2Angular and Linear Position SensorsSimple linear displacement transducers: Slide PotentiometerEsLxEout

SliderSimple angular transducers: Rotary Potentiometers, multi-turn or single,Wire-wound or carbon compositeEsEout

et438b-5a.pptx2Potentiometer Resolutionet438b-5a.pptx3Wire-wound potentiometers do not have infinite resolution due to wire diameterCross sectionResistance varies withpositionResolution (%) = 100/N

Where N = number of turns in the pot.Number of turns per unit length determines resolution of the potentiometeret438b-5a.pptx3Potentiometer Loading Erroret438b-5a.pptx4

Loading error LE defined as = aEs -Eout Percent Loading ErrorRp = total potentiometer RaRp = fraction of potentiometer R from wiper to ground

RL is load on potentiometer. Must include in calculationSolve using voltage division

ReqE0RLEsRpaRp+-et438b-5a.pptx4Potentiometer Loading Exampleet438b-5a.pptx5A linear wire-wound potentiometer has a totalresistance of 50,000 ohms The voltage output of thepotentiometer will be converted to a digital value by a 12 bit ADC. Determine minimum numberof turns required so that the resolution of thepotentiometer does not exceed the quantization error ofthe ADC.

What percent loading error can be expected if the inputresistance of the ADC is 100 kW and the range ofmeasurement is from 20% to 80% of the potentiometervalue?Problem Statementet438b-5a.pptx5Example Solutionet438b-5a.pptx6Find the resolution of the 12-bit ADC then convert it to a percentage. Assume 1 volt range

et438b-5a.pptx6Example Solution (cont.)et438b-5a.pptx7

Loading error depends on position of potentiometeret438b-5a.pptx7Linear Variable Differential Transformers (LVDTs)et438b-5a.pptx8PrimarySecondaryVs1Vs2LpLs1Ls2Note: dots indicatesinstantaneously positivevoltages in transformersMovable CoreCore Motion causes Vs1 and Vs2 to changeVp must be AC typical frequency 50k - 15 kHzLp and Ls1 coupled Vs1 IncreasingLp and Ls2 coupled Vs2 IncreasingVpet438b-5a.pptx8LVDT Outputet438b-5a.pptx9Coils connected so voltages subtractOutput VCore Position+-00.060.06V out +V out -opposite phase+-corepositioncore coupling Lp and Ls1core neutralcore coupling Lp and Ls2et438b-5a.pptx9Rotory Position TransducerSynchro Systemset438b-5a.pptx10 Three parts to system 1.) Control Transmitter 2.) Control Transformer3.) Control Differential

ControltransmitterControltransformeracsourceVout+-Sinusoidal output with maximum value from this positionVouttimeet438b-5a.pptx10Synchro Systemset438b-5a.pptx11Output voltage is zero when rotors in this position

ControltransmitterControltransformerVout+-acacsourceet438b-5a.pptx11Synchro Systemset438b-5a.pptx12

Vout+-ControltransmitterControltransformeracacsourceOutput voltage 180 degrees out of phase from initial positionet438b-5a.pptx12Synchro Systemset438b-5a.pptx13Output voltage magnitude is a function of the angular displacement between the control transmitter and the control transformer

Where Em = the maximum amplitude of excitationq = the angular position difference between the transmitter and the transformer rotor w = frequency of excitation voltageet438b-5a.pptx13Synchro Systemset438b-5a.pptx14Control differential transformer can be added to add constant phase shift.

Sending and receiving devices will have a constant angular difference given by the value of qd.System can be used to maintain a constant position difference between two shafts. It can also be used to keep two shafts synchronized.et438b-5a.pptx14Synchro Exampleet438b-5a.pptx15A syncho system operates at a frequency of 400 Hz. The maximum amplitude of the transformer rotor voltage is 22.5 V. Determine the ac error signal produced by each of the following pairs of angular displacementsa.) q= 90 qd=0b.) q= 60 qd=0c.) q= 135 qd=-15d.) q= 100 qd=-45At 400 Hz

a.)

b.)

et438b-5a.pptx15Synchro Example (Cont.)et438b-5a.pptx16

et438b-5a.pptx16Velocity MeasurementsAngular and Linear VelocityAngular Velocity Measurement Methods- dc tachometer- ac tachometer- optical tachometerDC tachometerNSDc generator usingpermanent magnets forfield flux

Brushes and CommutatorsField PolesMagnetic Field17et438b-5a.pptx17et438b-5a.pptxVelocity Measurements Dc TachometerTachometer produces a dc voltage that is proportional to angular velocityProportionality constant = emf constant KE (V/rpm)KE depends on the construction of tachometer

Induced emfemf constant

WhereE = tachometer output (V)KE = emf constants = angular velocity (rpm)w = angular velocity (rad/s)R = average radius (m)B = flux density (Wb/m2)N = number of conductors L = length of conductor in field (m)18et438b-5a.pptx18et438b-5a.pptxVelocity Measurements Dc TachometerExample: A dc tachometer has the following parametersR = 0.03 mN = 220L = 0.15 m B = 0.2 Wb/m2Find KE and the output voltage at the following speeds s = 1000, 2500, and 3250 rpm

For s = 1000 rpm

For s= 2500 rpmAnd 3250 rpm

19et438b-5a.pptx19et438b-5a.pptxVelocity Measurements Ac TachometerAc Tachometers Construction : a 3-phase alternator with a 3-phaserectifier to convert the output to dc. Must have constant field excitation - Permanent magnet field. Non-linear at low speeds due to the forward drop of diodes Limited to lower speed ranges due to this. Range 100-1

Ac Tachometers can also produce a variable frequency output that has a constant voltage.

Use frequency-to-voltage conversion to get proportional dc20et438b-5a.pptx20et438b-5a.pptxOptical TachometersDigital encoder attached to shaft produces a sequence of pulses.

3 light sensors3 light sourcesEncoder tracksInner locates homeMiddle - gives direction infoPhase shift between outerand middle tracksMiddle leads or lags outerbased on direction 21et438b-5a.pptx21et438b-5a.pptxOptical Tachometer OperationPulses counted over time interval. Counter is then reset. The number of pulses counted in interval is proportional to the angular velocityOptical TachometersFormulas

Wheres = shaft speed (rpm)N = number of pulses per shaft revolutionC = total count during time periodTc = counter time interval (sec)22et438b-5a.pptx22et438b-5a.pptxOptical Tachometer ExampleIncremental encoder produces 2000 pulses/rev.a.) determine count produced by shaft speed of 1200 rpm with a count interval of 5 mSb.) determine the speed measured at a count of 224 for a timer interval of 5 mS

a.)Number of counts for 1200 rpm speed

b.)Speed for 224 counts23et438b-5a.pptx23et438b-5a.pptxAcceleration MeasurementDefinition - acceleration is rate of change of velocity

Sensing MethodsNewtons Law f = Ma Where: f = force acting on body M = mass of body a = accelerationCan measure acceleration by measuring force required to accelerate known mass.For angular acceleration, differentiate the velocity signal from velocity sensors24et438b-5a.pptx24et438b-5a.pptxAcceleration MeasurementFor angular acceleration, differentiate the velocity signal from velocity sensorsSensing MethodsFor sampled data systems, derivative is given by difference of readings

Whereat = acceleration at time tvt-1 = velocity sample at t-1vt = velocity sample at tTs = sampling time25et438b-5a.pptx25et438b-5a.pptxAccelerometersGeneral StructureSpringsSpringsMassDisplacement Sensor (LVDT)Accelerometer attached to device under test and experiences same acceleration as measured object. Motion of mass damped by viscous fluid around massTheory of operation same forIntegrated devices.ApplicationsGamingAutomotiveAppliance controlDisk Drive protectionBearing Condition MonitoringMK/2K/226et438b-5a.pptx26et438b-5a.pptxAccelerometersAccelerometer forms a second order mechanical system.Accelerometer in actionDirection of accelerationf = MaFor small deflections,spring force offsetsforce due to acceleration so....Kx = Ma Which gives

x = (M/K)a

so acceleration is proportional to displacement27et438b-5a.pptxDisplacement caused by acceleration27et438b-5a.pptxAccuracy of Acceleration MeasurementsAcceleration is dynamic measurement, interested in a(t), acceleration as function of time. Consider second order response

Wherefo = resonant frequency of accelerometer (Hz)z = damping ratioK = spring constant (N/m)M = mass (Kg)b = damping constant (N-s/m)fa = max. frequency of a(t)28et438b-5a.pptx28et438b-5a.pptxAccuracy of Acceleration Measurementsif fa >fo then the mass does not have time to react incorrect measurementfa = fo then displacement is greatly exaggerated incorrect measurement

Make fo at least 2.5 times greater than fa max for < 0.5% errorAccuracy of response related to resonant frequency of device Must have sufficient range to measure changes29et438b-5a.pptx29et438b-5a.pptxAccelerometer ExampleThe accelerometer shown below has the following specifications:M = 0.0156 kgK = 260 N/mb = 2.4 N-s/mxmax = +- 0.3 cmFind the followinga.) maximum acceleration that can be measuredb.) resonant frequencyc.) damping ratiod.) maximum frequency that can be used with 0.5% error or less30et438b-5a.pptxMK/2K/2b30et438b-5a.pptxAccelerometer ExampleM = 0.0156 kg K = 260 N/mb = 2.4 N-s/m xmax = +- 0.3 cma.)

b.)

d.) Maximum frequency of a(t) with 0.5% error is..

c.)

31et438b-5a.pptxMK/2K/2b31et438b-5a.pptxForce Measurementset438b-5a.pptx32All force measurement based on force balancef = MaWhere : f = force (N) M=Mass (kg) a=acceleration (m/s2) Null Balance unknown force off set by know weight (beam balance)Weight= fMaWhen weights equalscale balancedForce Measurementset438b-5a.pptx33Displacement displacement of elastic material with unknown balancing force determines measurement (Spring Scale) (Strain gage load cell)FElastic properties of beam determinesDisplacement due to external force Strain Gageset438b-5a.pptx34Strain gages turn changes in displacement into changes in electric resistance. Fine wire bonded to plastic base.Bonded strain gages measure strain at specific location on deformable body. Cemented to material and change length when body deforms.

L

DLDefine strain:Change in length = L+DL

Where DL = change in length due to force (m)L = unforced length (m)Strain Gages- Gage Factoret438b-5a.pptx35Gage factor determines the sensitivity of the sensor

Typical values of strain gage parameters:

G: 2 to 4R: 50 to 5000 ohmsL: 0.5 to 4 cm (unstrained)Stress/Strain and Modulus of Elasticityet438b-5a.pptx36Define Stress

Stress and strain related through the modulus of elasticity for a given material

Where E = modulus of elasticity (N/m2 )S = stress (N/m2)e = strain (m/m)Stress and Forceet438b-5a.pptx37Stress depends on the geometry of the object. Consider the cantilever beam (diving board) below.

Strain Gagef

Where:

S = stress (N/m2)L= distance from fixed end (m)f = applied force (N)b = width of beam (m)h = height of beam (m)Combining previous equations

Normalized gage resistance change proportionalto forceStrain Gage Exampleet438b-5a.pptx38

fThe beam structure shown has the following parameters

Length =L = 2 mWidth =b = 20 cmHeight=h = 6 cm

It is made from Aluminum with a modulus of elasticity ofE = 6.9x1010 N/m2

The strain gage has anunstrained R=100 G = 3DR =0.073 Strain GageFind the applied forceStrain Gage Example Solutionet438b-5a.pptx39Define the variables

Restate the formula

Solve for force

Substitute values and simplifyTemperature Measurementet438b-5a.pptx40Resistance Temperature Detector (RTD)-change in resistance of pure metals relates to temperature. Key features: wide temperature range, high accuracy,excellent repeatability, good linearity. Need constant current source and other electronics to produce output signalSurvey of TypesThermistor temperature-sensitive semiconductor. Resistance inversely proportional to temperature. Increasing temperature causes decreasing resistance. Key features: high sensitivity, small size, fast response., narrow temperature range Not recommended in applications requiring high accuracy. Thermocouple junctions of two dissimilar metals produces small (mV) voltageswhen placed at different temperatures. Magnitude of voltage depends on temperature difference. Key features: small size , low cost, rugged, wide measurement range. Limitations: noise pickup, low signal levels, high minimum span (40 C.) Temperature Measurementet438b-5a.pptx41Survey of TypesIntegrated Circuit Temperature Sensors precision solid-state devices with linear output to temperature. Directly calibrated to various temperature scales ( Celsius, Fahrenheit, Kelvin, Rankine). Key features: calibrated output voltages, linear scaling, low voltage and current draws, good linearity. Typical devices LM34, LM 35. Limitations: low temperature range typically (-55 C to 155 C) Resistance Temperature Detectors (RTDs)et438b-5a.pptx42Construction: Coil of Nickel or Platinum wire in protective tube. Need to detect small changes in resistance.Platinum high accuracy, linearity, and cost Nickel moderate cost, higher output than Platinum

Typical RelationshipWhere:R = resistance at given Temp, T CRo = resistance at 0 degrees CT = temperature a1, a2 = constants

Resistance Temperature Detectors (RTDs)et438b-5a.pptx43Finding constants from dataTypical values for PlatinumT(C)Resistance (W)0100.0025109.9050119.8075129.60100139.30Use table values to find constantsRo, a1 and a2. Substitute data into previousequation.

Simplify equations and solve simultaneously

Mainly linearRTD Signal Conditioninget438b-5a.pptx44Must convert RTD resistance changes into usable voltage or current signals Direct Methods (2 and 4 wire) - Constant current supplied to RTD and voltage measured across it. The 4 wire method removes lead-wire error. Bridge Methods (2 and 3 wire) Use dc bridge to convert resistance changes into voltage changes. Three wire method removes most lead-wire resistance error.RTD Signal Conditioning- 4 Wire Direct Methodset438b-5a.pptx45

vs+

-isis4-20 mA outputZin very highIin approx. zeroIin0Design circuit using Platinum RTD

1.) constant current source is = 1 mA 2.) Instrumentation amp. G=503.)Summing amp 4.) V-to-I converter 4 mA @ 0 C20 mA @ 100 CRTD Circuit Design- Constant Current Sourceet438b-5a.pptx465.1 V regulated source available. Remember the V-to-I converter . Use LM324\quad OP AMPs.

IsNow design the Instrumentationamplifier using the two stage amplification circuitRTD Circuit Design- Instrumentation Amplifieret438b-5a.pptx47

Gain formula

Where R3=R4 R8=R9 and R6=R7G=50 . Divide gain betweenthe two stages.Av1 = 5Av2 = 10Av1Av2

RTD Circuit Design- Instrumentation Amplifier and V-to-I converteret438b-5a.pptx48Stage 2 gain is 10

Now determine the span of the RTD output voltage

AfterAmpDesired output span 16 mA 4 mAInput span -6.965 - -5.0Size the R of the V-to-I converter based on span ratio

RTD Design- V-to-I Converteret438b-5a.pptx49Now determine the offset voltage for the 0 degree input to the converter.Set Io to minimum and compute Vin using the computed R.

123 WIoVinVb@ 4 mAU2A inverting summerFind value of Vb

Zero SetSpan SetThermister Characteristicset438b-5a.pptx50

Very Non-linear- High sensitivity in (0-40 C range)Photoresistorhas similar characteristicThermister Characteristicset438b-5a.pptx51Semi-log plot (y axis logarithmic) of thermister data

Approximatelylinear over smallrange 40-100 C

Log(R)=mT+bet438b-5a.pptx52Thermister CharacteristicsLinearizing Thermister Characterisitcs

Changing value of R changes output curve shapeR=2000 ohms

R=1000 ohmsThermister0CThermocoupleset438b-5a.pptx53Junctions of dissimilar metals produces voltage proportional to temperature

HeatCold JunctionIronConstantanANSI Standard Type J-190-800 CL

A

A

SectionAA

b

h

L

A

A

SectionAA

b

h

Rs

VoltageToCurrentConverter

is

RT

R

Vcc

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